13||||||Everyone I have talked to has been stumped by this problem.%0D%0A%0D%0ATake a square one unit by one unit. Attach a rectangle to its lower right corner%2C which is 1%2F2 a unit high and 2 units long. Then attach another to that which is 1%2F4 of a unit high and 4 units long. Continue halving the height and doubling the length to produce a shape of infinite length. Each component has an area of one square unit and so the overall area is infinity.%0D%0A%0D%0ANo rotate this shape about its lower edge to produce a solid made of a sequence of spheres. All the spheres have a volume of pi%B7r%5Bsup%5D2%5B%2Fsup%5D%B7h. The first sphere therefore has a volume of pi%2C the next of pi%2F2 the next of pi%2F4%2C then pi%2F8%2C pi%2F16 etc. When all terms are summed to infinity you end up with a sum of 2pi. We have revolved a 2D shape with infinite area to produce a 3D solid with finite volume%21%0D%0A%0D%0AI think that this also means the outside of the shape can be painted with the volume of the paint contained in the sphere. So you can paint an infinite surface from a paint can of finite volume%21%0D%0A%0D%0ACan some please explain this or is my reasoning wrong. The last part may be %0D%0Aslightly dodgy%2C but I can see no problem with the volume of the shape.%0D%0A%0D%0AChris|||226|5.46666666666667|1 1|0|alexb|10/13/2000|20:42:02|Phil|math language|Hello%2C%0D%0A%0D%0ANice page. How do I go from English to math%3F In other words%2C I know how to average numbers and can explain it verbally. But||485|5.5026455026455|1 2|0|alexb|10/16/2000|16:01:36|Bernadette|spatial velocity gradient|I am trying to explain different measures%2Fquantities in terms of their dimensions%2C i.e. velocity would be l divided by t%5E2 %28 where l%3Dlength%||584|5.50967741935484|1 3|0|Balazs|10/18/2000|07:32:22|vb|Finding optimal koordinate transformation|Hi%2C%0D%0A%0D%0AI have a %28probably%29 small problem%2C but I alone can do nothing with it. %0D%0A%0D%0AWe have two sets of vectors a%28i%29 and b%2||516|5.49700598802395|2 5|0|alexb|10/18/2000|17:33:00|Vana Dany|polygon area|Hi %21%0D%0A%0D%0AMy name IS Danny Vana from Israel.%0D%0A%0D%0AI am interesting in Polygon area formula %3F%0D%0A%0D%0ADo you have such formula %3F%3||592|5.5|1 8|0|alexb|10/18/2000|21:41:21|Rodinalinquonte|How to remember the Pythagorean Theorem|%5Bp%5Di have no clue about how to remember the pythagorian theorem %28sp%29. i have tried songs and rymes and other happy thingy ma bobs but they don||509|5.47849462365591|1 9|0|Rip Stauffer|10/19/2000|08:39:26|Rip Stauffer|Schoolteacher page|%0D%0AAlex%2C%0D%0A%0D%0A%0D%0AI just read the teacher.html page%2C and was about to answer the questions in the survey%2C when I realized that I coul||470|5.46666666666667|0 10|0|alexb|10/19/2000|08:53:23|CHATTON Rodrigue|Zeno%27s paradox|Hi alex%2C%0D%0A%0D%0AI saw your great site because I was looking for the %22solution%22 of a paradox. %28I don%27t find it in your site. Here%27s the||261|5.33333333333333|1 14|0|alexb|10/19/2000|20:52:14|Philip Romano|a question on questions|Regarding the question%2C %22Is no your answer to this question%3F%22%2C one of my friends says that this is not really a question because a meaningfu||501|5.5|1 17|0|alexb|10/20/2000|13:28:16|Anton Adelson|Lewis Caroll%27s Pillow Problem|I found the question of Lewis Carroll about the pillow%3A%0D%0A%0D%0AA bag contains a counter%2C known to be either white or black. A white counter is||604|5.49519230769231|1 18|0|alexb|10/20/2000|13:38:23|Tom Brown|birthdays|I have 5 children. Three by my first marriage. Two by my second.%0D%0A %0D%0A3 of the children were born on the same day%2C November 17%0D%0A %0D%0Ath||473|5.5|1 19|0|alexb|10/21/2000|21:08:57|sabrina|tower of hanoi|Hi%2C I was wondering if you could answer me a question concerning the Tower of Hanoi%3F The Tower of Hanoi is often dismissed as a %22toy problem%22||555|5.50717703349282|1 22|0|alexb|10/21/2000|22:44:59|Mell Leonard|Pi and the base 12 number system|I have long held a theory that Pi could be divisible into a finite number in a base 12 number system %28as opposed to an infinite number in the base 1||1776|5.52173913043478|1 24|0|alexb|10/22/2000|13:26:05|Neo|Tesseract%3A math is cool|dude%2C i really hate math%2C but that tesseract thing kicks ass%21 i really wonder though%2C is it possible to construct a physical model even thoug||544|5.50704225352113|1 15|0|alexb|10/22/2000|12:18:54|smith slang|a logic puzzle|Dear Professor Bogomolny%0D%0A%0D%0AI am a student at Sacret Heart High School%2C San Francisco. Recently I encounter a very nice problem%2C but I can||766|5.5|3 23|0|alexb|10/22/2000|13:20:46|Josh Funk|Determining max diameter of oxygen in silicate molecule|Does anyone know of a formula for determining the maximum diameter of an oxygen atom in a silicate molecule%3F Basically it looks like you sat three s||565|5.50251256281407|1 21|0|JeanMarie|10/23/2000|17:13:46|Jean-Marie Vanroy|Lewis Carroll%27s problem|Hi%21%0D%0A %0D%0AThank you for your very interesting site.%0D%0A %0D%0AIn %22Probability %2F 23. Lewis Carroll%27s problem%22%2C you propose 2 soluti||658|5.48803827751196|4 26|0|alexb|10/23/2000|19:18:55|Mims, Matthew|random numbers for a contest|I need your help.%0D%0A%0D%0AI am running a contest for concert tickets as a thank you for our residents. I thought that I would just pull up ten numb||489|5.52|1 27|0|alexb|10/23/2000|19:31:57|Pin Tan|Self Reference question.|I was wondering how a person %22ask%22 a machine %22This machine will not say that this sentence is true%22%3F%0D%0A%0D%0AThank You.||484|5.5|1 25|0|alexb|10/23/2000|15:21:15|rhodgins|The bus stop problem|A friend was given this brain teaser in a graduate physics class%3A%0D%0A%0D%0AIf a bus comes to your stop every 15 minutes%2C but you don%27t know th||574|5.51428571428571|1 28|0|alexb|10/24/2000|01:04:03|Chris|Re%3A English words without vowels|I am stumped naad dont want to be shown up by my kid... She%28age 12%29 says that there are at least 5 words i the English language that have no %22a%||567|5.51141552511416|1 29|0|alexb|10/24/2000|08:34:05|Tomas Rolin|Non linear mathematics|I have asked my math teacher an many ohers what non linear mathematics is%2C b ut no-one had ever heard about it so i%27m hopeing I would find an answ||513|5.46354166666667|1 30|0|alexb|10/25/2000|15:52:06|Tzanev, Stefan|Kozma Prutkov|Dear Alexander%2C%0D%0A%0D%0AI wonder if you can point me some Internet resources with English translation of the Kozma Prutkov works%3F I liked very ||581|5.5|1 32|0|alexb|10/28/2000|12:45:51|B.G. Pedersen|What%27s in a hole%3F|Hi there%2C%0D%0A%0D%0AI%27m currently writing a screenplay for a movie. I%27m not a mathematician. Actually%2C to be quite honest%2C I rather suck at||523|5.5|1 35|0|alexb|11/01/2000|10:43:17|Tom Ballard|FLT and Pythagorean triplets|Hi Alex%3A%0D%0A%0D%0AI see from yoursite that you are interested in P. triplets.%0D%0A%0D%0AI have recently revised a treatise I had written some tim||504|5.5|1 34|0|alexb|11/01/2000|10:26:29|Steve|What is meant by %22significant to the 5%25 level.%22%3F|I have been asked to explain what the phrase %22significant to the 5%25 level%22 generally and in relation to experimental methods.%0D%0A||433|5.47651006711409|1 36|0|George Watson|11/03/2000|04:44:39|George Watson|combinations of numbers|I would like to find balanced tennis doubles combinations. We have 2 foursomes that play tennis. I would like to find a schedule for 8 players that pl||414|5.49593495934959|0 38|0|Gregory Keith Van Patten|11/03/2000|10:01:24|Gregory Keith Van Patten|mathematical games|Alexander Bogomolny%2C%0D%0A%0D%0A%22Cut-the-Knot%22 is quite entertaining%21 I like to invent abstract games%2C and a number of my game ideas are av||503|5.49640287769784|0 39|0|alexb|11/03/2000|19:48:30|Jed|Area and Constant Perimeter|I am wondering if my reasoning is valid here%3A%0D%0AGiven a length of string%2C the 2 dimensional figure of the greatest area that one can create is ||705|5.5|1 40|0|alexb|11/06/2000|22:32:30|Georg Menz|Theory of nim|Hello%0D%0A %0D%0AYour theory of nimm is very good.%0D%0A %0D%0ABut I just wonder%3A What happens if the player who takes the last match looses%3F%0D%||492|5.51677852348993|1 42|0|alexb|11/08/2000|00:55:47|Sergei Furs|arithmetic of fractions|Dear Professor Alexander Bogomolny%21%0D%0A%0D%0AMy name is Sergei Furs%3B I live in Minsk %28Belarus%29. I try to construct an axiomatic deductive th||384|5.4551724137931|1 45|0|alexb|11/14/2000|23:12:47|Tim Partridge (Guest)|Pizza consumption|Could you tell me how many slices of pizza are eaten each year in the world.%0D%0A %0D%0AThanks%2C%0D%0ATLC||345|5.43965517241379|1 47|0|RDillree (Guest)|11/17/2000|20:38:13|RDillree (Guest)|3 letter monograms- possible combinations|How many combinations of three letter monograms can you make%3F%0D%0Ai.e. AAA AAB AAC etc.||349|5.5|0 44|0|alexb|11/20/2000|10:42:22|jessica-linh dang (Guest)|twin brothers%27 problem|What is the answer to the riddle of the %5Ba href%3D%22%2Fimpossible%2Fbrothers.html%23guard%22%5Dtwins who guard%5B%2Fa%5D the two doors%3F this has ||395|5.45945945945946|2 48|0|alexb|11/21/2000|09:31:08|calle (Guest)|weight in ounces|Which weighs more an ounce of gold or an ounce of feathers%3F||342|5.52808988764045|1 49|0|alexb|11/26/2000|09:31:08|George Nurnberg (Guest)|Horse puzzle|I am interested in mythical horse puzzle %28Jig saw%29 seen in catalog on airplane - America West.||365|5.51020408163265|1 51|0|alexb|11/30/2000|01:50:54|Renee (Guest)|Pythagoras as a sole mate|Hi%2C this may seem straange%2C but I am going to ask anyway. I am a person who meditates and enjoys seeking answers from the subconscious. Anyway%2C ||356|5.5|1 52|0|alexb|12/01/2000|09:56:55|Evan Geno (Guest)|knot theory project|Hi%2C%0D%0A%0D%0AMy name is Evan Geno%2C and I am a Seventh grade student at Patrick Henry School. I am planning to do my science project this year on||383|5.47|1 53|0|alexb|12/01/2000|11:19:00|Bonnie Lake (Guest)|Combination square shapes|dear mr.Bogomolny%2C%0D%0A%0D%0Athanks for a terrific site%21 I%27ve got a group of little kids- ages 8 through 17- that I meet with twice a month for||373|5.5|1 55|0|Lon Thomas (Guest)|12/08/2000|18:34:14|Lon C. Thomas, Jr. (Guest)|mega vs. meta|I like your site ... but the term %5Ba href%3D%22%2Fpythagoras%2Fparadox.html%22%5D%22mega-puzzle%22%5B%2Fa%5D%2C I think%2C should be %22meta-puzzle%||365|5.6|2 57|0|Louis Mello (Guest)|12/17/2000|11:23:14|Louis Mello (Guest)|A Mathematical Quote|%22Chaos is the origin of the universe%2C mathematics is its language...%22%0D%0A%0D%0A1995%0D%0ALouis Mello%0D%0AMathematician||310|5.5|0 56|0|alexb|12/17/2000|11:23:14|Henry Heck (Guest)|Poisson processes|Thank you for your wonderful mathematical website%21%0D%0A %0D%0AI have encountered a problem in my research to which %28it seems to me%29 there are t||374|5.5|1 58|0|alexb|12/17/2000|11:23:14|José Luis Romero (Guest)|Self-reference statements|Hi%21 First I want to say I really like your site. I was reading the self-referenced statements %28the ones that claim to have%0D%0Amistakes%29 and I ||412|5.47474747474747|3 59|0|alexb|12/21/2000|00:18:59|Ron Shuler (Guest)|4d hyper-cube%3F|I have this question that I%27ve been getting to me. I%27m only 14 but I heard about this thing called a hyper cube and I was woundering what the hec||369|5.5|1 61|0|alexb|12/28/2000|19:13:37|GymNat1 (Guest)|irrational number to an irrational number is rational|i don%27t understand the leap from b%5Eb%5Eb to b%5Eb2. i originally thought it might have something to do with 2%5E%281%2F2%29%3D2%2F%282%5E%281%2F2||380|5.47058823529412|1 60|0|alexb|12/28/2000|19:13:37|Juan Forero (Guest)|moebius strip|Hello Alexander%2C%0D%0A%0D%0AI saw your page about the moebius strip and I would like to comment you an idea that thumbles in my head about it...%0D%||513|5.42424242424242|5 62|0|Boa Ben-David (Guest)|01/01/2001|20:08:15|Boa Ben-David (Guest)|x%5E2 %2B y%5En %3D z%5E%282n%29|Hi Alex%2C%0D%0A%0D%0AI wonder if you happened to know whether the expression%0D%0Ax%5E2 %2B y%5En %3D z%5E%282n%29 was ever addressed. x%2Cy%2Cz inte||769|5.42021276595745|6 64|0|alexb|01/01/2001|19:11:54|Conan K Woods (Guest)|Two rectangles%2C do they intersect%3F|Hi%2C I have a math problem I have to solve for a computer program I am writing. I have two rectangles%2C and I need an algorithm to see if at any po||365|5.45454545454545|1 63|0|alexb|12/30/2000|20:23:34|Jerry Iuliano (Guest)|Cheops pyramid%2Ffine-structure|Sirs%3A %0D%0AThe explanation of the Egyptian mystery concerning the fine-st||445|5.38095238095238|1 67|0|alexb|01/04/2001|16:00:14|Christina (Guest)|whack%3F|I am an elementary school teacher looking for great sites to use in my classroom. I read your warning. I do not know what %22whack%22 means. Would ||389|5.5|1 68|0|alexb|01/05/2001|12:26:33|Deborah Cox (Guest)|birthday odds|Hello%2C%0D%0A%0D%0AI would do like to have your help finding a solution for this little question. %0D%0A%0D%0AI tried to find an answer in many sites||366|5.48031496062992|1 70|0|alexb|01/08/2001|01:09:34|dream and weep (Guest)|Peg Solitaire|I was very interested in the package-purge method of playing peg solitaire%2C but I%27m a bit confused and was hoping you could help me. I have practi||362|5.47286821705426|1 66|0|Neil Simpson (Guest)|01/08/2001|10:55:37|simpsonn|Allocating Bonus Based On Balance|I have a problem where I want to allocate a bonus to one of four parties in ratio to their existing balance %28which can be positive or negative%29. ||437|5.5|2 71|0|alexb|01/12/2001|09:50:07|dejaniire dejaniire (Guest)|Teach me%21|Dear sir%2C%0D%0A%0D%0AI came across your site and found it quite interesting%21 I was wondering if you could help me. I%27m 22%2C live in Greece%2C a||497|5.5|3 76|0|alexb|01/12/2001|13:20:40|RAJITH RAVEENDRANATH (Guest)|Lewis Carroll%27s Pillow Problem|Reg. this problem %3A Lewis Carroll%27s Pillow Problem%0D%0A%0D%0AThis problem is cited by M. Gardner in his Mathematical Circus.%0D%0AA bag contains ||407|5.5|1 75|0|alexb|01/12/2001|13:20:40|David K. Sargert (Guest)|Paisley %3F|Is there a mathmatical formula for the pattern %22paisley%22 %3F ||363|5.5|1 74|0|alexb|01/12/2001|13:20:40|Xinding Sun (Guest)|the nine dots|You can connect them without leaving the rectangle in four straight lines.%0D%0A%0D%0ASuppose the rectangle is%0D%0A%0D%0A A B C%0D%0A D E F%0D%0A ||364|5.5|1 73|0|alexb|01/12/2001|13:20:40|Carissa (Guest)|a creative problem|Here%27s the problem I would like a solution to%3A%0D%0A%0D%0AIf you are given IX%2C come up with three ways to make that six by adding only one line.||406|5.5|1 72|0|alexb|01/12/2001|13:20:40|Dmbac (Guest)|fitting people into a room|My question is...I have been posed a challenge on guessing the MAXIMUM number of people that can fit into a room %28disregard things such as egress%2C||599|5.47945205479452|3 69|0|alexb|01/12/2001|13:55:43|allanb (Guest)|origins of binary|Hello%2C%0D%0A%0D%0AI wanted to send you an email and congratulate you on your very informative website. Do you know who invented binary%3F I have be||486|5.52173913043478|3 77|0|alexb|01/15/2001|00:22:43|Chris trailblazed@home.com (Guest)|Cutting cake|In your %27cutting cake%27 puzzle you ask%2C %22One needs 6 movements to cut a cube into 27 pieces. Can you get this many pieces with fewer cuts%3F%22||405|5.51079136690648|1 79|0|alexb|01/15/2001|23:43:03|Vujicic Bozur (Guest)|Bertrand%27s paradox|Dear Dr. Bogomolny%2C I have questions too.Where can I find your work about that paradox and your opinion about Ehren%27s message %3FThank You in adva||448|5.49056603773585|1 80|0|alexb|01/17/2001|10:23:08|Sandra Parsons (Guest)|Rounding Rules|How do you round a negative number%2C eg does -2.4 round up to -3.0 or -2.0 or is it just a round on the number not the sign%3F Is there a rule for th||401|5.5|1 81|0|alexb|01/26/2001|23:17:24|NAUTEL (Guest)|12 coins puzzle|I just came across your forum and the weighting of 12 coins. I was wondering if I can present you with a posible solution %3F.%0D%0A%0D%0Alets divide ||376|5.5|1 85|0|alexb|01/30/2001|14:49:49|Peter M. Gerken (Guest)|Sierpinski Triangle|Hi..%0D%0A%0D%0AJust visited your site ...%0D%0A%5Ba href%3D%22%2Fctk%2FSierpinski.html%22%5Dhttp%3A%2F%2Fwww.cut-the-knot.com%2Fctk%2FSierpinski.html||389|5.5|1 82|0|alexb|01/30/2001|14:49:49|kathleen tyson (Guest)|I am looking for a list of permutations|I%27m looking for a program to generate permutations for 13 %28or more objects%29%2C I found your site. Unfortunately%2C your site is%0D%0Arestricted||379|5.5|1 87|0|alexb|02/05/2001|08:39:18|adsum|Error Correction|I can not remember.%0D%0A%0D%0AThe names of the 3 mathematicians who proposed the method of correcting any one bit error%2C in a 16 bit word%2C by u||375|5.5|1 88|0|alexb|02/06/2001|20:10:53|erin726|please help with number guessing game|I am a public speaking student at the University of Florida and would like to demonstrate the number guessing game to the class. However I don%27t und||388|5.51260504201681|1 89|0|alexb|02/07/2001|16:14:19|Christian Snoad (Guest)|Isoperimetric shapes|Dear sir%2C%0D%0A I am investigating into isoperimetric shapes and got stuck at proving that an isosceles triangal has a larger area with a given p||495|5.5|1 90|0|alexb|02/09/2001|11:53:12|twokurka|Interest Rates Formula|I am looking for a formula to complete a computer program to determine the following%3A%0D%0A%0D%0AThe program relates to interest rate calculations. ||551|5.48387096774194|3 91|0|alexb|02/12/2001|16:19:07|Kerem Aycibin (Guest)|Trick for Adding%2Fsubtracting fractions|Hi%2C%0D%0AI was just wondering if anyone knows a trick on how to add and subtract fractions%28most preferably fractions with 2%2C 4%2C 8%2C 16 in the||396|5.5|1 92|0|alexb|02/12/2001|18:25:38|tari (Guest)|pythagoras|Hello%2C I have been in search of some info on pythagoras. I need info like history on the man himself as well as a possible picture. Anything that co||376|5.5|1 93|0|alexb|02/15/2001|08:41:00|steve (Guest)|meaning of x-fold%2C where x is any number|I am looking for a good explanation of whether or not a fourfold increase in something means the same as a 400 percent increase or a 4 times increase ||416|5.5|1 94|0|alexb|02/15/2001|13:41:53|TPS (Guest)|Sam lloyd%27s wheel puzzle|I remember this great puzzle from a Martin Gardner book%2C I think. It%27s composed of two concentric wheels with a partial scene on each of them. R||410|5.53781512605042|1 95|0|LJackson|02/20/2001|01:19:11|LJackson|Mathemeticians with Math Anxiety%3F|I%27m looking for anecdotes about mathemeticians who somehow overcame fear of math and went on to succeed at it. I%27d love to hear your story for us||350|5.48623853211009|0 96|0|berenguer (Guest)|02/20/2001|12:16:09|berenguer (Guest)|Distance between strings|You want to find similar words to one you may be thinking of against a dictionary in your computer. How to do so%3F%0D%0A%0D%0A1- Get only those words||346|5.5|0 86|0|alexb|03/03/2001|20:04:50|Ian|reflection in a curve%3F|hi%2C all%2C%0D%0A%0D%0Aim a 6th form further maths a-level student%2C and we%27ve done loads about reflecting a line%2C %28point%2C shape etc.%29 in ||875|5.52486187845304|6 97|0|alexb|03/13/2001|13:43:52|Blake Parkins (Guest)|RE%3A Never Ending Spiral|Hi%2C%0D%0A%0D%0AI know little about math so please excuse the ambiguity of this post. I%27m looking for the name and information of the phenomenon t||507|5.5|3 84|0|alexb|03/16/2001|14:49:49|JAIMENJONATHAN (Guest)|Answer to %22Inside a spherical mirror%22|If i seem illogical%2C forgive me. I%27m only 10%2C and I%27m still in 5th grade. %0D%0A%0D%0AAnyway I think%2C assuming that the mirror is ONLY the i||912|5.53719008264463|7 100|0|alexb|03/23/2001|13:16:05|Joe Banafato (Guest)|Where can I find a proof%3F|Hello everyone%2C%0D%0A%0D%0AI am wondering if anyone knows where I can find a proof for the statement %22any non-negative integer can be identified a||372|5.47826086956522|1 101|0|alexb|03/27/2001|21:14:33|guy (Guest)|prime number%3F|how can this be proved%3F%3A%0D%0A%28%285%5E125%29-1%29%2F%28%285%5E25%29-1%29 is not a prime number.||585|5.72289156626506|3 102|0|peachlandlab|03/30/2001|20:37:29|peachlandlab|Mount Everest Math Puzzles |Here is a new web site with progressively more complex word problems for Middle School %28and up%29 Students. http%3A%2F%2Fmteverest.homestead.com ||378|5.5|0 104|0|alexb|04/01/2001|00:41:05|stancioff|Responding to x%5Ex%5Ex%3D3|I can%27t seem to figure out how to respond directly to a topic in the arithmetic%2Falgebra column%2C so I%27ll say it here. I remeber being given th||641|5.5|6 103|0|Muthukumar (Guest)|04/01/2001|16:08:56|breezy|a very simple question|If anyone could settle this difference of opinion between my husband and I%2C it would be appreciated.%0D%0AWhat percentage is %2410%2C000 of %24185%2||429|5.5|2 106|0|Ian|04/01/2001|14:26:52|Muthukumar (Guest)|Tests of divisibility|I came across this question in book called %22Mathematical Challenge%22 by A.Gardiner%3A%0D%0A%0D%0AWe can say if a number is divisible by 2 by lookin||453|5.42424242424242|2 111|0|alexb|04/19/2001|11:45:53|garethgibson (Guest)|peg solitaire strategy and variations|I have a simple question about peg solitaire. Is there any way of knowing if a game board variation is solvable%3F I have created a couple of peg so||380|5.5|1 112|0|garethgibson (Guest)|04/19/2001|17:45:08|Stephen Thorne (Guest)|%22Reducing%22 large numbers|Hope you can help me solving a peculiar problem or at least giving me a hint about how it could be solved.%0D%0AI%27d like to know if it does exist a ||391|5.5|1 113|0|alexb|04/21/2001|21:23:52|Jason Lackner (Guest)|Fractals|from the very basic to the top if i wanted to learn how to do Fractals what steps should i take. eg.. Algebra%2C Geometry%2C Calculus i just want to k||364|5.5|1 114|0|DavidT442|04/28/2001|06:47:53|DavidT442|Adding time on a calculator|Once upon a time%2C a long time ago%2C my dad showed me an easy way to add several times %28ie... 3 minutes 42 seconds plus 4 minutes 38 seconds%29 us||311|5.5|0 115|0|mp (Guest)|05/03/2001|13:04:45|mp (Guest)|binomial dist. derivation|can anyone show me a derivation of the binomial distribution%3F%0D%0A%0D%0AB%28x%29%3D n%21%2F%5B%28n-x%29%21 x%21%5D %2A p%5Ex %2A %281-p%29%5E%28n-x||296|5.59574468085106|0 116|0|alexb|05/15/2001|13:51:56|Dan Saltzman (Guest)|weight conversion|This might be an easy one for most of you%2C but not me...thats why im here. I would like to know how to convert grams per square meter%2C to oz. per||335|5.67441860465116|1 117|0|alexb|05/18/2001|07:01:41|Patrick (Guest)|Infinite series|What is wrong with this%3F%3F%3F Surely something must be%3F%3F%0D%0AConsider%3A%0D%0A1%2F2 %2B 1%2F3 %2B 1%2F4 %2B ..... %3E 1%2F2 %2B 1%2F2 %2B 1%2F||336|5.70454545454545|1 118|0|alexb|05/21/2001|17:19:56|Veronika (Guest)|cut an equilateral triangle into two with half the size|hi.%0D%0Adoes anyone know how i can cut an equilateral triangle into two equilateral triangles of the same area%3F%0D%0Ai%B4ve tried many ways%2C but ||314|5.52173913043478|1 120|0|alexb|05/28/2001|08:01:22|Fisch (Guest)|moebius strip|hello%0D%0Acan anybody please help me%3F%0D%0Ai%27m deeply interested in the special property of moebius strip-one-sidedness%0D%0Aso%2C i%27m planning||308|5.5625|1 121|0|alexb|05/31/2001|09:26:55|Darrell Boomgaarden (Guest)|Index Math when Base or Actual is Negative|We use indexes as a way to simply state how some key business variable %28e.g.%2C profit%29 is comparing to a standard or budget. For example%2C if a||298|5.5|1 122|0|alexb|06/08/2001|07:56:26|p_22_iglet (Guest)|Tower of Hanoi|Is there a version of your Tower of Hanoi that I can download and use without being connected to the site%3F||310|5.56410256410256|1 99|0|alexb|06/20/2001|12:47:11|conrad schlundt (Guest)|THE MANDELBROT MONK|Hi%2C%0D%0A%0D%0AIf you haven%27t seen this%2C you should. It suggests that a 13th century monk discovered the Mandelbrot set.%0D%0A%0D%0A%5Ba href%3D||447|5.5|2 124|0|alexb|06/25/2001|09:15:49|literaryguy (Guest)|what is a number%3F|Is zero a number%3F Is it an even number%3F How is %22even number%22 defined%3F%0D%0A||313||1 125|0|Danny kattan (Guest)|06/27/2001|12:54:32|Danny kattan (Guest)|Trading card probabilities|I am trying to find mathematical models that can help me simulate how many packets of trading cards does a person need to complete a collection. in t||291||0 119|0|alexb|06/29/2001|09:56:28|JohnMann|Puzzle%3A%22Then%2C I know your sum%22%2C%22Then%2C I know your product%22|I have been trying to solve the following puzzle%3A%0D%0A%0D%0ATake two integers n and m%2C selected from the range of integers 2 thru 100. Give the S||568|5.5|4 126|0|alexb|07/03/2001|08:06:08|ofer (Guest)|Symmetries in a triangle |I didn%27t anderstood the proof%0D%0Afor Symmetries in a triangle %0D%0Ain the proof section in Charming proofs%0D%0Ain this site.%0D%0APlease if you ||292||1 127|0|alexb|07/03/2001|14:31:06|Michael Short (Guest)|Which statistical tool should I use%3F|I have a problem in which I have six sets of results obtained in sequence from the same chemical test procedure over a period of four months. I know ||292||1 128|0|alexb|07/05/2001|20:01:13|Brendan (Guest)|Variations Of A Group of Numbers|I wonder how to calculate the number of possible arrangements in a group of numbers.%0D%0A%0D%0AAn Example%2C usiung the numbers 1 and 0 only%2C how m||290||1 131|0|activeco|07/08/2001|08:18:05|activeco|Three Dices %22Paradox%22|%0D%0AThree dices are thrown simultaneously.%0D%0AYou can bet %241 on a single number%2C 1 to 6.%0D%0AThe odds are rightly 1%2F2 so you get %241 for e||253||0 132|0|Tonio (Guest)|07/09/2001|08:45:28|Tonio (Guest)|Group Theory|Is there an infinite non-abelian group with all its proper subgroups abelian%3F%3F%0D%0AThanx%0D%0ATonio||250||0 83|0|Don (Guest)|07/19/2001|14:49:49|Bart Verhaeghe (Guest)|Question about a 15%2F16 sliding puzzle|Dear Sir%2C%0D%0A %0D%0A %0D%0AI wonder if it is possible to solve a 15 sliding puzzle from a given starting position to the finishing position in a m||501|5.5|2 133|0|Klaus (Guest)|07/20/2001|11:40:18|Klaus|phi %26 %3F2 rational%3F|Dear Alex%2C%0D%0AYou write that a number r is rational if it can be written a fraction r %3D p%2Fq where both p and q are integers.%0D%0ADoes that me||583||6 134|0|alexb|07/20/2001|21:35:46|JJe (Guest)|distributive law|Hi%21%0D%0A%0D%0AI was reading this page on this site%3A %5Bhttp%3A%2F%2Fwww.cut-the-knot.com%2Fdo_you_know%2Fmul_num.html%5D. At the bottom%2C there ||285||1 135|0|imdonny|07/21/2001|22:41:37|imdonny|ONE FOUR %3A 14 %3D |In the article ONE FOUR%2C the entry for 14 is empty. I suggest an entry%3A 14 %3D %5Bln%21%7B10%7D%5D.%0D%0A%0D%0ADon||237||0 136|0|alexb|07/31/2001|07:36:50|khaled moustafa kamel (Guest)|finding a mathematical equation between sine and inverse sin|coming across a problem in microsoft excel%2C i was un able to find a function that gave the inverse of sin%2C o i decided to acquire a method to find||277||1 129|0|alexb|07/31/2001|08:58:15|zander|playing with permutations...|First let me say that this is a neat site%2C I wish we would have had access like this when I was in school. We still did pretty good though...%0D%0A||367||2 138|0|Frederick|08/04/2001|11:04:15|Frederick|LaPorte| What is first name of LaPorte as in %22LaPorte formula%22%0D%0AThis takes the form f%28a%29 %3D sin%28h%2Asina%29.%0D%0A%0D%0Aa %3D angle of take of||237||0 139|0|alexb|08/07/2001|17:26:01|José Alberto (Guest)|Mastermind - Maximum number of trials|Hi all%0D%0A%0D%0AThanks in advance for answering my question.%0D%0A%0D%0AI%27m programming a MasterMind game and I%27m stuck on how to assign the max||302||1 123|0|mhbrill|08/10/2001|08:45:45|jawahar|Prove equilateral triangle...|It might be difficult to say this in words but I need to know iff anyone can prove the following%3A%0D%0A%0D%0ADraw a scalene triangle%28all sides une||419||3 140|0|alexb|08/14/2001|11:25:42|mhbrill|Morley%27s Trisector proofs use more than angles-why%3F|After reading the various proofs of the Morley Trisector Theorem on this site%2C there still seems to be a miracle. The Morley Trisector Theorem is t||776||1 141|0|Tony (Guest)|08/18/2001|09:18:00|Tony (Guest)|Torus cutted up with plane|Dear Sirs%2C%0D%0A%0D%0AI have heard something about a puzzle in a M. Gardner%27s book.%0D%0AIt should exist a solid that when it%27s cutted ub by a p||268||0 142|0|alexb|08/20/2001|13:10:55|Juan Manuel Tamayo (Guest)|Length of a function|Let%27s imagine the graphic of the sine function%2C and we take an interval from %5Ba%2Cb%5D. if we take a string%2C or a metric tape%2C and measure ||286||1 137|0|R. Bumby (Guest)|08/22/2001|21:59:36|Manoj Nair (Guest)|Exchanging information between n persons|Hi%3A%0D%0A%0D%0ACame accross an interesting problem. Dont know%0D%0Aif this is the right folder. Apologise if it isnt.%0D%0AThere are N people each o||1210||14 143|0|alexb|08/24/2001|15:47:08|pmbrown|Pythagorean Theorem Proof %239%3A any history or educational materials%3F|I am very enthusiastic about this proof%2C which could readily be used in the third or fourth grade. I expect to use it at that level. The proof is ||355||2 145|0|alexb|08/30/2001|22:02:35|bdesany|Tower of Hanoi Recursion Inequalities|Hi%2C%0D%0A%0D%0AI am confused about the 2 inequalities that lead to the Tower of Hanoi recursion formula%3A T%5Bsub%5Dn%5B%2Fsub%5D %3D 2T%5Bsub%5Dn||389||1 146|0|Tina (Guest)|08/31/2001|12:39:06|Tina (Guest)|conversion table|I need to know the conversion between feet and inches to cm and meters and then to convert to SI. %0D%0AIf I were 5 foot 3 inches tall how tall would ||237||0 148|0|Michel Colman (Guest)|09/16/2001|19:08:14|dana (Guest)|5%2B5%2B5%3D550|Add a single straight line to make this equation correct. The equal %28%3D%29 sign cannot be touched.||390||1 149|0|Michel Colman (Guest)|09/16/2001|22:48:19|Michel Colman (Guest)|13 Coins|In the twelve-coin problem where one coin has a different weight%2C you state the following%3A%0D%0A%0D%0AYou cannot fail to notice that this method s||243||0 150|0|ArthurvanHoudt|09/25/2001|11:15:56|ArthurvanHoudt|Question About the Breathing Square of Misha Pavel|In the applet on this site one can change between a square and an triangle. But imho the triangle is positioned different than the squares. The middle||305||2 152|2|alexb|09/28/2001|13:36:11|Dave|Parrondo|Ref%3A Your site http%3A%2F%2Fwww.maa.org%2Feditorial%2Fknot%2Fparrondo.html%0D%0A%0D%0AHi%2C%0D%0A%0D%0AMy kudos - best reality check on Parrondo I ||238||1 147|0|brian|10/08/2001|23:14:48|Barnes (Guest)|Odds at the race track|I picked three horses in a trifecta at the track the other day %28Nos. 8%2C 2 and 7%29. My wife picked three horses %28Nos. 8%2C 2 and 3%29. There wer||285||1 153|2|alexb|10/08/2001|11:41:33|Daniel Radoff|Incidence of birthdays|I understand how to solve the standard %5Ba href%3D%22%2Fexchange%2Fbirthday.html%22%5Dbirthday problem%5B%2Fa%5D. My question is%3A What if instead||483||5 156|0|Whymme|10/09/2001|21:45:22|Whymme|The pillow problem and Monty Haul|This is my first time here%2C and I really love this site. I already spent several hours that I should have spent sleeping%2C so that I%27d be able to||233||0 157|2|alexb|10/11/2001|20:01:16|carladler|Axiomatic Models|Long ago %28%7E20 years%29 I heard a reference to the effect that there could be a truth model to which two separate sequences of Axiomatic Models cou||269||1 158|2|alexb|10/12/2001|20:56:48|eddie|Random sets of integers|Hi%2C%0D%0A%0D%0AGiven a set of N items%2C be it a vector v containing the first N integers%2C my problem is to find an algorithm to tandomly chose a ||264||1 155|0|Manoj Nair|10/12/2001|13:52:12|Peter Lloyd|Base 8|Does anyone know a simple way to convert from base 10 %28ie normal numbers%29 to Base 8%3F||418||4 161|2|Whymme|10/14/2001|22:43:19|GrazerMorphAbd|Believe the unbelievable|Consider a right triangle AC%3Csub%3E1%3C%2Fsub%3EC%3Csub%3E2%3C%2Fsub%3E constructed on the start point of a ray with C%3Csub%3E1%3C%2Fsub%3E as the ||270||1 154|0|alexb|10/15/2001|00:21:28|Mark Galecki|a probability puzzle|Alex%2C%0D%0A%0D%0AI like %28some parts of%29 your cut-the-knot site. My favourite mathematics professor in college - Marcin Kuczma%2C Warsaw Univers||377||2 159|0|Liliya|10/16/2001|13:02:08|brandon|what if%3F%3F%3F%3F%3F%3F|what if the world stopped spinning%2C how far would your house slide%3F%3F%3F||329||2 163|0|alexb|10/19/2001|11:06:32|Paul Slattery|Language misuse|Hi Alex%2C%0D%0A%0D%0AWhat a great site. One piece of language misuse %28amongst many%29 that has always amused me is the following %28seen on many a||261||1 164|2|Jaime|10/27/2001|11:09:09|Justin |Permutations|I understand to find the different combinations of 4 objects%2C this can be calculated by 4%21. However%2C for example%2C I am looking for a formula ||254||2 165|3|Mike Kutz|10/30/2001|15:51:45|Mike Kutz|Golf Tournaments|I%27m involved in setting up a golf tournament in a few months and was trying to figure out what formulas I needed to use to make a generic form that ||198||0 169|2|Piers Haken|10/31/2001|06:37:51|Piers Haken|Weighing %28more than%29 12 coins|Okay%2C this may have been bashed to death%2C but I%27m still playing. Please indulge me.%0D%0A%0D%0A%28In reference to %5Blink%3Ahttp%3A%2F%2Fwww.cut||216||0 173|3|MOWMAN|11/08/2001|19:04:12|MOWMAN|HOW TO FIGURE SCALE|I AM TRYING TO COMPARE A MOWER TO A CAR IN TERMS OF USE COMPARED TO MILES DRIVEN%3F%3F%3F%3F A CAR IS APROXIMATELY 12FT. LONG AND HAS 14 INCH WHEELS W||192||0 175|0|alexb|11/09/2001|01:02:22|blazefghtr|Lottery probability|To all interested math buffs......during the last big lottery jackpot a coworker of mine and i had a debate regarding odds...he stated that if the odd||376||3 176|0|alexb|11/13/2001|14:35:32|Sean McIlroy|origin of real numbers|Formal theories of integers and rationals are well motivated in the sense that they give definite shape to an intuitive idea that was there already. I||220||1 170|0|w.kuehnert|11/13/2001|21:24:54|jscrivener|Fractal dimension in music|Hi%2C this is my first time here%2C and I hope someone can help%21 I am writing my dissertation in music theory%2C and it includes a chapter in which ||436||3 178|0|alexb|11/13/2001|11:20:14|raganwald|Hypergame Paradox %26 Sliders|The %22impossibility%22 of constructing a slider interface for choosing slider puzzles struck me as resembling Raymond Smullyan%27s %22Hypergame%22 de||255||1 179|0|Claude|11/15/2001|07:06:04|Claude|Melting ICE|I need some help with calculating the time it will take for a certain amount of ICE to melt. I have decided to use the following%3A%0D%0A%0D%0AQ%3DSH ||208||0 174|2|Richard Bradley|11/16/2001|00:23:56|James Griggs|Pattern Equation|A few years ago%2C I came upon a site that provided an algorithm for ANY pattern of numbers. It would prove any mess of numbers was a pattern and you||478||5 180|0|John H|11/16/2001|15:34:30|John H|Sporting teams draw|We run a Golden Oldies rugby competition.We will have 12 teams.We wish to play 7 rounds during the comp.Each round consists of games between 3 teams.||188||0 181|2|alexb|11/18/2001|09:03:59|R. Dixon|sequence|Trying to figure out the following sequence%3A 31%2C21%2C13%2C12%2C11%2C10%2C7%2C7%2C7%2C7........%0D%0A%0D%0ASo far%2Cno luck....any ideas%3F Thank||258||1 182|0|alexb|11/19/2001|23:31:10|hjackman|Division %26 Precision|I have an algorithm that calculates the reciprocal of a number to a good deal of precision. I now need to implement a division algorithm that simply ||534||5 183|2|alexb|11/20/2001|14:33:24|kayesrus|speed of a moving vehicle|How fast is a car moving if it goes 10 miles in 10 minutes%3F||251||1 162|2|alexb|11/22/2001|22:18:57|matt|does 1%3D2%3F|In high school I saw a proof showing 1%3D2. Iguess it was a brain teaser before class or something but I would like to see that again. Or else know th||834||10 166|3|Richard Bradley|11/22/2001|15:51:45|Mitch|Number of Digits %2F Highest Number|If I have the maximum number of digits allowed in a number %28the precision of a number%29%2C what is a mathematical way to determine the highest poss||251||1 172|3|alexb|11/23/2001|12:04:46|DarkOmen|Towers of Hanoi|We know that the rule to the solution is %282%5En%29-1%2C but what would be the rule if there were four pegs instead of the original three%3F||416||3 177|0|alexb|11/26/2001|23:36:11|Roger Wibberley|Delian problem|Dear Alexander%2C%0D%0A%0D%0AI%27ve enjoyed your interactive maths site - even though I%27m a musician%2C not a mathematician%21 I was especially inte||495||3 50||||19:09:34|sujaikumar|do all mathematicians do rec math%3F|Do all the members of this forum %28and other people you know%29 feel that recreational math is something that all mathematicians do%3F%0D%0A%0D%0AIs ||99||-1 186|0|sujaikumar|12/01/2001|19:09:34|sujaikumar|do all mathematicians do rec math%3F|Do all the members of this forum %28and other people you know%29 feel that recreational math is something that all mathematicians do%3F%0D%0A%0D%0AIs ||399||4 187|4|Glen|12/03/2001|00:30:42|Sarah|An answer to O%2CT%2CT%2CF%2CF%2CS%2CS|I encountered this puzzle in a children%27s book about the origins of chess. Unfortunately%2C the author does not give the answer. The question%2C of ||280||1 188|0|marlin eller|12/04/2001|20:18:35|dpocius|Domino theory|Hi all%21 I ran across something interesting concerning numeric patterns with dominos. I had been thinking of making a set of %22deluxe%22 dominos f||256||1 189|0|Arthur Siegel|12/06/2001|20:51:40|Arthur Siegel|Dynamic Projective Geometry|I have recently gotten to the point in a project I have been%0D%0Aworking on for some time - creating a 3d Geoemtry Visualiztion%0D%0Atool - such that||296||2 190|0|raganwald|12/11/2001|23:29:41|raganwald|An Address to the Graduating Class|The renowned Management Consultant S. Molly Ann needs no introduction. For several decades she has helped organizations achieve breakthrough success t||216||0 191|4|alexb|12/14/2001|00:20:12|pat05|value of an infinite series|Hello everyone%21%0D%0A%0D%0AThis is my first post.%0D%0A%0D%0AI%27ve been trying to calculate an approximate value of the Series %28from 1 to infinit||247||1 192|0|alexb|12/14/2001|00:20:12|Sean McIlroy|Monty Hall Dilemma|The %22standard%22 Monty Hall problem%3A%0D%0ALet the doors be A%2CB%2CC with the prize behind A%2C and assume that Monty opens B if your first choice||245||1 193|0|alexb|12/15/2001|19:02:33|lance2345|Pythagorean theorem -- new proof%3F|I%27ve looked through the many proofs of this theorem on this site and did not exactly see the one I came up with. I would appreciate 1%29knowing whi||268||2 195|0|alexb|12/16/2001|00:28:41|Omar|Triangle Construction|I have a quibble about your construction of a triangle%2C given the feet of the altitudes. %28The question came up in http%3A%2F%2Fmathforum.org%2Fep||493||1 197|0|alexb|12/17/2001|20:57:57|Sean McIlroy|Three-pancake Puzzle|It appears to me that the alternate solutions of the three-pancake puzzle correspond to the following alternate assumptions%3A%0D%0A%0D%0AAssumption %||248||1 194|0|Sean McIlroy|12/18/2001|01:55:05|Sean McIlroy|Lewis Carrol%27s problem|I feel that your Solution %231 of Lewis Carrol%27s problem is an oversimplification of the %22real%22 mistake%2C which %28as I see it%29 is this%3A Th||639||9 198|0|alexb|12/18/2001|20:15:46|Sean McIlroy|isoperimetric theorem|I have two questions about the proof of Lemma %232 on Geometry page %2371 %28Isoperimetric Theorem and Inequality%29%3A%0D%0A%0D%0A1%29 Why is it that||367||1 199|0|alnoth|12/22/2001|12:26:01|alnoth|two conic sections%3F|what is the euclidean way of finding the intersections of two given conic sections%3F%0D%0A%0D%0Afrom analytic geometry%2C finding intersections of tw||272||2 204|0|alexb|01/04/2002|12:26:38|dekahler|Easy solution for12 coin problem|Divide the coins into three stacks of 4%2C numbered stack 1%2C2%2Cand 3%0D%0A%0D%0APut stack 1 on the left side of the scale and stack 2 on the right ||343||2 206|0|alexb|01/08/2002|20:36:04|Al Lehnen|Bertrand%27s Paradox|I really liked your discussion%2Fdemonstration of Bertrand%27s Paradox. I%27m preparing a paper and have posted a website on another counter-intuitive||267||1 208|3|yaronkretchmer|01/09/2002|14:59:30|yaronkretchmer|L-system desc. of a Moore curve|Hi All.%0D%0AFirst of all%2C apologies if this is the wrong forum to be posting this message.%0D%0A%0D%0AI%27m looking for a lindenmayer-system %28a.k||211||0 207|3|alexb|01/09/2002|14:59:30|Bill Puetz|Game Algorithm|Over the holidays%2C I was playing a game with my father-in-law. I don%27t know the name for it%2C but it%27s the one where you have a cross of pegs ||213||1 209|0|sa_pattam|01/11/2002|08:18:23|sa_pattam|The 3 glass puzzle|It is my first time to browse to your web. And I want to share my solution for the puzlle with the number 6 in the sequence.%0D%0AThe sequence are%3A%||184||0 200|0|alexb|01/12/2002|23:45:11|Sean McIlroy|mistakes noticed|Your page %22http%3A%2F%2Fwww.cut-the-knot.com%2Frecurrence%2Fr_solution.html%22 has the following mistakes near the bottom%3A%0D%0A%0D%0A... %3D 2%28||275||3 196|0|alexb|01/13/2002|08:18:42|robert|category|can someone tell me which group do %22square root%2C sine%2C tangent%2C etc%22 belong to%3F I know that %22sine %26 tangent%22 belong to trigonometry ||288||3 210|0|Laocon|01/14/2002|07:57:09|Sean McIlroy|dicey|Suppose you roll a fair die until the sum of all the numbers rolled exceeds some given number n%3E%3D5%2C and let k be the sum of all the numbers roll||280||4 202|0|Phildonnia|01/14/2002|07:22:09|Judith Ross|Breaking chocolate bars| When I first read this problem%2C it seemed as if I had thought something similar before. Then I realized that I had seen it in an inverse form. ||254||1 212|4|Kris W.|01/15/2002|18:22:56|Kris W.|Peg-Solitaire Algorithm|Hello%2C%0D%0A%0D%0AI am a graduate student who is need of some samples of algorithms used to solve the peg-solitaire %28Hi-Q%29 game.%0D%0A%0D%0AI ca||208||0 215|2|alexb|01/18/2002|07:14:09|Laocon|Having an odd day%3F|Here%27s a few things I was thinking of last night in bed...%0D%0A%0D%0AToday is not an odd day. It is however partly odd%2C but mostly even. How%3F||214||1 216|3|dworth1|01/18/2002|08:58:17|dworth1|Tablemates together but separate|If there are 10 tables with 6 people at each%2C is it possible for one person to remain at the table at all times and the other 50 people to rotate am||173||0 203|0|alexb|01/18/2002|22:13:19|Jack Wert|Odd weight coin problems|%0D%0ARegarding the recent posting of solutions to the 12 coin problem%2C%0D%0AI am surprised that I have not been able to find a simple solution to t||487||7 218|4|alnoth|01/19/2002|09:30:23|tvarhegyi|geometric construction|The Braikenridge-MacLaurin construction produces an ellipse if %0D%0A5 appropriate points are given. I would like to find out how to construct the fo||217||2 219|0|Gunes|01/20/2002|00:01:01|martbark|Coins|This is probably a very simple question but it has been bugging me for a while. If you have 6 coins with heads on one side and tails on the other and||230||3 221|0|Gunes|01/20/2002|10:47:43|Gunes|%27things impossible%27|for those interested in dr. b%27s article %28and especially the subsequent responses%29 on machines that cannot utter certain statements in %27things ||181||0 214|0|Gunes|01/20/2002|20:07:51|Jaap Bak|two-var polynomial never square%3F|I think that%2C for m and n integers%2C%0D%0Am%5E4 - 2 m%5E3 n 3 m%5E2 n%5E2 2 m n%5E3 m%5E4%0D%0Ais never square.%0D%0ACan someone plea||187||1 223|4|alnoth|01/22/2002|23:23:56|Elisha Roe|Proof Conclusion...Q.E.D.%3F| I%27m taking a pre-calc and discrete mathematematics class right now. My teacher gave us this challenge to find out what the initials Q.E.D stand fo||224||2 217|3|alnoth|01/22/2002|00:07:20|calvin|Latest fractal puzzle%3F|Here is a problem recently posted by %22fractal%22 to a geocaching.com page that requires a solution to continue to the correct lat%2Flong coordinates||286||4 222|0|Doug Stitt|01/24/2002|23:26:30|Douglas Stitt|Twenty race cars on ten race tracks|Dear Sir%3A%0D%0A%0D%0AI have a very ambigous two-part question. One that%2C I%27m sure%2C deserves and ambigous answer.%0D%0A%0D%0AAssume that we me||203||2 226|0|alexb|01/24/2002|15:51:10|Yasemin|triangle given three heights|This is probably a silly question%2C but I%27ll go ahead and ask... %0D%0A%0D%0AWhen you construct a triangle given 3 heights %283 random numbers%29%2||190||1 201|2|Laocon|01/25/2002|16:48:26|briant|counting digits|Specific Question%3A%0D%0AI am trying to count the number of 1%27s in a binary representation of a given integer. So for example 2 with binary repres||258||3 229|0|alexb|01/27/2002|14:12:18|dflora|java enabled|I have installed both jre 1.3 and 1.2%2Cand java is enabled in browser preference%2C but when I access this site from netscape 6.1 I get %22java not e||224||3 230|0|Bob Ellwood|01/29/2002|14:54:42|Bob Ellwood|Latin Squares|If anyone has an answer for this problem the help would be appreciated. Say a group of golfers%2C 8%2C 12%2C 16%2C 20%2C 24%2C go on a trip for six o||153||0 231|0|alexb|01/29/2002|14:54:42|SirVLCIV|Negative Bases|Any information available%3B I%27d be surprised if I%27m the only one researching this.%0D%0A%0D%0AI%27m giving a colloquium on Feb. 20th on bases%2C ||203||1 233|2|Bryan Hranek|01/29/2002|19:24:13|Bryan Hranek|odds in keno|Here in NY%2C we have a lottery game called Quick Draw which is based on the casino game keno. It is played by picking anywhere from 1 to 10 numbers ||168||0 232|0|Phildonnia|01/31/2002|14:54:42|SirVLCIV|Cosines%2FSines in Exact Values|Ok%2C for a frame of reference%2C I%27m working on a topic concerning trigonometric functions in exact values %28figure out how first%2C secondly writ||250||3 234|0|alexb|02/01/2002|19:10:05|dflora|mis-type|http%3A%2F%2Fwww.cut-the-knot.com%2Fhtdocs%2Fdcforum%2FDCForumID4%2F133.html%0D%0A%0D%0A%0D%0ABoth triangles CQT and BQT are equilateral%28read ISOSOL||175||1 211|0|quodlibet|02/02/2002|20:50:16|Phildonnia|Cyclic numbers in Hexadecimal|I was searching for %22cyclic%22 numbers on my computer.%0D%0A%0D%0ACyclic numbers are numbers whose digits rearrange when they are multiplied by inte||1101||14 236|0|Sean McIlroy|02/05/2002|15:00:43|Sean McIlroy|What if it doesn%27t exist%3F|Is there an agreed-on way of interpreting statements about %28possibly%29 nonexistent things%3F For example...%0D%0A%0D%0A1%29 Is it correct to say th||311||4 238|0|m759|02/07/2002|19:05:55|m759|New permutations puzzle|A new puzzle like the classic 15 puzzle%2C %0D%0Abut with a new way of permuting the squares%2C %0D%0Acan be found at http%3A%2F%2Fm759.freeservers.co||163||0 239|4|alexb|02/08/2002|14:19:32|3_2_clave|base 3 programming|I%27ve heard that people have tried to program computers in base 3%2C but failed. I would like to know where I can find information to research this.||204||1 237|2|alexb|02/10/2002|22:35:31|mr_tomasino|Squaring a circle article|In the article titled %22Squaring a circle%22 %28http%3A%2F%2Fwww.cut-the-knot.com%2Fimpossible%2Fsq_circle.html%29%2C referencing the paragraph %0D%0||523||9 241|2|alexb|02/12/2002|19:51:13|Judy Walhs|polygon names|What%27s the real name for 11-gon and 13-gon%3F%3F%3F%0D%0AWhere did you find the answer%3F%3F%0D%0AThanks%21||267||1 242|3|alexb|02/13/2002|07:43:37|Dominic Gagnon|Ceva%27s theorem|Am getting something wrong in there...%0D%0A%0D%0ALet%27s say I have a triangle ABC of any kind%2C and on each side I draw an equilateral triangle. P||187||1 243|2|nm|02/14/2002|14:37:00|nm|Formula for Sam Loyd%27s Fifteen|Is there any kind of formula or computer program that gives the solution to the Sam Loyd%27s Fifteen%3F One that if you give the solvable initial con||165||0 244|4|Steven Keays|02/15/2002|20:32:36|Steven Keays|Fermat%27s last theorem|Wyles%27 proof of the FLT relates to X%2C Y and Z. Is there a proof for higher dimensional expressions of the form X%5En Y%5En Z%5En ... A%5En||167||0 247|2|unimportant|02/19/2002|19:05:34|unimportant|relation to phythagoreus%3F|The shortest distance between two points can be shown to be something other than a straight line. If two points are moving closer together at a very f||163||0 240|0|Stuart R Scott|02/19/2002|08:50:45|kcw|Looking for an old chinese puzzle|The puzzle was about a bunch of oranges distributed to a number of brothers in a way tht makes it appear that there were more oranges distributed than||213||1 248|2|unimportant|02/20/2002|19:19:06|unimportant|general|Going the other way if anyone read yesterday%60s posted ramblings %28including the person who oversees all print%29 what happens when two points grow ||158||0 249|3|alexb|02/21/2002|07:05:16|dtham81|Centerpoint for curves|hi%21%0D%0A%0D%0AI am desperate to find out how to get the centerpoint or midpoint of a curve. The curve could be of any type%2C such as bezier curve||205||1 251|0|alexb|02/23/2002|19:05:51|belial|Learning Maths|%5Bb%5DI wonder if you can help me.%5B%2Fb%5D%0D%0A%0D%0AI%27m in College%2C doing a computers course. I%27ve always had a good empathy with and aptit||196||1 250|3|alexb|02/23/2002|19:05:51|rperich|functions with two unknows|I am trying to figure out that if I have two positive integers x and y%2C is there some functions F%28x%2Cy%29 %3D z and F%27%28z%29%3D%7Bx%2Cy%7D tha||243||3 252|0|HP|02/24/2002|23:09:12|HP|Prime number question|I read this somewhere and tried to solve it but the proof seems not to be coming my way. Can anyone help%3F%0D%0A%0D%0AIf p is a prime number greater ||217||2 253|0|alexb|02/25/2002|14:30:48|Wentu|balls in n different urns%2C3 probs|It seems to me these following problems are strictly related. I%27d like to find the solution at least to the first one.%0D%0A1. I have B black balls ||210||1 254|0|spdrcr0524|02/28/2002|11:04:23|spdrcr0524|Eye Opener series|I was first amazed at what you showed in the eye opener series. Then I watched the applet more closely%2C and with fewer squares. I noticed that the||170||0 235|0|magpie10|03/05/2002|18:06:38|magpie10|Combinations or permutations%3F|This is my first submission.%0D%0AIn the UK an international fast food retailer is advertising a menu with eight items for a standard price. On large ||381||5 256|4|alexb|03/05/2002|18:48:48|stapel|arrows at the ends of axes|High-school texts put arrows at both ends of just about every line%2C including at both ends of the x- and y-axes in the Cartesian plane. College tex||197||1 260|3|enquote|03/11/2002|17:39:03|enquote|co-ordinate geometry%2Ftrignometry|Cosider a point P%28x%2Cy%29 . The line joining the origin to P makes an angle %27theta%27 with respect to y axis.%0D%0ANow suppose that the co-ordina||157||0 262|3|rperich|03/13/2002|16:53:44|rperich|function with two unknows cont.|This is a follow-up to a question I posted in Feb.%0D%0Athe original question was%2C given f%28x%2Cy%29 %3D z%2C is there a g%28z%29 -%3E %7Bx%2Cy%7D%||147||0 263|3|alexb|03/13/2002|21:01:57|phil grady|3 houses with 3 services|hi everyone%2C%0D%0A%0D%0Ai have been presented with a puzzle%2C which i cannot solve%2C the puzzle is this%3A-%0D%0A%0D%0Athere are 3 houses and 3 se||205||1 265|3|Dave|03/14/2002|23:25:37|Dave|Squares problem| Here is a square constituted by 4 small squares.%0D%0A %0D%0A___________________%0D%0A%7C %7C %7C%0D%0A%7C ||155||0 266|0|Vesselin|03/15/2002|19:58:39|Vesselin|homogeneous functions|I am looking for a book or an article which discusses a series expansion%2C similar to the Taylor expansion%2C but for a general homogeneous function ||171||0 255|4|Gunes|03/15/2002|23:31:51|Gunes|n-queens references|hi dr. b et al.%2C%0D%0A%0D%0Along time no see. %3A%29%0D%0A%0D%0Ai was wondering if you could help direct me to papers regarding the number of soluti||214||2 264|3|stapel|03/21/2002|07:22:40|francois|irrational series and limits|Are there any theorems referring to the fact that an irrational converging series will have an irrational limit as %28n%29 goes to infinity. Your idea||191||1 268|0|stapel|03/22/2002|20:16:08|Steve|Average Percent Vs. Total Percent|This is not a problem%2C but rather a request for help on an explanation. I need to explain to someone the why the average percent comes to a differe||198||1 269|3|50FOXY_CL|03/25/2002|13:58:18|50FOXY_CL|forming a square|I am looking for the solution for forming a square when putting together 4 other shapes. I am not totally sure what the shapes are but I believe it is||155||0 267|2|Quincunx|03/25/2002|14:17:01|Quincunx|Dense sets on the unit circle|If S %3D %7Bxn%7D is the set of points on the unit circle such that the angle that the x-axis makes with the radius from the origin to xn is n radian||319||5 270|2|SteveSchaefer|04/03/2002|22:55:21|marlin|Probability of a Probability|If I had a database of racing results%0D%0Aand selected a sample set of races at random from the%0D%0Apopulation of database%2C example%3A%0D%0A Even||215||1 274|3|Laocon|04/08/2002|22:18:11|padhani|EQUATION|RELATIONSHIP BETWEEN FOUR POINTS - A%2CB%2CC%2CD IS AS FOLLOWS%3A%0D%0A MIN MAX AVE%0D%0AA TO B - 0 580 130%0D%||177||1 273|2|SteveSchaefer|04/18/2002|23:03:25|SteveSchaefer|The field of rational functions|I had thought that the integers could be defined starting from their field properties%2C but I don%27t seem to be able to put a definition together th||440||7 278|0|astronut|04/20/2002|07:21:17|astronut|hyperbolic orbits|How does one calculate time-of-flight for a hyperbolic orbit%3F For example%2C if one were to launch a probe on a hyperbolic path that intersects the||149||0 277|2|alexb|04/22/2002|12:59:38|John Mahon|combination of 20 numbers|I am trying to write a programme to workout every single combination of 20 differnt numbers positioned in every single possible combination. For examp||223||1 280|0|acastaldo|04/28/2002|20:11:16|dkloehr|deferred loan|I have a loan for the amount of 13%2C445.60 %40 2.9%25 per annum rate for 48 months. My payments are 298.45%2Fmonth and the total interest to be paid ||177||1 281|2|jrr7|05/04/2002|14:44:21|Mark Elcombe|Can odds be calculated%3F|I%27ll do my best to try to explain this.%0D%0A%0D%0A This involves the Jon benet Ramsey Murder.The killer left a 3 page ransom note.At the end of||252||2 282|3|jrr7|05/04/2002|00:31:46|millies mum|find the last value for c|I need to find one more value for 1%2Fa %2B 1%2Fb %3D 1%2Fc where c %3D 6. I already have 12 %26 12%2C 18 %26 9%2C 24 %26 8%2C and 42 %26 7. I cannot ||194||3 257|2|jrr7|05/04/2002|22:57:02|shocan|NCAA Basketball Tournament|I would like to know what the probability of correctly picking the winning teams for all 63 games that will be played. I would like to know what the ||183||1 285|2|bluediamond|05/07/2002|21:34:41|Crystal|Law of Cos%2C SSA%2C and Quad. Equation|If the law of cos is used to solve a triangle given the SSA condition%2C a quadratic equation results. How can I show that this quad. equation will al||168||1 288|0|RicBrad|05/20/2002|07:50:44|RicBrad|Lewis Carroll%27s Pillow Problem|I found Lewis Carroll%27s Pillow problem really striking and interesting. %5Ba href%3D%22http%3A%2F%2Fwww.cut-the-knot.com%2Fcarroll.shtml%22%5D%28gam||184||1 286|0|alexb|05/20/2002|13:33:53|correctmath|whole and natural %23%27s%2C integers|Alexander Bogomolny%27s definitions for whole numbers and integers under%0D%0A%22W%22 in his glossary are wrong. Also%2C if you read them you will se||263||4 289|0|Omar|06/01/2002|12:45:20|Russ Warren|Three pancakes|I suggest a different answer%3A%0D%0A%0D%0AAs there are 3 pancakes%2C there must be 6 sides%3B 3 brown%2C 3 white. I look at one side and see that it||191||1 287|0|stapel|06/07/2002|16:29:57|numberexpert|standardized test questions|It is important to know what definitions are needed so that when you take%2C for example the SAT%2C you can answer the question correctly.%0D%0AAn exa||243||3 291|0|alexb|06/07/2002|14:47:26|understands|standardized test questions|To%3A bluediamond%0D%0A%0D%0AI think anyone reading this carefully enough will realize that Dr. B%0D%0Anot only chose the definitions he did%2C but th||361||5 293|4|alexb|06/21/2002|13:06:19|Cristina|Zeno%27s dichotomy paradox|I%27m doing some research in zeno%27s dichotomy paradox. I%27m trying to compile the diferents solutions to the paradox%2C but up to now i just have a||148||1 294|0|Omar|06/23/2002|16:17:45|Omar|Triangle construction|In the notations portion of %22The many ways to construct a triangle%22 page%2C you mention S%2C the area of a triangle. None of the constructions on ||125||0 295|2|Sean Turvey|06/26/2002|11:31:49|Sean Turvey|Statistical calulation%3F|%5Bb%5DHi%3A%5B%2Fb%5D%0D%0A%0D%0AI have what most would probably think an easy question but I have wracked my brains for a simple solution. I would p||146||2 296|2|Mike D|06/27/2002|15:33:22|Mike D|sine equation from random samples|I%27m sampling a sine wave at random intervals%2C and I%27d like to reconstruct the equation for the sampled wave from the samples. I imagine a forma||222||6 292|0|Simon|07/01/2002|09:14:33|Rajit |e and pi are transcendental|How does one prove that e and pi are not roots of algebraic equations %3F Someone please help out.%0D%0A%0D%0AThanks%0D%0A----rajit chatterjea||208||2 297|2|Simon|07/03/2002|16:08:25|Simon|%7B2%5En%7D a %22universal%22 set|Does anyone knows about the proof that you can find any sequence of number in the powers of 2 written in the decimal system %3F||195||4 299|2|Laocon|07/04/2002|21:12:41|Ben|the properties of 1|Why is it%2C exaclty%2C that 1 is not considered a prime number%3F I was going through a math lesson with my gre class and though I found a statement||158||3 301|2|Laocon|07/09/2002|22:48:20|ka_ds12|Probability|Hi%21%0D%0AHow can one pick the next figure%2C if the first figure has already been picked from 575757 numbers%3F How would one determine the probabil||150||1 302|2|Chris Tynan|07/12/2002|12:12:02|ka_ds12|Probability|Assuming you choose a number from 575757 numbers without replacing them%2C supposing you chose 516585 number first.What formular will you use to deter||152||2 303|2|alexb|07/18/2002|21:56:56|jman_red|Site name%3F|Why is this site cut-the-knot.com instead of interactivemath.com%2C etc.%3F%0D%0AJust wondering.%0D%0A%0D%0Ajman_red||350||7 304|2|alexb|07/19/2002|11:05:43|ctynan|Mathematical Competitions|A question for all ages really.%0D%0A%0D%0AWhat sort of mathematical competitions exist in the US %5Band other countries%5D at both High School and Co||129||1 305|0|Jake Foley|07/20/2002|22:25:07|Jake Foley|3%2C5%2C8 oz glass answer with 6|Here are the two quickest ways to solve the equation%2C%0D%0A%0D%0A008%0D%0A035%0D%0A332%0D%0A152%0D%0A107%0D%0A017%0D%0A314%0D%0A%0D%0AAnd%0D%0A%0D%0||127||0 309|0|josdavi|08/04/2002|18:53:31|josdavi|A Special Math Problem|Please teach me%3A%0D%0A%0D%0AI made a new puzzle 5 months ago and found a special%0D%0Amathematical problem%2C this problem is still unsolved.%0D%0A%||154||0 246|0|Cino Hilliard|08/15/2002|17:15:18|Jack Fox|least squares regression of a cubic|I want to program the least squares regression of a cubic equation%2C%0D%0A%0D%0Aa0 %2B a1X %2B a2X%5E2 %2B a3X%5E3.%0D%0A%0D%0AMy elementary linear a||314||2 310|0|Whymme|08/18/2002|09:54:26|Mr. Smith|Discrete Math Question|You have a set with N elements. You need to put each element into an ordered array with K slots%2C K being greater than or equal to N%2B1. Given one||137||1 311|0|Cino Hilliard|08/20/2002|18:56:51|DarkPlague17|The function K%28p%29 %3D %28x%2B1%29%5Ep - x%5Ep|I have sent this to other places but they just can%27t respond.%0D%0A%0D%0ADefine the function K%28p%29 %3D %28x 1%29%5Ep - x%5Ep given the following ||132||1 307|2|andrew cooke|08/21/2002|20:15:36|Kate|meaning of %22elegance%22|What is the math-related definition of %22elegance%22%3F||159||3 308|2|andrew cooke|08/21/2002|10:00:56|Mirek|Probability. Please help|Please help%21 Well%2C I%27ve stuck on one question and I don%27t know the answer. I%27ve been thinking and thinking but I cannot understand this one.||276||5 313|3|Whymme|08/25/2002|22:28:45|Whymme|Dicey probability question|This is for a game that I am developing. The game uses three ten-sided dice of different colours %28red%2C blue and yellow%29. Each of these dice is c||95||0 314|0|zorgalina|08/28/2002|22:28:45|zorgalina|Inventor%27s Par%28adise%2Fanoia%29|%22answering a more general question is easier than finding an answer to a specific one%22 - you mentioned on your page that you%27d like more example||96||0 312|2|NJZ|08/29/2002|11:00:45|andrew cooke|Book on Sets%2C Logic%2C Philosophy|Hi%2C%0D%0A%0D%0ACan anyone recommend a good book on sets%2C logic and the philosopy of maths%3F I%27m currently reading Grattan-Guinness%B4s Search ||196||6 316|3|Whymme|09/02/2002|22:28:45|Michael|imputation calculation|Can some one tell me how many 3-letter combinations are possible in the 26 letter alphabet||121||1 315|0|cino hilliard|09/03/2002|22:28:45|Vivek Narayanan|Prime numbers|I recently read an article that some mathematician has solved the problem of finding a generalization formula for prime numbers. Can anyone help me an||160||1 317|2|cino hilliard|09/05/2002|11:09:12|d_v_leeuwen|trigonometry|i have the following equation%3A%0D%0A%0D%0Asin%28a%29%2Fsin%28b%29 %3D g%2C with a and b in %5B0..pi%2F2%29 and g a constant%0D%0A%0D%0Ai%27m looking||143||3 321|3|Keith Dierberg|09/06/2002|08:08:01|Keith Dierberg|Modulo 2 In Random Digit Table|In a table of random digits %28i.e. RAND Corporation%29%2C you are instructed to blindly pick a starting block of 5 digits %28i.e. 72380%29%2C then ||100||0 258|0|Venu|09/06/2002|06:27:24|Jawahar|Probabilty problem|It must be quite simple but probability somehow beats me. The question I came across was this%3A%0D%0AWhat is the probability of a woman having at lea||388||4 322|0|shadow|09/09/2002|23:25:16|shadow|Impossible constructions|The cube root of 3 units is between 1 and 2 units and unconstructable. Therefore%2C bisecting a line segment that is between 2 and 4 units in length ||228||1 324|2|Schmerzner|09/09/2002|16:47:40|Schmerzner|Three 2s|Does anyone know of a solution similar to the one listed here - http%3A%2F%2Fwww.cut-the-knot.com%2Farithmetic%2Ffunny%2F3_3.shtml - using only three ||111||0 323|0|alexb|09/10/2002|23:25:16|jman_red|Correction|Alex%2C on your page%2C %0D%0Ahttp%3A%2F%2Fwww.cut-the-knot.com%2Farithmetic%2FKline-Loyd.shtml%0D%0AThere is an error in the scenario where one job o||139||1 320|0|NJZ|09/10/2002|06:40:28|NJZ|Summation Formulas for Powers|I am working on deriving a general formula in terms of n and p for expressing the sum of the first n integers raised to a given power p. I know the p||163||1 327|0|alexb|09/10/2002|07:43:59|skutch|Magician Needs Help|At one time I had a book on probabilities to use on stage as a %22mind reading gag%22. It gave the probabilities of facts according to the size of au||144||2 329|0|alexb|09/10/2002|21:03:19|_weh|Means inequality%3A correction|Sorry%2C%0D%0A%0D%0Abut I noticed two mistakes in my previous message. The reason was that I used square brackets which led to the omission of the cha||113||1 328|2|Daniel|09/12/2002|21:03:19|_weh|Means inequality|The webpage http%3A%2F%2Fwww.cut-the-knot.com%2Farithmetic%2FMeans.shtml provides a very good and clear presentation of inequalitites related to vario||145||2 276|3|alexb|09/14/2002|15:53:01|Jim Reynolds|1%2B1%3D3|The subject message probably looks strange to many -- but I seem to remember a math teacher in Jr. High flawlessly and logically %28at least to us jr.||792||13 318|0|alexb|09/16/2002|06:40:28|barb|GCD in real examples%3F|I%27m giving a presentation on Euclid%27s Algorithm %28Greatest Common Divisor%29. And after I show my class how to use the GCD algorithm%2C I need to||309||5 330|2|alexb|09/21/2002|07:09:59|aohara|Factorials|I know n%21%21 exists %28eg. 6%21%21 %3D 6 x 4 x 2%29 but what about n%21%21%21%2C n%21%21%21%21 etc for repeating factorials%3F And if they do exist ||131||1 332|0|alexb|10/06/2002|11:48:04|lilzeus|9-1-1 lottery probability|What is the probability that the New York lottery draws 9-1-1 ON Sept 11th%3F%0D%0A%0D%0AMany say its merely 1%2F1000. This is true to an extent but ||140||1 227|2|RicBrad|10/07/2002|12:51:01|Steve|Infinity|Is it possible that infinity can come in different sizes. For example%2C does all numbers have a larger infinity that even numbers%3F%0D%0A||584||8 334|4|alexb|10/10/2002|16:53:16|perrick|placing n circles inside a square|I am trying to find some algorithm that could %2Anicely%2A place n circles inside a square %28or rectangle%29.%0D%0AI know that %2Anicely%2A is a some||108||1 319|0|Cino hilliard|10/11/2002|06:40:28|cino hilliard|x%5En %2B y%5En %3D z%5E%28n%2B1%29 F.L.T.%3F|Hi%2C%0D%0A%0D%0AI Ran across this in si.math. Solution was provided but no derivation.I have a derivation if any one is interested. You should try it||149||2 335|0|Cino hilliard|10/12/2002|08:12:52|Cino hilliard|a new twist on the golden ratio Phi|Consider this twist on the golden ratio. The square of the lessor is to the greater as the square of the greater is to the whole.%0D%0Afor real x%0D%0||162||1 336|0|alexb|10/13/2002|02:27:12|Shai Simonson|Two Jug Puzzle|I am interested in the earliest references anyone knows to the two jug puzzle. %0D%0A%0D%0AThat is%2C given two integer size jugs%2C and an unlimites ||130||1 339|0|NJZ|10/17/2002|23:03:12|NJZ|A new twist on some old statistics|In linear regression the quantity Sxx %28used in calculating the slope of the least squares fit regression line and correlation coefficient%29 is defi||114||0 340|3|emily_ems|10/18/2002|10:20:13|emily_ems|the degree and diameter problem|greetings%2C%0D%0A%0D%0A i am a new user of this cite and i%27m a high school student%2C doing a research paper on the problem i saw on the net about||115||0 342|2|Dave Wiggins|10/21/2002|06:27:12|lei you|n%5E2%2Bn%2B1 is not a factor of 180%3F|for integral value of n %3E 1%2C%0D%0An%5E2 n 1 is not a factor of 180%3F%0D%0A%0D%0Ai know that n%5E2 n 1 is a odd number%2C but now how do you proof||135||2 343|0|no_hateration|10/22/2002|10:32:36|no_hateration|tower of hanoi|can anyone help me out with this program. Here is what I got so far Option Explicit%0D%0A%0D%0APrivate Sub cmdSolution_Click%28%29%0D%0A Dim disks%2||114||0 341|0|Zach Wegner|11/02/2002|17:22:13|Shai Simonson|Probability|Does anyone know if there is a permutation of a standard deck of cards%2C such that when you split it in half and play %22War%22%2C the game never end||133||1 344|3|RicBrad|11/07/2002|11:31:59|ghafners|Ancient Quinary Number System|My 4th grade daughter has an advanced math project on the quinary numver system. We are looking for possible uses of this system in our everyday live||277||5 347|0|alexb|11/08/2002|13:57:49|golland|Construction| Hi all%2C%0D%0A%0D%0A Another geometry construction problem%3A%0D%0A%0D%0A Inscribe a parallelogram into a triangle so that one angle is common%0D%0A||151||3 346|3|Garry|11/11/2002|10:20:04|Garry|e %2B compound interest|%281 %2B 1%2Fn%29%5En is supposed to converge on e%5E1%3F But I find that %0D%0An %3D 2%5E64 approximates e%5E2. Does anyone agree%3F %0D%0A%0D||146||2 349|0|alexb|11/13/2002|09:53:38|Thomas Lam|Math Magic|Do any one have any good suggestions for books%2C web sites%2C etc that talk about math magic %28Martin Gardner have provided some%29 %3F%0D%0A%0D%0AI||144||3 350|3|for michelle|11/16/2002|13:59:07|michelle|math prblem|my son bring a math problem home every week and as a family we all try to solve it first. I%27ve never won. can anyone help me with this one%3F Using||193||4 348|4|luca|11/18/2002|09:53:38|Luca|Topology|I%27m looking for an example of convergent net in a topological space%2C with no subsequences.%0D%0A%0D%0AThanks||160||4 352|0|Cino hilliard|11/18/2002|13:59:07|Cino hilliard|mass of the universe| I was told that this formula gives the mass of the universe. %0D%0ASum%28%28x-a%29%28x-b%29%28x-c%29...%28x-z%29%29%2Fg %2B 10%5E38 kg where a %3D 1k||168||4 333|0|alexb|11/19/2002|11:18:50|RicBrad|%27Almost every number has a 3 in it%27|%28when I say %27number%27 please read %27natural number%27%29%0D%0A%0D%0AI have been puzzling over the %5Ba href%3D%22http%3A%2F%2Fwww.cut-the-knot.c||271||8 353|3|Karl Kewl|11/20/2002|09:51:13|Karl Kewl|Tricky brainteaser|Hi there%2C%0D%0A%0D%0Athe questionmarks in the picture below shall be replaced by characters or numbers. Honestly%2C I have no clue and that drives m||144||0 354|0|Whymme|11/20/2002|09:51:13|Ben|Hour Glass Problem%2C solution.|I%27m not sure if anyone has pointed this out before but how about the following solution%2C could find it with a quick search.%0D%0A%0D%0A1%29 Start ||216||2 357|0|Whymme|12/04/2002|23:20:56|JPUCUL|fractions|What seven unique fractions add up to 1%3F%0D%0A1%2Fa %2B 1%2Fb %2B 1%2Fc %2B 1%2Fd %2B 1%2Fe %2B 1%2Ff %2B 1%2Fg %3D 1||156||1 360|0|alexb|12/09/2002|22:15:27|sheba0907|Name of a formula|What is the name %28or is there a special name%29 for when you do something like this%3A add your birthdate together to get 1 number%0D%0A%0D%0Aexampl||128||1 358|0|Cino hilliard|12/10/2002|13:36:20|Golland|fraction reduction| Hi all%2C%0D%0A %0D%0A Any ideas on the following problem%3A%0D%0A%0D%0A Is it possible to reduce %282n%5E2-1%29 %2F %282n%2B1%29 %3F What is n if re||202||5 345|0|Order|12/14/2002|02:58:49|Deadeye Dragoon|Monty Hall %22solution%22 is wrong IMO|I%27m just amazed at the number of very intelligent folks who are missing the picture on this one. I%27ve never taken probability theory so perhaps my||328||11 356|2|Order|12/16/2002|21:06:55|Chaosman|%2450%2F6 months or %24100%2Fyr raise%3F|There%27s a puzzle on this site asking what is better%3A A %2450 dollar raise every six months%2C or %24200 every year. This is the answer given%3A%0D||208||3 361|0|Cino Hilliard|12/26/2002|04:01:59|Cino hilliard|It adds up to 6|Cute little puzzle I heard the other night.%0D%0A%0D%0AGiven the basic operators %2B - %2A %2F and sqrt%2C apply to the%0D%0Athe following so that you||186||5 363|3|MrToad|01/04/2003|00:53:33|guest|rational or irrational%3F|I want to know %2C%0D%0Alog2%28x%29%2Alog2%28x%29%3D2%2Cthen x is a rational number or irrational number%3FAnd why%3F %28log2%284%29%3D2%2Clog3||150||1 364|0|Cino Hilliard|01/09/2003|23:12:07|Cino Hilliard|True Test|The following short quiz consists of 4 questions and%0D%0Awill tell you whether you are qualified to be a%0D%0A%22professional.%22 Scroll down for eac||172||2 365|0|alexb|01/10/2003|11:19:55|Order|English versus Probability|I%27m not sure why%2C but problems involving conditional probability seem to be especially difficult to write correctly using English. Perhaps it is ||182||3 366|0|Henk Koppelaar|01/12/2003|09:03:26|yaronkretchmer|Looking for L-system description|of some fractals%0D%0ASpecifically Peano%2C Wunderlich %28%22Meandering%22%29.%0D%0AAlso %2C an explanation on how to construct them from the graphic ||119||1 331|0|Jenny cortez|01/13/2003|15:47:43|Kathy|multiplying with Napier%27s bones|My children and I made sets of Napier%27s bones from the book %22How Math Works%22 by Carol Vorderman. It appears to only be possible to multiply a mu||146||2 368|2|B. Grantham|01/20/2003|21:14:58|B. Grantham|Fibonacci pyramid|I would like to know if anyone sees any significance in the following%3A%0D%0A%0D%0AWork is based on Scott E. Brodie%27s page %22Inscribing a regular ||196||1 370|0|alexb|02/03/2003|13:34:14|Graham C|A problem in checker-jumping|There%27s an example here of the inadequacy of plain-English expositions.%0D%0A%0D%0A%22Everybody knows the leap-frog jump in the game of checkers. Th||114||1 367|3|Graham C|02/05/2003|20:09:41|Henry Casson|Test for convexity|Simple question has me stuck.%0D%0AI have a closed plane path made up entirely of arcs.%0D%0A I know everything about each arc.%0D%0A%0D%0AI want to k||188||5 372|0|alexb|02/10/2003|21:31:15|porter|POLYGONS|Does anybody have any references to algoritms for calculating the area of overlap of two convex polygons using coordinate geometry %3F%0D%0A%0D%0Arjp||93||1 374|2|alexb|02/12/2003|21:54:25|jlahens|Real Raised to a complex|Hello%2C%0D%0A%0D%0ACan anyone tell me what it means to raise a real number to a complex power%3F I suppose a more general question is%2C what does i||106||1 373|2|BoBo Brazil|02/13/2003|15:09:39|RICK|QUESTION|IS THERE A WAY TO TAKE ANY NUMBER AND APPLY A FORMULA TO IT WHICH RESULTS IN THE ANSWER BEING THE SAME FOR ANY NUMBER USED%3F%3F%3F%0D%0ACAN YOU APPLY||119||3 369|0|alexb|02/14/2003|12:32:29|Cynthia Mullis|An interesting site|I was especially interested in the discussions of %5Ba href%3D%22%2Flanguage%22%5Dmath as language%5B%2Fa%5D and the imprecision of English. I have a||274||14 375|2|RicBrad|02/16/2003|12:41:01|franky|diameter from minor segment|Looking at the attached picture%0D%0APoint A and B have a fixed distance between them. If you measure the distance between the tangent and the interse||95||2 377|2|Graham C|02/17/2003|08:31:20|Graham C|Did Martin Gardner believe in God%3F|Some years ago Martin Gardner analysed the following problem %28the wording may not be identical%29%0D%0A%0D%0AOn the surface of a planet being explor||121||0 376|0|Graham C|02/19/2003|07:05:30|Cino Hilliard|easy mind reader trick|Here is an easy carnival trick. See if you can figure it out.%0D%0A%0D%0Ahttp%3A%2F%2Fwww.ebaumsworld.com%2Fmindprobe.html%0D%0A%0D%0ACino||181||6 379|2|alexb|02/20/2003|02:28:38|Greg S|Five Regular Polyhedra|If you join equilateral triangles at a vertex%2C you have the choice of three%2C four%2C or five. With squares you must use three%2C and the same with||132||2 382|3|Jack Wert|02/24/2003|23:03:12|marsha|annual earnings|What equation do you use to figure out what your annual income is%3F||89||2 384|0|alexb|03/04/2003|19:03:33|Casaretto|Organisation of PPT.|H. Andres L%F6nnemo and Alexander Bogomolny%0D%0A %0D%0AI%27m interested in new method about organisation of Primitive Pythagorean Triples.%0D%0A %0D%||103||1 381|3|mathmorob|03/05/2003|09:56:00|rclough|modular arithmetic|a %29I am using the numbers 1-7 for modular arithmetic %28mod 7%29%0D%0Abecause these have metaphors assigned to them. Can I just add 1 to%0D%0Aresult||120||6 385|0|Graham C|03/12/2003|18:11:29|Gireesh|Latin Sqaures with Constraints|Hi%2C%0D%0A%0D%0AI have to connect N inputs to N outputs in N timeslots. This translates to creating a latin square where the rows are represented by ||88||1 387|0|NJZ|03/21/2003|15:20:42|NJZ|Distance Along a Curve|Given a function f%28x%29 which is continuously defined over the interval x%3Da to x%3Db%2C I am trying to derive a second function g%28f%28x%29%29 wh||100||2 389|2|Annabelle|03/26/2003|15:38:42|Annabelle|Cut a pie%3A 8 pieces with 3 lines|Hello%2C I may sound a bit... but I haven%27t managed to work it out. I can only come up with 7 pieces. Please could someone kindly show how it%27s||96||2 391|0|CSpeed0001|04/05/2003|10:29:05|CSpeed0001|Calculator calculating Sine|How does a cheap scientific calculator calculate trig functions%3F My best guess is Power Series. I also thought it might be interpolating and using||141||3 392|0|SteveSchaefer|04/07/2003|19:37:00|SteveSchaefer|Math Exercises%2FQuestion Pools|This is a math education question. I have a discussion going with another college math professor. Both of us use Blackboard course management softwa||90||4 390|0|SteveSchaefer|04/07/2003|06:19:44|Rinaldo|14 coins|Dear all%2C%0D%0AI am new of the forum and also my interest in logic problems is very recent. I came here because interested in the problem of the 12 ||115||2 396|4|Budi Darmawan|04/11/2003|10:10:19|Budi Darmawan|Math test name|Hi%2C %0D%0A%0D%0ASome times ago I stumble on an exciting site that has a collection of annual math tests for some of the brightest america%27s colleg||84||0 397|2|db|04/16/2003|08:47:52|db|What does %22cake%22 mean%3F|I recently came across a question regarding numerical sequences that %0D%0Aasked%3A How many parts contain the cake%3F Is this a typo%3F If anyone has||84||0 399|0|alexb|04/20/2003|23:35:14|Maxim|Inversion%3A analytical approach|A few additions to%0D%0Ahttp%3A%2F%2Fwww.cut-the-knot.org%2FCurriculum%2FGeometry%2FSymmetryInCircle.shtml%0D%0A...%0D%0AConsider the inversion with r||108||1 398|2|alexb|04/20/2003|20:22:22|Ted77|The liar%2Fhonest guard question|I would like to know an answer to the question in which there are two guards to two doors%2C one which leads to life and one which leads to death. One||111||2 393|2|Graham C|04/26/2003|17:24:59|Pavel|Incompletness and Undecidability|Hello%2C first of all%2C AWESOME site%21%0D%0A%0D%0AHopefully%2C I won%27t be out of context here%2C but I%27m looking for either a good explanation o||150||8 394|0|alexb|04/27/2003|19:03:08|Maxim|Two Coins Puzzle|In the excellent Two Coins Puzzle %28http%3A%2F%2Fwww.cut-the-knot.org%2Fpythagoras%2Ftwo_coins.shtml%29%2C I think there is an even simpler argument ||110||1 404|3|Greg|05/08/2003|19:56:10|Greg|Changing between arbitrary bases|I%27m working on a problem where I want to be able to change a number from an arbitrary base to another arbitrary base. For example%2C I might have a ||91||4 408|0|alexb|05/15/2003|10:42:44|Zach|weight|I have 3 salaries for 3 job functions that I would like to get an average of the 3 salaries based on a weight assigned to each salary. The result shou||82||2 409|0|taran|05/18/2003|19:18:50|taran|calculus|I want to know whether there exists a theorem like that%3A%0D%0ALim %26%238710%3Bx -%3E 0 %28%C4n y%2F%26%238710%3Bn x%29 %3D dn y%2Fdn x%0D%0Awhere %||100||0 410|4|JJ|05/25/2003|09:31:55|Curt Tigges|triangle article|Hello%2C%0D%0AA while ago I was going through this site and found an article with an illustration. The illustration was of a triangle over a grid that||90||4 412|0|Diego Calderon|05/27/2003|21:05:50|Diego Calderon|Series Summation|What is the exact sum of a the P-Series where P%3D3. This is tricky subject. Euler could solve for p-series where p%3Dan even integer%2C but not for||113||2 378|2|Michael Klipper|05/31/2003|02:28:38|cavfancier|Computer as magician|This site has a game on it that reminded me of the %22Computer as Magician%22 tricks that I saw here on CTK. Would love to know exactly how this one ||127||2 406|0|Whymme|06/06/2003|23:26:10|Rob|filling a circle|I was listening to Click and Clack%2C the Tapitt bros. a couple of Saturdays ago%2C and on their program%2C CarTalk%2C a trucker posed the following q||101||2 388|0|Cino Hilliard|06/08/2003|22:48:38|Cino Hilliard|n%2B1 problem|Consider the recurrence%0D%0ATake a number.If it is even divide by 2 else add 1. %0D%0A%0D%0AAfter a finite number of steps you will get the terminal ||133||9 413|0|Sik|06/11/2003|10:54:43|Jack Fox|theorem of number theory|There%92s a fundamental theorem of calculus and a fundamental theorem of algebra. Is there a fundamental theorem of number theory%3F||109||2 411|3|sfwc|06/13/2003|08:07:56|patrick|Modular Arithmetic too%21%21|I%27m working on a cryptography assignment. I%27ve to solve this problem in order to move futher.%0D%0A%0D%0Amy question is by using modular arithmet||97||2 414|0|sfwc|06/14/2003|21:11:59|sfwc|A property of a%5En|In this article%2C www.cut-the-knot.org%2Fproofs%2Fpowers.shtml%2C it would be almost as quick and nice to prove FLT. Then we could see exactly which ||103||1 415|0|Graham C|06/17/2003|14:35:24|Golland|NBA Finals| Hi all%2C%0D%0A%0D%0A On Sunday the SA Spurs became US basketball champions%2C beating the%0D%0A NJ Nets in 6 games. Congratulations %21%21%21%0D%0A%||84||1 416|2|sfwc|06/18/2003|09:01:59|siksite|Double negation and rules of sign|Negation is in the center of central questions%2C as in Wittgenstein%27s intriguing one%3A Does %7E%28%7EP%29 affirms P or negates %28%7EP%29%2C or bo||183||1 420|0|Cino Hilliard|06/30/2003|07:52:24|Cino Hilliard|Base conversion and compression|Hi%2C%0D%0AI have been using free the python interpreter lately because of it%27s%0D%0Aarbitrary integer precision. This allows for the implementation||218||2 422|2|RicBrad|07/04/2003|15:18:26|Erica|Undecidability and proof|Can a theorem such as the Goldbach conjecture be undecidable%3F%0D%0A%0D%0ASuppose that it could be proven to be undecidable. Then it must be true th||132||1 401|0|liketogo|07/06/2003|15:39:11|tokai|PythagoreanTheoremProof by Einstein|a proof I found at the following address%3A%0D%0A%0D%0Ahttp%3A%2F%2Fwww.camtp.uni-mb.si%2Fcamtp%2Frobnik%2Fnovacella2001%2Fquantenchaos%2Fnode2.html%0||117||2 421|0|alexb|07/14/2003|14:32:04|RicBrad|Ap%E9ry%27s Constant|I saw this in a couple of places %28including %5Ba href%3D%22http%3A%2F%2Fmathworld.wolfram.com%2FAperysConstant.html%22%5DMathworld%5B%2Fa%5D%29%3A%0||154||4 395|0|Eric Shrader|07/16/2003|19:03:08|Maxim|Maximizing the box volume|There is a famous problem which probably nearly everyone has encountered in basic calculus courses. We take a square%2C cut off four equal squares at ||147||2 405|0|Vladimir|07/20/2003|17:16:21|david thorne|Fourier rep. of Keplerian Motion %26| When simple harmonic motion is represeted by a point moving on a circle at constant angular velocity%2C the X and Y projections along the time axis g||144||1 298|0|Vladimir|07/21/2003|21:12:41|naveennagar|Speed Calc. for Oscillations|I am implementing a project in which a piece of glass is to oscillate forward and reverse on rollers in a furnace. The sequence of operation is as fol||169||1 359|0|Vladimir|07/22/2003|22:15:27|NJZ|Definitions|Can anyone give me a concice definition of the terms %22mechanics%22 and %22dynamics%22 as they are used in mathematics and physics%3F In my expreien||150||1 423|0|alexb|07/23/2003|10:42:03|jman_red|false proofs|Im doing a project on false proofs right now%2C and I wonder if anyone can give me any hints on how to generate my own false proofs. Ive seen most of ||251||19 425|2|alexb|07/25/2003|09:22:56|chess|3 glass problem for 2 glasses.|Help.%0D%0A1 If you take two glasses of volumes %28in whole numbers%29 P and Q where P and Q share no common factor and P%3EQ. Add in an infinite drai||95||3 427|0|Michael Klipper|08/01/2003|17:16:01|Michael Klipper|Definition of Infinite|This isn%27t really a problem%2C but it%27s more of a curious fact I noticed once. Obviously%2C two finite sets must be the same size if there is a o||87||0 417|2|Vladimir|08/01/2003|18:37:44|sfwc|The aliquot game %28modified%29|At www.cut-the-knot.org%2FSimpleGames%2FAliquot.shtml%2C it says near the end %27You may even introduce an additional rule that precludes subtracting ||157||1 407|0|Ed Shields|08/02/2003|15:59:12|Rob|infinity|If time stretches out infinitely in the past and future%2C then any given moment in time equals one divided by infinity. Since one divided by infinity||146||4 371|2|alexb|08/02/2003|09:51:07|Graham C|The pragmatics of infinity|Browsing through some of the older forums %28maybe I should have been doing something useful%2C but there you go%29 I came across a posting %28by PAR ||217||11 428|3|Vladimir|08/11/2003|00:35:46|Brian|Interesting number ordering problem|Hey everyone%2C this is my first post here and I%27ve been racking my brains with this problem for about a week now. I have been trying all sorts of ||118||1 432|2|alexb|08/12/2003|09:12:38|Kavi|Implications|In the section on the definition of implication%2C it is carefully mentioned that the falsity of A implies the truth of %22A implies B%22%2Cwhatever b||96||1 433|2|Does it matter|08/14/2003|15:24:52|Does it matter|Compounding interest|It%27s easy enough to do the math of compounding a fixed interest rate on X amount of money in a spreadsheet program such as Microsoft Excel. However||97||2 424|0|alexb|08/15/2003|07:51:30|Larry_H|Morley%27s theorem|Hi all%2C%0D%0ASince CTK has such a good account of Morley%27s theorem%2C I thought I would point out this little sidelight on it%3A%0D%0Ahttp%3A%2F%2||113||2 430|0|Graham C|08/19/2003|00:35:46|moondog|The 15 peg Triangle puzzle|Hi%2C%0D%0AI have long been interested in a popular puzzle%0D%0Awith 15 pegs in a triangular pattern. One peg is %0D%0Aremoved and one may jump over a||243||3 435|0|hillcino368|08/21/2003|22:25:46|hillcino368|sqrt of prime p is irrational|I searched the CTK archives and did not find these proofs%2C unless%0D%0Athe proofs for the sqrt%282%29 are sufficient to describe the argument%0D%0Af||722||0 437|0|alexb|08/25/2003|18:02:23|Michael Klipper|Interesting Puzzle and Studies|I came upon an interesting math puzzle a little while ago. After having found out how it worked%2C I set out to prove some properties concerning it. ||114||2 434|0|Vladimir|08/25/2003|22:25:46|hillcino368|Pythagorean Theorem proof|Hi%2C%0D%0AI came up with a proof some time ago of the Pythagorean theorem that %0D%0Agoes like this. %0D%0A%0D%0A%28First I apologise I could not dra||126||3 400|0|neat_maths|08/26/2003|15:41:48|Cino Hilliard|8 divides %288x%2B3%29%5Em %2B %288y%2B5%29%5Em|Hi%2C%0D%0AI just discovered this last night using Pari.%0D%0A%0D%0ATheorem 1%3A%0D%0A8 divides %288x %2B 3%29%5Em %2B %288y %2B 5%29%5En for integers||178||5 419|2|neat_maths|08/28/2003|23:07:08|sameermarathe|Area of a triangle|Hi%0D%0A%0D%0AI was reading the numerous proofs of the Pythagoras theorem on the website today. Many proof utilise the fact that area of a right angle||165||2 436|2|neat_maths|09/02/2003|06:03:19|neat_maths|Sum of Squares equal to Odd Powers|I have been looking for posiitive integer solutions to the equation%0D%0Ax%5E2 %2B y%5E2 %3D z%5E%282%2An%2B1%29 ie z%5E3%2C z%5E5%2C z%5E7 etc.%0D||146||6 402|2|Greg S|09/10/2003|17:49:02|Greg S|Flat Space with Finite Volume%3F|The data from the WMAP satellite has given information regarding the age and composition of the universe. I know that%27s cosmology. It was also repor||250||7 438|0|Andy Nisbet|09/11/2003|16:47:21|Andy Nisbet|math puzzles|I have lost a puzzle where a chequerboard-style area 10 squares by 13 is cut into shapes that can be re-assembled into two chess boards%2C apparently ||195||8 441|4|JJ|09/22/2003|06:01:18|JDZ|Angle Trisection Blues|I%27m looking for a collection of different methods people have tried and failed to solve the angle trisection problem with a compas and straight edge||101||1 440|0|Vladimir|09/23/2003|06:01:18|NJZ|Summation Notation|I am trying to figure out how to express the following problem in summation notation. Given a series of points in the xy plane%2C find the average di||139||3 442|0|Vladimir|09/24/2003|09:24:15|J|finding the radius|i need to know how to find a radius as it rises up the cylinder. the actuall radius is 73.5%22 and the rise is 123%22 and 90 degrees from start to fin||204||1 439|2|Vladimir|09/30/2003|16:47:48|Chris Fenwick|Bizarre sequence|1%2C2%2C4%2C8%2C16%2C31%2C37%2C43%2C67...%0D%0A%0D%0AHow is the above sequence generated%3F%0D%0A%0D%0AThis came up as a problem on a Maths CD that my||1196||15 443|3|UHeinema|10/01/2003|11:31:44|UHeinema|Max. Triangel|Hello%2C this is a problem I have pondered for some time now%2C and have not found a solution..while I am sure one exists %28and probably an elegant o||123||2 445|0|Vladimir|10/14/2003|13:08:51|golland|Rational cut of a triangle| Hello all%0D%0A%0D%0A%0D%0A This is a look at the cut the triangle in half problem from a%0D%0A%0D%0A different point of view.%0D%0A%0D%0A%0D%0A ||139||1 446|0|JJ|10/27/2003|13:10:51|varhegyi|pentagon within a pentagon|Hello %21 %0D%0A%0D%0AWhile constructing a regular pentagon I discovered the following relationships.%0D%0A%0D%0ALet ABCDE be a regular pentagon with ||142||1 245|3|alexb|10/27/2003|10:49:55|Tracy|Peg solitaire|I know this must sound very trivial to all of you geniuses out there but could someone please let me have the solution to the very basic peg solitaire||417||6 447|3|neat_maths|10/30/2003|01:31:53|vbenares|Euler%27s expansion of %281%2B1%29%2A%2A%28p-1%29|I am trying to understand Ed Sandifer%27s short column on Fermat%27s Little Theorem%3A http%3A%2F%2Fwww.maa.org%2Feditorial%2Feuler%2FHow%2520Euler%25||162||1 448|0|neat_maths|10/31/2003|09:28:38|neat_maths|Regarding Pythagorean Trios|If x%5E2 %2B y%5E2 %3D z%5E2 then x%2C y and z can be called a Pythagorean trio and lines of integer length x%2C y and z will form a Pythagorean trian||161||0 451|3|studentt|11/13/2003|09:47:13|studentt|Weightings and Profiles|What is a suitable yet flexible model for the following scenario%3A%0D%0A%0D%0AWe have a database of stock market trades and traders records. We have||88||0 453|0|alexb|11/23/2003|19:25:57|shai|Paradox%3F|The function x%5Ex%5Ex%5Ex.... converges for a small domain of real numbers including x %3D square root of 2. I wonder what the function actually con||109||1 456|2|alexb|12/04/2003|10:41:09|Graham C|%7CR%7C%3D2%5Ealeph_0|If R is the set of reals%2C then is%0D%0A%0D%0A%7CR%7C%3D2%5Ealeph_0 %0D%0A%0D%0Aa proven result%2C or an assumption linked to the continuum hypothesi||110||1 457|3|alexb|12/04/2003|13:29:52|Mark Hughes|Kepler%27s Third Law and Morris Kline|I need some help understanding how Kepler %22discovered%22 his Third Law. In his %5Bi%5DMathematics and the Physical World%5B%2Fi%5D%2C Morris Kline ||201||1 454|2|Cino Hilliard|12/04/2003|14:51:38|AlphaRomeo|Absurd proofs|Here is a proof that 2%3D1.%0D%0A%0D%0A x%3Dy%0D%0A x%5E2%3Dxy%0D%0A x%5E2-y%5E2%3Dxy-y%5E2%0D%0A%28x%2By%29%28x-y%29%3Dy%28x-y%29%0D%||139||4 458|0|R.Sathish|12/05/2003|09:16:00|R.Sathish|Pan cake puzzle 2n-3 flips|For n%3D2%0D%0AFlips %3D 1%0D%0AFor n%3D3%0D%0AFlips %3D %28Flip for n%3D2%29 Flip to make n%3D3 as n%3D2.%0D%0Ai.e the third biggest cake wherever it||95||0 452|2|Cino Hilliard|12/07/2003|13:58:28|briant|prime factorization|Recently I came across the problem%0D%0A%0D%0A6P %2B 1 %3D n%5E5%0D%0Awhere P is a prime number%0D%0A%0D%0ASolve for all values of P and n.%0D%0A%0D%0||155||2 460|2|Siim|12/08/2003|23:26:43|Siim|Pizza Hut pans|Take two Pizza Hut pans which are perforated %28they use them for thin pizza%2C not for Pan-pizza%29 and lay one on another. Rotate the upper one slow||118||0 459|0|alexb|12/12/2003|20:29:59|Bryan|Sierpinski Gasket from 2D algorithm|I came up with a way of generating a Sierpinski Gasket that I didn%27t see listed on the website. Imagine a Cartesian grid in which each cell is eith||115||3 462|0|alexb|12/18/2003|09:47:24|mcgivney|history of the radical axis|The term %22radical axis%22 for two circles was coined by Louis Gaultier in 1813. %0D%0A%0D%0ADoes anyone know a short history %28or references%29 to||85||1 272||||11:35:19|jorge|mohr-mascheroni construction|I have tried to prove that the mohr-mascheroni construction of the regular pentagon does give the length of a side of the regular pentagon inscribed i||65||-1 429|0|Ralph Boles|12/23/2003|00:35:46|Pavel|Mathematical Induction|This might be boring%2C but could somebody please explain to me%2C in layman%27s terms%2C the validity of the Mathematical Induction as a sound way of||289||9 450|0|sfwc|12/28/2003|01:28:33|K. M|Three Utilities Problem is Solved|the three utilities problem in the geometry section %28the very first one%29 IS SOLVABLE whilst still remaining planar.%0D%0Ai%27m sure everyone is fa||135||1 465|0|Maxim|12/30/2003|14:38:47|Maxim|Boat chase|%7C...................%2F%0D%0A%7C..................%2F L%0D%0A%7C.................%2F%0D%0A%7C................%2F%0D%0A%7C...............%2F%0D%0A%7C||148||2 464|0|alexb|01/02/2004|14:38:47|Maxim|A brilliant false proof|Let x%5En %2B y%5En %3D z%5En %3C%3D%3E %28x%2Fz%29%5En %2B %28y%2Fz%29%5En %3D 1.%0D%0A%0D%0ANow choose two events A%2C B such that%0D%0A%0D%0AP%28A%||151||5 467|0|alexb|01/02/2004|08:38:12|Maxim|A solid geometry problem|In the cube ABCDA1B1C1D1 point P is the middle of the edge CC1%2C point K belongs to BC and BK%3DCK%2F2. Take the plane passing through the points A1%||117||1 463|0|Cino Hilliard|01/05/2004|11:35:19|jorge|mohr-mascheroni construction|I have tried to prove that the mohr-mascheroni construction of the regular pentagon does give the length of a side of the regular pentagon inscribed i||650||3 466|0|Whymme|01/22/2004|10:31:48|Hercule|Probability Question|A friend and I were discussing probability when he came up with this question%3A%0D%0AThere is a square table. At each corner on the underside there i||139||3 470|4|alexb|01/22/2004|21:30:57|Cara Konkol|Permutations of numbers 1 thru 10.|Hi Everyone%2C%0D%0A%0D%0A I have a problem I want to solve in my lifetime.%0D%0A I have a friend at my therapy classes we ||124||1 469|0|auro_writes|01/23/2004|13:17:44|Samuel Clarke|on Mathematics|Hi%21 %0D%0A%0D%0AI am a biology student and am planning to write popular science article as part of freelancing. I am planning to write on the natura||112||4 471|0|Graham C|01/24/2004|23:43:20|ShadowFire|ShadowFire%27s Ideas|Hey All. Ever since I read the book %27Fermats Enigma%27 by Simon Singh%2C I have been hooked on mathematics. I am also into philosophy%2C and often t||108||4 472|0|Selby Anderson|01/29/2004|22:33:17|Selby Anderson|Carrick Bend series|To whom it may concern%3A%0D%0A%0D%0AI was experimenting with a well-known knot %28technically%2C a bend as it joins two cords%29%2C the Carrick Bend.||192||0 473|2|schizophoenix|01/31/2004|11:07:22|schizophoenix|Multi-dimensional tic-tac-toe|The concept of tic-tac-toe %28ttt%29 can be extended to other dimensions and sizes besides 2d 3-length. Basically%2C both players%27 aim is to place t||96||0 475|0|Mark Huber|02/04/2004|07:47:45|Sorting in o(n)|Fliping pancakes|Pancakes can be sorted at a maximum bound of 2n-3.%0D%0AIf pancakes be flipped in o%28n%29%2C then a pancake array can be sorted in o%28n%29.%0D%0ALin||92||2 468|0|KL_GB|02/13/2004|10:39:19|schizophoenix|Multistage Monty|I refer to M. Bhaskara Rao%27s extension of the Monty Hall dilemma %28see the Monty Hall page%29. The logic is certainly intuitive for anyone who has ||215||22 480|3|japam|02/16/2004|08:47:25|japam|chinese remainder theorem|i had this question%0D%0A%0D%0Ais possible%2C with the aid of the chinese theorem answer this%0D%0A%0D%0Aa%29 to find a number THAT IS NOT a solution ||92||0 479|0|japam|02/17/2004|19:06:28|japam|if a number end in 9 is square|is easy to probe that%0D%0A%0D%0AA NUMBER ENDING IN 9 IS A PERFECT SQUARE IF AND ONLY IF THE NUMBER L AT THE LEFT OF THE 9 CAN BE REPRESENTED BY ONE O||114||2 478|0|KL_GB|02/17/2004|07:36:26|japam|squaring a number end in 9|hi all%0D%0Ai have the pleasure of introduce me in this excelent forum%0D%0A%0D%0Aim eletronics eng but love fun with numbers%0D%0Aover the years i h||128||4 483|0|(10X+3)*(10X+7)|02/24/2004|19:15:40|(10X+3)*(10X+7)|JAPAM|The rule have two cases%0D%0A%0D%0Acase a%29 X greater than Y%0D%0A%0D%0A1. %28Y%2B1%29%2AX%2A100 %3D A%0D%0A2. %28%28X-Y%29%2A3-2%29%2A10 %3D B%0D%0A||90||0 484|0|JAPAM|02/25/2004|10:58:08|JAPAM|Is 1231 prime%3F my proof|In an old archive a guy ask how he can probe that 1231 is prime%0D%0ADr Bogomolny used a complicated theorem to do it%2C but i think is not necesary%0||131||0 485|3|sfwc|02/26/2004|15:10:37|Garrett|Grouping|Hi%2C I am a novice computer programmer that is looking to create a small application for a totally separate interest. I%27m having trouble coming up||109||1 486|2|japam|02/27/2004|10:51:47|japam|numeric avalanches|i try to figure out how to visualize the powers of a number n in the real world%2C and found that powers are like perfect avalanches where every point||92||0 487|3|alexb|03/02/2004|09:43:33|markp|Why hex2dec %21%3D hex2bin2dec%3F|Can anyone explain whats going on here%3F%0D%0A%0D%0AFFFFFFC converted to decimal is%3A%0D%0A%0D%0A15%2A%2816%5E7%29 15%2A%2816%5E6%29 15%2A%2816%||112||1 489|0|sfwc|03/03/2004|15:05:18|KL_GB|Probability question 2|Another game%3A%0D%0A%0D%0AYou have a chessboard%2C of a rows and b columns. On each square is a counter. On each turn a counter is removed %28chose||91||1 490|0|JJ|03/07/2004|13:02:17|LemonEyes|Comment on Bertrand%27s Paradox|Those who have read or are familiar with Bertrand%27s Paradox might find the following point interesting%2C if not already thought of.%0D%0A%0D%0AThe ||121||1 488|0|KL_GB|03/08/2004|15:05:18|KL_GB|Probability question 1|I hope I am able to explain this clearly.%0D%0A%0D%0AConsider a %22game%22 with four boxes and a large supply of counters. At the start of the game a||103||4 491|2|sfwc|03/11/2004|13:07:58|japam|RULES FOR 63 AND 07|%0D%0AHi its me again%0D%0A%0D%0Ai found this 2 simples rules but i have no proof%2C maybe somebody can give it%0D%0A%0D%0A1st rule%0D%0A%0D%0A%2810N%||121||7 494|4|sfwc|03/18/2004|11:09:39|wjd|question on primes|Hello%2C%0D%0A%0D%0AI remember%2C I think%2C that n%21-1 %28n factorial minus 1%29 is prime for all integers n greater than 1. Can anyone either prove||105||2 481|0|japam|03/25/2004|21:16:48|japam|The primality of 100N %2B79|After a long time i came up with this result%0D%0A%0D%0AA number of the form 100N %2B 79 is PRIME if and only if N DONT SATYSFIES anyone of the follo||171||9 496|0|alexb|03/28/2004|22:24:08|Anonymous2|about%3A %2Fpythagoras%2Farchi.shtml| I enjoyed running the applet%2C but %3A%29%0D%0AIf the initial angle exceeds 135 degrees %28 90 45%29 the applet gets confused. Limiting the angle m||103||1 495|0|sfwc|04/05/2004|19:19:50|japam|prime curiosity|i post this result that i found. Somebody can say me if it is only a coincidence or not%3F%3F%0D%0A%0D%0A7%2A%287%29______________________%3C 7%2A10%0||121||2 499|0|sfwc|04/06/2004|19:28:55|sfwc|Another proof of OI%5E2 %3D R%5E2 - 2Rr|A proof follows quickly from the configuration at%0D%0Awww.cut-the-knot.org%2FCurriculum%2FGeometry%2FThreeEqualCircles.shtml%0D%0A%0D%0ALet P and Q b||99||2 492|0|japam|04/13/2004|14:03:11|japam|prime quest|well i post this quest%0D%0A%0D%0A we have 4 prime numbers %0D%0A11%2C13%2C31 and 37 that satisfies 11%2A37- 31%2A13 %3D 4%0D%0A%0D%0A17%2C19%2C53 an||205||15 505|0|Anuj Mukherjee|04/13/2004|16:21:49|Anuj Mukherjee|Universal solution|Respected Sir%2C%0D%0A%0D%0AThis message consists of two Mathematical proves with their astonishing results%2C under the caption%3A- %22What about the||114||0 506|3|alexb|04/13/2004|18:06:24|anuj_17|Posting Difficulty|To%0D%0AThe Competent Authority%0D%0Awww.cut-the-knot.org%0D%0A%0D%0ARespected Sir%2FMadam%2C%0D%0A%0D%0AI intend to send you two Mathematical proves ||133||1 504|0|Graham C|04/14/2004|18:49:34|jvwert|Worm On a Rope problem|I recently came across an old puzzle I had filed away without giving it much thought%2C but when reviewing it%2C I was taken in by the thought that it||1066||4 493|0|bs_9999|04/20/2004|11:09:39|japam|complete rule for 9 and 11|%0D%0Anot only you can probe that a number is multiple of 9 and 11 adding and substracting its integers%2C also you can get the divisor%0D%0A%0D%0Afo||143||1 507|2|jonnie303|04/30/2004|21:32:55|jonnie303|Pythagorean triangles|I have been investigating Pythagorean triangles with sides %28a%2Cb%2Cc%29 where %28a%2Cnb%2Cd%29 forms another Pythagorean triangle for some integer ||162||5 509|0|Timc|05/06/2004|13:51:20|Timc|Parrondo Paradox|I work in a factory%2C and was discussing the Parrondo Paradox in the pub this lunchtime with a couple of the operators from the shop floor%2C one of ||145||2 513|2|harry2312|05/11/2004|19:59:42|harry23123|Cubes in cubes|I will state my question in two ways for better understanding %3AP%0D%0A%0D%0AWhat is the maximum number of completely bounded volumes that can be for||10267||2 517|0|alexb|05/16/2004|21:08:06|Maxim|Random triangle|Pick at random three points on the circle%3B what is the probability that the triangle will be acute-angled%3F%0D%0A||109||1 516|2|sfwc|05/17/2004|21:08:06|ibutton77|4 color map%3A simple proof|Is anyone here familiar with the four color map theorem%3F%0D%0AI%27ve read that in 1976 a couple of guys made a widely accepted proof that is unfortu||152||1 514|3|CSpeed0001|05/20/2004|22:35:02|CSpeed0001|Calculator people%3F|I%27m a university student and an employee at a community college.%0D%0A%0D%0AAt the community college%2C I%27m trying to get a class on calculator lo||127||3 518|5|Jan Nordgreen|05/21/2004|21:19:17|Jan Nordgreen|Seductive math problems|This is a plug for my new weblog called %27think again%21%27 at %5Burl%5Dhttp%3A%2F%2Fthinkagain.simpler-solutions.net%5B%2Furl%5D started today.%0D%||131||0 521|0|sfwc|05/31/2004|14:05:54|japam|property of power of 2|this is an example of a relation between powers of 2 and 11%0D%0A%0D%0A%A8power of 11...............closest power of 2 %0D%0A%0D%0A 11%A8%A80 ...||155||1 515|0|alexb|06/01/2004|22:02:38|harge14836|LIMITS|I enjoy proving limits to functions%2Cas x approaches 0%2C for example. I%27ve been unable to solve lim %28sin x%29%5E tan x as x approaches 0 from th||173||7 525|0|alexb|06/07/2004|12:57:45|mberlin|Bathroom Tile|I%27m putting in a new bathroom and thought it%27d be fun to put some mathematics in the tile.%0D%0A%0D%0AI%27ve had two thoughts%3A Pythagorean Theor||126||1 524|2|Quentin|06/13/2004|08:22:50|Quentin|True angle of sun on sloping roof%3F|For any given day I know the suns altitude %28angle above horizon%2C call %0D%0Ait x%29%2C azimuth %28angle clockwise from North%2C call it y%29%2C th||262||4 526|2|joe|06/23/2004|09:17:52|Casey|adult self education|I am an almost 40 year old public interest attorney. I really enjoyed math in high school. I enjoyed it less in college. I would like to %22relearn%22||116||2 527|2|alexb|06/27/2004|21:32:07|Matt|Geometric mean|I am collating survey responses and one question asked people to respond with percentage%2Ceg. x%25 of time spent at shops. If i want to know the mean||101||1 529|0|alexb|07/05/2004|19:07:52|marc|generalisation of Morley theorem|I try to find a interrative graphical animation %28JSP or java based%29 for the generalisation of morley theorem.%0D%0AI try to find that animation bu||104||1 500|0|alexb|07/07/2004|00:50:11|Ed Smart|Angle Trisection|http%3A%2F%2Fwww.cut-the-knot.org%2Farithmetic%2Frational.shtml%0D%0A%0D%0AI was reading the above page and I saw that in the section regarding the tr||150||3 531|0|alexb|07/17/2004|07:22:52|dimoskon|a useful tool%3F|hello%2Cmay i ask u a question.i wonder if there is any kind of recognised symbolism and coding system in use for everyday life so that somebody can ||105||1 501|0|dan|07/20/2004|20:01:01|JAPAM|TWO QUESTIONS|Im interested now in these topics not related%2C%0D%0A%0D%0A1%29If a number is prime in base 10 %2C it still prime for any other base%3F%0D%0A%0D%0A2||139||4 532|0|alexb|07/21/2004|08:53:37|dan|square triangle numbers|I am planning ahead for September%27s new term and thought I%27d set a problem along the lines of %27which square numbers are also triangle numbers%3F||154||5 533|2|alexb|07/22/2004|00:22:12|Michael|Lewis Carroll%27s bilateral diagrams|I was wondering why it is ok to place a red dot on a line between two cells %28giving a statement like%2C some y%27 exits%2C for example%29 but it is ||112||1 534|2|alexb|07/28/2004|07:42:10|Monty|Egyptian Geometry|The Rhind papyrus %28I believe that%27s the source%29 indicated that the ancient Egyptians believed the area of a quadrilateral with sides a opposite ||148||1 535|0|RW|07/28/2004|10:13:53|RW|Google Puzzles|The other day I found this interesting post%3A%0D%0Ahttp%3A%2F%2Fwww.google.com%2Fgoogleblog%2F2004%2F07%2Fwarning-we-brake-for-number-theory.html%0D%||191||0 537|0|alexb|08/03/2004|11:38:14|Cian|Alpha null%28N%292 %2F 9 %3D N %3F%3F|Alpha null is the number of whole numbers and i want to know if when you square it and divide it by 9 does the answer equal alpha null%3F If so it wil|on|212||7 539|0|japam|08/10/2004|20:08:41|japam|sphere tiling|whats the best method to tile a sphere in such a way that you use the less quantity of paper||135||0 542|0|goodbar|08/12/2004|20:08:41|goodbar|Weighted Graphs|In Alexander%27s discussion of maze generation%2C he alludes to assigning weights to the edges of his graph prior to executing either Prim%27s or Krus||92||0 544|0|alexb|08/24/2004|20:08:41|Monty Phister|Primes between n and 2n|I recently read that%2C for any integer n greater than 1%2C there is at least one prime number between n and 2n. Is this true%3F Can it be proven%3F||203||1 538|2|alexb|08/24/2004|07:01:02|daveking|Triangle of Errors|In the practice of navigation%2C when bearings are taken on a single point from three separate points%2C it is normal %28due to measurement errors and||145||3 541|0|alexb|08/26/2004|20:08:41|rewboss|Good old Monty Hall|Hi.%0D%0A%0D%0AI stumbled across the Monty Hall problem a few months ago%2C as described at http%3A%2F%2Fwww.cut-the-knot.org%2Fhall.shtml . I am not ||152||3 523|2|Silas|09/01/2004|13:37:54|japam|Ancient Fermat%27s proof%3F|ive never heard about this%0D%0A%0D%0Ahttp%3A%2F%2Fwww.hti.umich.edu%2Fcgi%2Ft%2Ftext%2Ftext-idx%3Fsid%3D33ded730256196644cad64909cce5f51%3Bc%3Dumhist||235||9 474|0|Lloyd|09/03/2004|20:37:40|jvwert|Another Vos Savant challenge|It looks like Marilyn may have stirred up another problem that tends to separate the %22men from the boys%22 when it comet ot seeing a problem from th||343||17 546|3|alexb|09/07/2004|20:55:52|kristinbl|clever card capers|I am sure many of you are familiar with this puzzle%2C it uses six cards%2C with numbers from 1 to 63. You ask a player to pick a number%2C you then d||209||1 547|0|jass|09/10/2004|06:50:55|jass|What%27ll be d unit digit|Its an intresting logic. In my last practice test there was a question %0D%0A%0D%0AWhat%27ll d unit digit when 7%5E71 %2A 6%5E59 %2A 3%5E65%0D%0A%0D%0||221||0 548|3|alexb|09/12/2004|14:38:52|Bruce Douglass|Source code to Maze Generation|In the article %22Cut the Knot%22 a little Java applet runs that applies some algorithms for maze generation and solving. Is that Java source code ava||123||1 522|0|Inga|09/13/2004|11:44:07|Olga Skrunts|Algebra at elementary school|In the Manifesto authors of this site try to investigate the hate for the Math among students. I think that the problem lies in elementary education. ||164||4 549|0|GottfriedHelms|09/15/2004|12:04:27|gottfriedhelms|n%5Ep - 2%5Eq is never 1|intended subject%3A %0D%0A%5Bb%5Da pretty argument%2C why N%5EP-2%5EQ is never 1 ... %28Catalan%29 %5B%2Fb%5D%0D%0A%0D%0AI printed out something like ||115||1 545|0|alexb|09/16/2004|18:58:39|Monkey|Prisoner Problem|I stumbled across this little puzzle some time ago%3A%0D%0A%0D%0AThere are three prisoners on death row%2C A%2C B and C. One day%2C the guard comes in||222||12 553|0|Ramsey_KJ|09/23/2004|06:38:00|Ramsey_KJ|Re Square Triangular Numbers|In regard to the web page on square triangular numbers http%3A%2F%2Fwww.cut-the-knot.org%2Fdo_you_know%2FtriSquare.shtml%2C I found two algebraic iden||128||0 449|3|alexb|09/28/2004|11:35:01|bruinyuko|zero with zero power|I have a stupid question to ask%3AP %0D%0A%0D%0AWhat is the value of zero with zero power%3F I took a genetic analysis class this quarter%2C in the ho||375||26 555|0|Help|10/05/2004|16:41:02|Help|Mobius Strips%21|Id don%27t really understand this formula%21 Here it is%0D%0A%0D%0AIt all starts with an observation I gleaned surfing MathSoft pages. For a fixed ran||138||2 557|0|alexb|10/06/2004|14:00:59|sfwc|More Monge|Another random 3D proof of Monge%27s Theorem%3A%0D%0A%0D%0AConsider 3 right cones on the three circles as bases. Now consider their common tangent pla||117||1 559|0|alexb|10/06/2004|07:12:08|LawrenceMcLean|Powers of phi|I would like to know if there is a proof for the following relationship of the powers of phi %28golden section%29%3A%0D%0A where F%5Bn%5D represents t||124||1 554|4|George|10/08/2004|16:19:42|George|analitical solution of the problem|The nonlinear equations are very impotant in many areas of physics%2C%0D%0Abut the exact analitycal solutions are known only for some equations%0D%0||138||3 558|0|alexb|10/09/2004|14:00:59|sfwc|Three isosceles triangles|This is about http%3A%2F%2Fwww.cut-the-knot.org%2FCurriculum%2FGeometry%2FThreeIsoscelesTriangles.shtml%0D%0A%0D%0AFirst I shall provide a different %||157||3 562|0|Ramsey_KJ|10/10/2004|23:37:38|Ramsey_KJ|NewProof%3A SquareTriangularNumbers|Two algebraic identities explain the recursive relationships for S%28n%29 and Q%28n%29 and work for complex numbers as well as for integers. Intrigui||113||0 564|0|alexb|10/14/2004|11:12:03|sfwc|Another alternate proof|This relates to http%3A%2F%2Fwww.cut-the-knot.org%2FCurriculum%2FGeometry%2FCircleOnCevian.shtml%0D%0A%0D%0AA%28H_c%29C %3D A%28H_a%29C so A%28H_c%29%||98||1 563|0|Ramsey_KJ|10/14/2004|14:02:08|Ramsey_KJ|Bowling Leauge Schedule|The object is to have every team bowl on a given night and bowl each other team in the league once and only once or the like. If the number of teams ||117||2 355|0|Claus Jensen|10/16/2004|09:51:13|Mountainman|Ellipsograph|I was browsing through an old book one day and I came across a picture of a mechanical device that draws ellipses of varing size called an ellipsograp||255||3 556|0|Cino Hilliard|11/05/2004|14:00:59|Cino Hilliard|x%5E%28p-1%29 - y%5E%28p-1%29 is dividible by p|Theorem I%0D%0AIf p is prime and p does not divide xy then p divides x%5E%28p-1%29-y%5E%28p-1%29.%0D%0A%0D%0AI discovered the above theorem in the ear||186||2 551|2|Cino Hilliard|11/05/2004|13:52:38|Cino Hilliard|Tina pop up|Professor%2C%0D%0AHow do we get rid of the Tina pop up%3F%0D%0A%0D%0AIt startles the heck out of me when I log on to your site.%0D%0A%0D%0A||324||8 569|2|alexb|11/18/2004|13:03:41|Monty|Specifying a polygon|I can%27t seem to find this anywhere. Maybe it%27s too trivial or obvious. How many numbers does it take to specify an n-sided polygon%3F Answer%3A 2n||148||10 565|0|Graham C|11/21/2004|09:38:54|alexb|help with memory problems|It looks like one of my private emails has been intended for broader public. I%27d be grateful for any help. The message follows.%0D%0A%0D%0AThank you||146||7 571|0|Zededarian|11/24/2004|23:44:42|Zededarian|Confusion w%2FCorollary and GCD|I think I have the basic concept of GCD down%2C but Corollary is still confusing me. It states that%3A%0D%0A%0D%0Aas bt%3Dgcd%28a%2Cb%29 where a%2Cb%||116||2 570|2|sfwc|11/28/2004|00:17:09|John|Difficult Probability Problem|You make a series of %24100 bets on a fair coin flip. If you win%2C you are paid %24110. If you lose%2C you lose only %24100.%0D%0A%0D%0ANow assume ||163||7 573|0|hr|12/01/2004|09:14:42|hr|christmas maths prize problem|Here is a new maths problem for Christmas.%0D%0AWho dares to participate%3F%0D%0Ahttp%3A%2F%2Fwww.petericepudding.com%2Fprobe04.htm%0D%0A||648||0 572|0|sfwc|12/02/2004|14:39:34|sfwc|A small generalisation%3A|At http%3A%2F%2Fwww.cut-the-knot.org%2FCurriculum%2FGeometry%2FHalfPlaneTest.shtml%0D%0A%0D%0AYou say %22In fact%2C the intersection of any number of ||413||5 455|0|sfwc|12/09/2004|09:33:58|mangel|12 coin puzzle|Hi%2C%0D%0A%0D%0AThe puzzle has 12 coins one of which is either heavier or lighter than the others. Using a lever scale you have three weighings to f||151||4 512|0|rewboss|12/16/2004|21:40:56|Hannah|1infinity%3D2infinity|Apologies if this is terribly trivial or self-explanitory%2C but I think I might have something interesting. I%27m fairly sure I read once that mathem||208||4 561|0|Silas|01/04/2005|08:07:21|LawrenceMcLean|Sums of digits|I would like to know if there is a function to describe the pattern that the sum of the digits follows for multiplication tables%2C what I mean is%3A%||203||5 578|5|hr|01/06/2005|08:36:21|hr|solutions prize problem|Here are the solutions for my last Christmas maths prize problem%3A%0D%0Ahttp%3A%2F%2Fwww.petericepudding.com%2Fsole04.htm ||104||0 577|0|Graham C|01/10/2005|08:36:21|rclough|triangular tiling of a sphere|The tai xuan jing %28tai hsuan ching%29 is an ancient chinese document that contains 81 hypertexted tetragrams. I would like to represent it with regu||132||3 576|2|Monty Phister|01/14/2005|13:55:57|Monty Phister|Squares and lines|Cantor proved that the points in a square correspond one to one to the points on a line. You show the proof elsewhere on your site%2C but I find the p||153||12 579|0|alexb|01/26/2005|00:38:38|Monty Phister|Plane-filling curves|On the page with the above name%2C it%27s stated%2C %22The least we can say is that %5Bthe curve%5D passes arbitrarily close to any point in the squar||166||13 581|0|frank|01/29/2005|16:03:56|frank|regarding the Twins riddle|Nearing the end of this article%2C says that if an inaccurate liar were asked the question%2C%0D%0A%0D%0Aare you the truth-teller%3F%0D%0A%0D%0Athen h||98||0 580|0|teh win|01/30/2005|15:51:03|Frank|regarding the 3 jugs puzzle.|I do not believe the java representation of this is feasible%2C seeing that 8 can not be divided into 3 and still be a whole number. ||117||5 583|2|Mark Huber|02/07/2005|22:58:12|MathHead Ed|When did Q ever get|Hi.%0D%0A%0D%0AThis is my first visit to CTK. Delightful web site.%0D%0A%0D%0AOn the page entitled%3A%0D%0A%22No two integers are equidistant from th||124||7 584|2|Cynthia|02/09/2005|09:05:38|Cynthia|Romantic gesture......%3F|My husband is a High School Math Teacher and recently a friend gave me the following equation%3A%0D%0A r%3Da%281-cosA%29%0D%0AI was told it is some ki||204||2 585|0|anXZMouse|02/17/2005|00:09:26|anXZMouse|3 Jugs again%3A how to do it in one easy step%21|I found a solution%2C of course%2C involving repeated pourings between the 8%2C 5 and 3 litre %28or was that quart%3F%29 jugs%2C to get 4 in each of t||114||2 575|0|Abhishek Sharma|02/22/2005|00:28:40|martha123_pe|combinations|could somebody refresh my memory and tell me what%27s the formula to combine an %22x%22 amount of numbers%3F PLEASEEEEEEEEEEE...no%2C this is not my h||127||2 586|2|Bractals|02/23/2005|15:07:00|Shee_Mack|window cleaning problem|Window cleaning problem%0D%0A----------------------------------------------------------------------%0D%0ABy Julian Steed on Tuesday%2C March 28%2C 200||126||3 588|3|sfwc|02/24/2005|16:55:42|dimbles|Engineering Problem - could make an entertaining puzzle%21|Whilst on work-experience with a large engineering company%2C the following problem arose. I ended up leaving it and using experimental data%2C but I%||129||1 590|2|Mark|03/11/2005|18:12:44|Monty Phister|Latitude and Hipparchus|I have read that Hipparchus proposed that one can find %28or maybe actually did find%29 the latitude of a place from the ratio of the lengths of the l||95||2 591|0|alexb|03/17/2005|18:26:16|sfwc|Arbelos and square|A slightly easier proof of the second property of the arbelos mentioned at http%3A%2F%2Fwww.cut-the-knot.org%2FCurriculum%2FGeometry%2FArbelosRect.sht||121||10 592|0|CliveT|03/19/2005|23:25:33|CliveT|Hour glass problem - typing error%3F|I notice that the following is stated on the %22Hour Glass Problem%2C solution%22 page%3A%0D%0A%0D%0A%0D%0AThus%2C starting with one problem we actual||116||2 594|0|David Zelenka|03/30/2005|18:53:27|David Zelenka|Sine Wave Harmonics Generator|This Flash-base mini-app is available free on-line at the address above. It%27s a bit addicting to play with%2C but it really gives the lay-person a g||90||0 599|0|alexb|04/15/2005|11:26:31|Fontwell|3 fractions%2C all the digits|A number of years ago I was given the following brain teaser which was written in this fashion%3A%0D%0A%0D%0A x%2Fxx %2B x%2Fxx %2B x%2Fxx %3D 1%0D%0A||96||1 600|2|m jones|04/18/2005|07:57:09|m jones|die rolling probability|My basic math skills are pretty good%2C but I%27ve forgotten most of the probability formulas since I finshed undergrad. I was wondering if anyone co||121||2 601|0|alexb|04/20/2005|09:41:23|Silas|An Interesting Number.|A famous story among mathematicians tells of the great mathematician G.H. Hardy visiting his famous %28but very sadly short-lived%29 prot%E9g%E9 Srini||116||1 603|2|Silas|04/29/2005|06:58:42|Chaitanya|A Pattern that needs explanation%21|Hi Everyone%2C%0D%0A%0D%0AAccidentally%2C I have come across this pattern in the 9th Table that I am astounded to find. This may have been discovered||115||1 607|0|apuci|04/30/2005|15:20:14|apuci|2n%5E2-1|This is just a note on the integer sequence 2n%5E2-1%2C A056220 in the On-Line Encyclopedia.%0D%0A%0D%0AA few numbers in the sequence%3A%0D%0A%0D%0A1%||90||0 608|0|alexb|05/02/2005|13:19:37|apuci|Query relating to Fermat%27s Last Theorem|Although there is no integer solution for a%5En %2B b%5En %3D c%5En for n%3E2%2C there are solutions for%0D%0A%0D%0Aa%5En %2B b%5En %2B c%5En %3D q%5E||110||2 605|0|neat_maths|05/06/2005|08:20:27|neat_maths|A Theorem on Squarefree Numbers|If two numbers a and b are defined to be relatively prime then they have no prime factors in common.%0D%0A%0D%0AA number is defined as squarefree if n||315||19 602|0|Ramsey2879|05/07/2005|15:13:45|erszega|sums of integer sequences being squares|I would like to find out whether what I have found has been described already%3A%0D%0A%0D%0A%0D%0A%0D%0AThe sum of the sequence n%2Cn%2B1%2Cn%2B2%2C%8||178||6 609|2|sfwc|05/07/2005|12:33:11|woodenmike|Riddle%2FPuzzle|Would any of you know what this is%3F%0D%0A%0D%0AThanks%21%0D%0A%0D%0Ahttp%3A%2F%2Fwww.ourcolony.net%2Fimages%2Fchallenges%2Fdot_1.jpg%0D%0A%0D%0A%0D%||134||1 611|0|Ramsey2879|05/15/2005|17:47:21|Ramsey2879|A Riddle|In the city of Pythagorean there was a street having between 50 to a 1000 houses on the north side of the street numbered with odd numbers starting fr||122||0 610|0|Kris|05/17/2005|11:39:25|Warjat|3 point on a circle|A long time ago %28when I was still in high school%29 I came up with something that I have never come accross before%2C therefore I thought that perha||144||3 552|2|alexb|05/26/2005|07:43:07|melt|Pythagoras Proof|%0D%0AHas anyone seen this proof of pythagoras%27 theorem before %3F I was motivated to write this down because my 12 yr old son is studying Pythagora||231||3 65||||21:53:12|Neil_Parker|Pythagorean triple generator|%2AALL%2A pythagorean triples are derivatives of t%2C %28t%5E2%2B1%29%2F2 and %28t%5E2-1%29%2F2. In other words given any triple%2C a corresponding ra||115||-1 16|0|Don Stockbauer|01/24/2010|12:18:54|Don Stockbauer|Cantor%27s diagonal method|I know there has to be some simple error in the following %22proof%22 that the cardinality of the integers and reals is the same%2C but I cannot easil||1152|5.51550387596899|7