993|0|alexb|05/21/2011|15:50:42|nikolinv|One equal zero|Do you know that%3A%0A%0Ahttp%3A%2F%2Fwww.dodaj.rs%2Ff%2F3x%2Fh0%2FruwKW1L%2Foneeqzero.png%0A%0A||8||2
985|0|alexb|05/16/2011|16:25:31|jmolokach|%22Proof of the Cosine Rule completely independent of the PT%22|Alex%2C%0A%0AAt your page%3A%0A%0Ahttp%3A%2F%2Fwww.cut-the-knot.org%2Fpythagoras%2Fcosine.shtml%0A%0AYou mention %22I%27ll be extremely curious to lea||73||14
992|0|alexb|05/11/2011|13:38:08|ranjitr303|divisibility|if %28A %2B mX%29%2F%285 or 10%29is divisible by m%2C then A is divisible by m. %0Aalso if %28A - mX%29%2F%285 or 10%29is divisible by m%2C then A is ||2||1
991|0|alexb|05/09/2011|19:24:10|nikolinv|Is Every  Parallelogram Rectangle%3F|Let a and b denote sides%2C d1 and d2 denote diagonals of a parallelogram ABCD. Triangle ABC %28with sides a%2C b and d1%29 and triangle ABD %28with s||20||5
990|0|alexb|04/26/2011|19:09:29|nikolinv|How old is John%2C how old is Maria%3F|Peter%3A How did you get such an ugly polynomial f%28x%29 with so many unknown coefficients%3F It looks terrible%21%0A%0APaul%3A This is polynomial wi||10||3
983|0|alexb|04/25/2011|12:37:15|C Reineke|Determinants|Alex%2C%0A%0AI would like to post my determinant problem .%0A%0Ahttp%3A%2F%2Fwww.cut-the-knot.org%2Farithmetic%2Falgebra%2FDeterminant.shtml%0A%0ALet ||24||7
986|0|gaespes|04/06/2011|11:23:12|gaespes|Pythagorean theorem and determinants|The Pythagorean theorem as an application of the determinant properties in the plane%3A%0A%0A  http%3A%2F%2Fw3.romascuola.net%2Fgspes%2Funitary.html %||10||2
969|0|alexb|04/05/2011|06:46:16|jmolokach|Calculus Proof for Pythagorean Theorem %28again%29|Thanks to Alexander Giventhal at Berkley%2C I am giving yet another shot at proving the Pythagorean Theorem using Calculus.  I have been told that my ||199||43
989|0|drferris68|04/03/2011|22:07:19|drferris68|Calculating raw probabilities|     I am presently using a skip%2Fshift-of-one transposition equidistant letter sequence in an effort to decrypt possible intentionally placed letter||0||0
988|0|hewman123|04/01/2011|09:23:14|hewman123|some fun stuff|On Impossible Figures %7Bor On Evans%27 %28Most%29 Impossible Triangle%7D%0A%0ARegardless of the type or number of arguments that can be leveled at a ||0||0
987|0|hewman123|04/01/2011|00:32:19|hewman123|angle trisection|its interesting that although we cannot trisect the angle%2C we are able to provide a diagram of what a successfully trisected angle would like if we ||0||0
981|0|jmolokach|03/23/2011|11:30:10|jmolokach|A question|Is it possible to algebraically derive the law of cosines from the law of sines%2C without recourse to the Pythagorean Theorem%3F||143||61
978|0|gaespes|03/20/2011|11:30:10|jmolokach|Shoestring Proof of the Pythagorean Theorem|I think this is somewhat simpler than what I have written before.%0A%0AOccam%27s Razor or just a restatement of Proof 4%3F  I think this is slightly d||104||24
984|0|jmolokach|03/07/2011|10:00:21|jmolokach|Equivalence of the Law of Sines%2C PT%2C and Law of Cosines|Here%27s the link to the paper.%0A%0Ahttps%3A%2F%2Fdocs.google.com%2Fviewer%3Fa%3Dv%26pid%3Dexplorer%26chrome%3Dtrue%26srcid%3D0Bwc0zPMWJ9wqYmFmNzdlND||27||5
982|0|gaespes|02/18/2011|19:22:59|gaespes|distance vs orthogonality vs choice|Since the mid-seventies%2C during my first university studies%2C I was unsatisfied with the way of introducing the metric in the usual treatments of t||55||12
932|0|jmolokach|02/15/2011|16:06:04|C Reineke|Trigonometric Proof of the Pythagorean Theorem|http%3A%2F%2Fwww.cut-the-knot.org%2Fpythagoras%2FTrigProof.shtml%0A%0ADear Alex%2C%0A%0Ait is very easy to derive the subtraction formulas from Euler%||41||4
942|0|gaespes|02/09/2011|19:01:52|jmolokach|A complex number approach...|In a recent discussion during a high school math class%2C my students learned that a %2B bi multiplied by it%27s conjugate gives the real number a%5E2||64||20
980|0|alexb|01/24/2011|12:36:21|mr_homm|PT by area sweeping|Here is another approach%2C based on a couple of simple ideas about flow across a boundary.  First%2C consider a triangle moving smoothly around in th||7||2
979|0|alexb|01/20/2011|12:06:37|jmolokach|Nondifferentiability without limits|I found this link for %22derivatives without limits%22%0A%0Ahttp%3A%2F%2Fwww.cut-the-knot.org%2Fwiki-math%2Findex.php%3Fn%3DCalculus.DerivativesWithou||1||1
975|0|jmolokach|01/15/2011|08:54:58|sbrodie|Calculus Proof of PT|The late Edwin Moise was co-author of my first Geometry textbook back in 9th grade. He later wrote a fascinating text%2C %22Elementary Geometry from a||73||14
976|0|jmolokach|01/11/2011|13:14:44|jmolokach|An inequality of Archimedes %28and a claim...%29|Alex%2C I would like to thank you for characterizing me as a %22devoted Pythagorean.%22%0A%0ASo now it seems I have shifted my focus from the Pythagor||23||4
977|0|ranjitr303|01/10/2011|13:14:44|ranjitr303|to find log of  a number|i have found that the mantissa%28M%29for a number X can be approximated by a simple formula%0AM%3D y%2819-y%29%0Awhere y%3D X written such that 3%3Ey%||0||0
973|0|jmolokach|12/29/2010|04:20:13|jmolokach|Age old debate|Doing these PT proofs has got me thinking about the amalgamation of geometry and algebra...  For instance...  The integral from -1 to 1 of 1%2Fx ... g||33||13
974|0|alexb|12/28/2010|23:58:19|sbrodie|Calculus Proof of PT|The recent posting of a %22Calculus-based%22 proof of PT draws me into this discussion. I%27m afraid I am still skeptical. The problem is deeper than ||5||3
936|0|jmolokach|12/23/2010|18:05:52|John Molokach (Guest)|Variation of proof %2343 - Pythagorean Theorem|OK%2C here is yet another one I have done.  I have not seen anything like this exactly on your page%2C but I feel it is a variation somewhat of proof ||46||7
972|0|jmolokach|12/23/2010|08:21:47|jmolokach|Parallelogram Proof of the PT|I seem to be obsessed with these...  here is another...%0A%0Ahttps%3A%2F%2Fdocs.google.com%2Fviewer%3Fa%3Dv%26pid%3Dexplorer%26chrome%3Dtrue%26srcid%3||5||2
971|0|alexb|12/21/2010|16:45:10|dwstout|Models of the regular solids|I am looking for nice models of the 5 regular solids.  Wood would be great but nice plastic is OK.  Any ideas where I can buy some.  I%27ve done a lot||4||3
970|0|C Reineke|12/02/2010|07:44:00|ranjitr303|prime finder|take m as a number such that %28m-1%29and %28m%2B1%29 are prime. eg%3A 4%2C 6%2C 12%2C etc.%0Atherefore either %28n%2Am %2B1%29 and%2For %28n%2Am -1%2||7||1
964|0|jmolokach|11/28/2010|08:54:49|ranjitr303|circle in circle|how many circles of radius r can fit in a bigger circle of radius R %3F%0A%0Aans%3A let n denote the maximum number of circles that can fit in the big||18||7
963|0|alexb|11/22/2010|19:35:18|jmolokach|Proof %2323 using Wolfram Alpha|I have been having fun using Wolfram Alpha.  This is likely an identical manifestation of proof %2323 of the Pythagorean Theorem%2C but thanks to Wolf||13||9
957|0|alexb|11/10/2010|20:37:09|martinrebas|Three Circles and Common Tangents proof|I stumbled onto the Three Circles and Common Tangents problem %28 http%3A%2F%2Fwww.cut-the-knot.org%2Fproofs%2Fthreecircles.shtml %29on the Futility C||2||1
956|0|alexb|11/09/2010|13:32:17|jmolokach|Arcsin as different of two radicals|In studying for upcoming topics for precalculus course%2C I was venturing into the ideas of the sum and difference formulas for sine%2C cosine%2C and ||1||1
949|2|alexb|10/27/2010|20:41:57|Julian Fleron (Guest)|Linguistics%3A  Names of different components of numbers.|The number 462%2C000%2C000%2C000 is named%2C in English%2C four hundred sixty-two billion.  The roles of %93four hundred sixty-two%94 and %93billion%9||19||6
950|0|Eric M|10/20/2010|20:13:49|Eric M (Guest)|Math probability for a game|There is a game I play%2C it is a fighting game that a person %28fighter%29 can learn offensive techniques %28attacks%29%2C there are 144 attacks in t||0||0
934|2|alexb|10/12/2010|16:35:39|John Molokach (Guest)|Is MY proof of Pythagorean Theorem valid and original%3F|It seems that coordinate proof of the pythagorean theorem is frowned upon.  I know that the theorem was known to Descartes%2C but if we just accept th|on|456||42
948|0|jmolokach|10/09/2010|15:23:12|jmolokach|All-Russian Olympiad 2010 grade 9 P-8|The problem posted at%3A%0A%0Ahttp%3A%2F%2Fwww.artofproblemsolving.com%2FForum%2Fviewtopic.php%3Ff%3D47%26t%3D366012%26start%3D0%26%0A%0Astates %22out||2||2
947|0|alexb|10/05/2010|10:26:43|mr_homm|Asymmetric Propellor proof by tiling|Here is a way of seeing the Asymmetric Propellor theorem without using complex numbers.  Complex numbers give a much shorter proof%2C but the followin||7||3
946|0|alexb|09/29/2010|15:43:22|jmolokach|A better Calculus Proof of the Pythagorean Theorem%3F|I found the following at http%3A%2F%2Fwww.scribd.com%2Fdoc%2F30552%2FA-Calculus-Proof-of-the-Pythagorean-Theorem%0A%0AI do not know the author%2C but ||9||8
940|0|alexb|09/19/2010|19:48:45|mr_homm|Yet another Pythagorean Theorem proof|Looking at the three trapezoids proof has inspired me to try my hand at this.  The proof below is very unlikely to be new%2C but does not seem to be i||27||8
941|0|alexb|09/14/2010|16:15:12|Shawn (Guest)|Squaring the Circle... how close is close enough%3F|I find myself in an unusual position.  I can fully appreciate the complexity of mathematics%2C but have stumbled upon two interesting ideas and have n||7||3
937|0|alexb|09/05/2010|20:45:48|John Molokach (Guest)|3 trapezoids proof of the Pythagorean Theorem|OK%2C this is the last one I am going to post one of these... but I haven%27t seen one exactly like this either and I like it because it preserves the||136||34
939|0|alexb|09/03/2010|09:48:35|mr_homm|Pyramid volumes|Reading Owen Byers%27 new book %28Methods for Euclidean Geometry%29 today%2C the following nice relation occured to me.  Probably this is well known%2||7||4
938|0|jmolokach|08/24/2010|15:03:35|jmolokach|Comment about proof %2375.|I recently created a diagram that contains the same diagram from proof 75 but extended the height to create a larger isosceles triangle%2C whose sides||7||4
935|0|John Molokach|08/11/2010|15:33:32|John Molokach (Guest)|Variation of Proof %236 - Pythagorean Theorem|Alex%2C%0A%0AIn addition to the perhaps failed Calculus proof%2C I believe I have a variation of proof %236 which uses summing areas of the similar tr||12||2
933|0|alexb|08/01/2010|23:14:49|theblitz2010|Help With Publishing Conjecture|I %22may%22 have just solved the twin prime conjecture%21 %28possible%29 However%2C being that I only work by myself and I%27m an amateur%2C I don%27t||1||1
931|0|alexb|07/08/2010|11:57:28|maciejmad|Pythagorean themorem|I%27m math teacher in high school in Poland. Old mathematical books%2C ancient mathematics is my love which fill my spare time since many years. In on||1||1
930|0|alexb|06/29/2010|16:51:52|onecentrob|Is my proof of Pythagorean Theorem valid and original%3F|Following a brief correspondence with Eli Maor%2C he suggested I post my proposed proof of the Pythagorean Theorem to this forum%3A%0A%0Ahttp%3A%2F%2F||13||5
520|0|Jeff|06/17/2010|06:17:03|japam|battleship game|regarding to battleship%2Cwhats the best strategy for it%2C i think it is be related to the shape of the ships%2Cmaybe some modular arithmetic%3F%0D%0||344||8
929|0|r570sv|05/18/2010|14:08:36|r570sv (Guest)|I%92m trying to java Geometry game on the web|Hello%2C%0A%0AThere%92s a java game on the web that use to play but I lost the link when my hard disk crashed.%0A%0AIt involves having to find the cen||0||0
928|0|alexb|05/16/2010|20:30:02|jrosenb|What do you call a centipede%3F|About centipedes being called %22embu%E1%22  in Portuguese%3A I am Brazilian and I had never heard of it%2C but then I live in Rio de Janeiro and ther||1||1
927|0|alexb|05/16/2010|15:56:28|nikolinv|Who can resist%3F|As a truly mathematical lover%2C i can%27t resist to temptation. This is my proof of the Pythagorean Theorem%3A%0A%0Ahttp%3A%2F%2Fwww.cut-the-knot.org||7||3
926|0|alexb|05/16/2010|11:51:31|nikolinv|New article|My email doesn%27t work for several days. My new article about reflection in sidelines of the circumcenter is on the address%3A%0A%0Ahttp%3A%2F%2Fwww.||4||1
925|0|nikolinv|04/29/2010|08:09:33|nikolinv|Simple proof for Euler circle using elementary knowledge|1000 times thanks for%3A%0D%0Ahttp%3A%2F%2Fwww.cut-the-knot.org%2Ftriangle%2FReflectionsOfOrthocenter.shtml%0D%0AYou make me happy%21%21%21%21%21%21%2||15||4
924|0|alexb|04/24/2010|14:59:39|nikolinv|Reflections of the Orthocenter%3A simple proof|Thanks a lot for your comment%2C i am thrilled%21%21%21%21%21%21%21%21%21%21%21%21%21%21%21%21%21%21%21%21%21%21%21%21%21%21%0D%0AMore proofs%3F%0D%0A||5||1
923|0|alexb|04/23/2010|15:38:33|V. Nikolin|Simple proof for Euler line using elementary knowledge|Dear Alex Bogomolny%2C My name is Vladimir%2C and I am a elementary school teacher. %0D%0APlease look at this%3A%0D%0A%0D%0Ahttp%3A%2F%2Fwww.ptt.rs%2F||11||1
922|2|alexb|03/23/2010|20:42:27|Otto Murphy|proving the Chinese remainder theorem for more than 2 eqns|The proof provided on this website only proves the Chinese remainder theorem for two simultaneous equations. How can this be used to prove the theorem||18||7
919|2|alexb|01/06/2010|14:20:59|rabinca|Probability problem|Greetings%21%0D%0A%0D%0AThis is my first time here. I%27m long ago graduated from school. My knowlwedge of probability theory is not terribly advanced||16||1
917|2|alexb|12/04/2009|07:59:10|Bob H|negitive x negitive %3D positive - why%3F|Could someone explain why a multiple of two negitives is a positive%3F %0D%0AI know it is but I have been asked to explain it%21 Any help much appreci||16||1
888|2|alexb|11/21/2009|11:55:35|mbsq|Apollonian Circles Theorem|Hello%2C%0D%0A%0D%0AI was wondering if you could elaborate on the proof for the circles of Apollonius.%0D%0A%28http%3A%2F%2Fwww.cut-the-knot.org%2FCur||30||3
916|0|neat_maths|11/11/2009|07:20:56|neat_maths|Is this the greatest Fermat Prime %3F|Observe that%0D%0A1 plus 2%5E0     %3D     2 which is prime%0D%0A1 plus 2%5E1     %3D     3 which is prime%0D%0A1 plus 2%5E2     %3D     5 which is pr||18||0
912|0|alexb|11/03/2009|10:00:15|neat_maths|Sophie Germain and Fermat%27s Last Theorem|i%29 I can prove that all the prime factors of  %28x%5En %2B y%5En%29 %2F %28x%2By%29%2C where x%2C y%2C %28x%2By%29 and n are mutually prime and n is||64||9
914|0|alexb|10/16/2009|15:35:17|Gerenuk|Trigonometric identities with complex numbers|It is well known that powers of trigonometric functions can easily be derived with cos%28x%29%3DRe%28exp%28ix%29%29 and de Moivre. But I%27m not sure ||16||3
634|2|alexb|10/14/2009|17:18:57|iliaden|100 prisoners and a light bulb|A few years ago%2C I have encountered this problem%2C and ever since I haven%27t been able to find the most optimal solution. %0D%0A%0D%0AThis is the ||653||40
915|0|alexb|10/14/2009|15:35:17|Gerenuk|Intersection of ellipses|Just recently I found an answer to a question how to derive when two ellipses given in cartesian coordinates intersect.%0D%0A%0D%0ASee %5Bhttp%3A%2F%2||15||1
913|0|neat_maths|10/12/2009|10:00:15|neat_maths|Sophie Germain and Fermat%27s Last Theorem|Please see text file attached||5||0
910|2|Chris|10/01/2009|07:02:45|Chris|Triangle Problem%2C 60-70 Variant%2C Solution %23|http%3A%2F%2Fwww.cut-the-knot.org%2Ftriangle%2F80-80-20%2F60-70Sol1.shtml%0D%0A%0D%0A%3E%3EFind F on AB with BCF %3D 50%B0. This brings us into the cl||5||0
909|0|alexb|09/21/2009|23:44:51|Greg|Pascal%27s theorem%2C homogeneous coordinates|Hey Alex%2C%0D%0A%0D%0ALong time%2C no talk. I%27ve been looking at this proof%0D%0A%0D%0Ahttp%3A%2F%2Fwww.cut-the-knot.org%2Fpythagoras%2FChasles%2FP||10||1
908|0|Dominic |08/31/2009|19:24:17|Dominic |One Lane Highway Question|Found this puzzle on XKCD%2C attached is my solution.%0D%0A%0D%0AOne-lane Highway%0D%0A%0D%0AYou have N cars that are all traveling the same direction||20||4
898|0|alexb|08/30/2009|07:06:24|Aythan Avior|Euclid%27s Elements%3A Postulate 1 and the proof of Prop. 16|The article in   http%3A%2F%2Fwww.cut-the-knot.org%2Ffta%2FEat%2FEAT.shtml   is dealing with Proposition 16 of the %22Elements%22 of Euclid%2C which s||26||5
907|3|jprice2|08/22/2009|08:58:58|jprice2|Chinese Remainder Theorem|Hi%2C%0D%0AI had a question about the Chinese Remainder Theorem as presented on Cut-The-Knot%3A%0D%0Ahttp%3A%2F%2Fwww.cut-the-knot.org%2Fblue%2Fchines||16||2
906|2|alexb|08/19/2009|08:20:50|bryan Huh|wilson%27s theorem - geometric proof|Found this proof on this website%3A http%3A%2F%2Fwww.cut-the-knot.org%2Fblue%2FGeometricWilson.shtml%0D%0A%0D%0AAn important part of this proof is thi||14||1
905|2|jprice2|08/16/2009|13:26:59|Bui Quang Tuan|New Proof For Pythagorean Theorem%3F|Dear Alex and All My Friends%2C%0D%0AI have found following proof for Pythagorean Theorem. Please check for me if it is a new one%3F In any case%2C it||48||9
904|0|alexb|07/12/2009|23:19:37|neat_maths|Prime triples|It is conjectured%2C but not proved that prime number pairs that differ by 2 will exist ad infinitum.%0D%0A%0D%0AIs there another prime triple higher ||25||4
900|0|alexb|06/26/2009|21:55:51|Monty|Pythagoras and Euclid|Pythagoras died roughly 70 years before Plato%27s birth and 110 years before Aristotle%27s birth. Is there any evidence that either Plato or Aristotle||28||7
892|0|g_edgar|06/25/2009|01:26:20|xyline|learning how to solve proofs|Hello%2C I am looking for information on how to solve proofs.  I am going back to school and in looking in my old calculus text book%2C half of the pr||12||2
903|0|alexb|06/25/2009|13:05:42|Monty|Phthagoras%27 proof %2310|I guess I forgot to mention that the proof 10 of Pythagoras I sent you appeared in %22Arithmetic in Nine Sections%22 which was %27published%27 in Chin||15||3
901|0|Marcus Bizony|06/21/2009|13:37:41|NJZ|Right Tailed Distribution Function|I am trying to come up with a function y%3Df%28a%29 that includes a fixed parameter b such that the graph has a minimum at x%3D0%2C a maximum of 1 at ||13||2
902|2|alexb|06/08/2009|14:46:25|Steve|Calculating Averages|Is it possible to calculate the average of a series of numbers without knowing all of the values in the series%3F  An algorithm would be useful in com||10||1
899|0|alexb|05/22/2009|17:50:17|Monty|The square root of 2 is irrational|The article on this subject reports a conversation between Socrates and Theaetetus on the square root of 2.%0D%0A%0D%0AIt doesn%27t appear to be a %27||21||8
897|3|itineracy|04/30/2009|07:06:24|itineracy|Cutting a torus %282nd attempt%29|In a well-known puzzle%2C Martin Gardner asked for the maximum number of pieces into which a torus could be sliced by three planes. Based on the formu||9||0
896|0|alexb|04/29/2009|07:21:37|Chris|Moving through a 4D space|Hello Alex Bogomolny%2C%0D%0A%0D%0AMy name is Chris%2C and I am a high school student%2C fascinated by the fourth dimension. %0D%0AAt first I thought ||9||1
894|0|alexb|04/23/2009|12:22:01|Don Johnson|Desargues%27 Theorem|After numerous hours of searching I am unable to find a simple proof of this theorem%3B not a 3D analogy%2C but an actual proof. Some sites I have vis||15||1
893|2|Don Johnson|04/20/2009|14:41:42|Don Johnson|Monge%27s Theorem via Desargues|Off of the cut the knot website%28 %5Burl%5Dhttp%3A%2F%2Fwww.cut-the-knot.org%2FCurriculum%2FGeometry%2FMongeDesargues.shtml%5B%2Furl%5D %29 it shows ||16||2
891|0|alexb|04/03/2009|23:19:53|gkvp|Hex%2C Y%2C and Clutters %28Sperner Families%29|At the end is the list of references cited in this brief note.%0D%0A%0D%0AThis is a brief note on the games of Hex and Y %28with a new proof%29%2C and||25||2
890|3|alexb|03/25/2009|20:17:08|Max|Pythagoras Dissection|How does this %28 http%3A%2F%2Fwww.cut-the-knot.org%2FCurriculum%2FGeometry%2FHingedPythagoras.shtml %29%0D%0A%0D%0Aprove the Pythagorean Thm%3F%0D%0A||9||1
889|0|alexb|03/24/2009|06:59:20|alphabravo112|Question on barycentric coordinates|Suppose%2C we have a triangle A%28x1%2Cy1%29%2C B%28x2%2Cy2%29 and C%28x3%2Cy3%29. There is a point inside the triangle P%28xp%2Cyp%29%2C then%0D%0Axp||10||1
775|0|itineracy|01/02/2009|08:31:43|itineracy|Gardner%27s Torus cutting puzzle... 13 pieces%3F|In a well-known puzzle%2C Martin Gardner asked for the maximum number of pieces into which a torus could be sliced by three planes. Based on the formu||179||4
887|0|Mary|12/24/2008|07:51:00|Mary|mathematic language|hello there%0D%0AMaybe it is an obvious question but what is the meaning of %22by definition%22%3F I find the phrase very frequent in maths books and ||17||2
886|0|alexb|12/14/2008|15:34:19|parahacker|implying falsity|This is a%29probably a really stupid question and b%29possibly the wrong forum for it. But I%27m forging ahead.%0D%0A%0D%0AIn the article%2C falsity p||17||3
880|2|parahacker|12/12/2008|17:58:14|Lloyd Marks|concerning pi|I think I found an accurate method that converts the area of a circle into a square using only compass and straight edge. All I need to know is if the||277||5
885|0|Mayuresh|12/07/2008|00:57:52|Mayuresh|partioning 3 space into circles|Hello%2C%0D%0A%0D%0AI came across this problem of partitioning 3 space into circles %28http%3A%2F%2Fwww.cut-the-knot.org%2Fproofs%2Ftessellation.shtml||12||2
682|0|bohica|12/04/2008|11:47:44|junglemummy|Physics|Admittedly%2C this is more of a physics problem that a maths one%2C but since I don%27t know of any forums about physics%2C I was wondering if someone||107||7
884|0|MichaelD|12/03/2008|08:01:24|MichaelD|Dynamic Geometry Sketches updated|My dynamic geometry sketches site at http%3A%2F%2Fmath.kennesaw.edu%2F%7Emdevilli%2FJavaGSPLinks.htm %0D%0Ahas been updated with the De Villiers Point||9||0
883|0|MinusOne|11/27/2008|13:37:28|MinusOne|What is the smallest rational sqrt%28%29%3F|I am very new to this site %28great site%2C btw%29%2C and have looked around for a similar Q%2C but found none.  Much online talk about sqrt%282%29 be||30||4
770|0|itineracy|10/13/2008|08:30:45|Predrag Savic|Cube Sequence Difficulty|Hi%3A%0D%0A%0D%0A%0D%0APlease%2Cconsider the following problems%3A%0D%0A%0D%0Ahttp%3A%2F%2Fwww.mathlinks.ro%2FForum%2Fviewtopic.php%3Ft%3D105712%0D%0A||129||5
882|4|alexb|10/08/2008|21:45:02|qwendy|Interesting facts about hyperbolas|Hello%2C%0D%0A%0D%0AI hope this is not counted as homework%2C but I work for a science centre and would like some help writing one of the graphic pane||29||1
881|0|Randomer|08/30/2008|18:38:05|Randomer|k prisoners and k lightbulbs.|This is a rather more complex variant of the %27100 prisoners and a lightbulb%27 problem. %0D%0A%0D%0AThere is a prison%2C containing k prisoners. In ||94||0
879|0|wustvn|07/23/2008|10:08:17|wustvn|Can You See The Patterns..%3F|Hello to all of you guys%2C%0D%0AIs there any of you can help me finding the relationships%2Fpatterns of table that I attach at%3A %5Burl%3Dhttp%3A%2F||105||0
606|3|Vincent|07/19/2008|06:48:21|Titus|Golden Number linked to 666|Golden Number linked to 666%0D%0AFormal Proof needed%0D%0A%0D%0AHello%2C%0D%0A%0D%0AWhile working on my websites on 666 myth %28 http%3A%2F%2Fwww.666m||260||4
669|0|sks23cu|07/09/2008|08:06:07|junglemummy|Roman Numerals|This question will probably seem ignorant compared with some of the others on the forum%2C but it is something that has puzzled me since I was eight %||200||9
870|2|alexb|06/19/2008|13:18:10|ddixonslc|An Interesting Formula And Algorithm|Back in the 80%92s I worked out a formula that gives me a sequence of numbers specific to any power p%2C %28p %3D any positive integer grater than 0%2||121||1
826|0|Joe Tibiletti|06/17/2008|16:50:23|Monty|Distance to the horizon|The distance d to the horizon from a point h feet above the surface of the earth can be calculated if you know Pythagoras%27 Theorem and the Radius of||56||5
868|0|alexb|06/17/2008|06:51:45|John Faben|In Plain English|In the %22in Plain English%22 column%2C there is the following entry%3A%0D%0A%0D%0A%3CI%3EThe following was found in a jewelry shop window. Its two me||25||1
848|0|Monty Phister|05/30/2008|12:31:32|Monty Phister|Infinite series for e|I think I know that e%3Dlim%28n-%3Einfinity%29 %281%2B1%2Fn%29%5En%0D%0AAnd the ith term of this series is 1%2F%28i-1%29%21%0D%0ABut the ith term is a||41||2
781|0|phrend|05/23/2008|17:21:30|Cliff P|Question on the Limits on Paper Folding|I%27m having a little trouble understanding the exact meaning of %22L%22 in the %0D%0Aformula at the following web page%2C which relates to paper fold||90||4
836|0|frequency|05/12/2008|23:52:00|frequency|conway%27s game of life|Can anybody please give me a proof for a given garden of eden state which proves that that the given state is a garden of eden%3F||56||0
821|2|Mark Huber|04/14/2008|07:55:14|Zloty Lojak|Probability Problem|I have a tough question I cant get the answer for%3A%0D%0AI have L hats and N balls %28N%3CL%29 each hat can contain 0%2C1 or 2 balls%2C not more than||46||1
643|3|alexb|03/25/2008|22:13:08|Cutting a Pie|Cutting a pie in 8 pieces in 3 movements|http%3A%2F%2Fwww.cut-the-knot.org%2Fdo_you_know%2Fcake.shtml%0D%0A%0D%0AHow is that possible when the formula for this is 1%2F2%28n%5E2 %2B n %2B 2%29||141||5
817|0|alexb|03/22/2008|13:03:02|jprice2|Broken Link for Sangaku Puzzle|Hi%2C%0D%0A%0D%0AI just wanted to let you know that the link that says general formula for the page http%3A%2F%2Fwww.cut-the-knot.org%2Fpythagoras%2F1||50||1
815|0|dingdao|03/15/2008|17:12:02|dingdao|3 circles and line tangent to another circle -- Name%3F|What is the name of this puzzle%3F -- it has been around a long time.%0D%0A%0D%0Athe solution is 1.090943011547.  I have the work %28mostly symbolic%2||64||0
814|0|Thank You!|03/06/2008|08:10:44|jprice2|Question on the CTK article Chain of Inscribed Circles|Hi%2C I was trying to follow the proof of the first result in this article and i still don%27t get the final step which states %22However%2C the circl||53||2
813|2|alexb|02/27/2008|07:17:23|bilateralrope|Are there any faster ways to solve this puzzle %3F|The puzzle is similar to the %5Blink%3A%2F%2Fwww.cut-the-knot.org%2Frules.shtml%7CMagic Squares%5D puzzle. The rules for right box in the puzzle I%27m||60||1
812|0|alexb|02/26/2008|20:44:31|gkvp|elementary number theory problem|Let P and Q be two different odd natural numbers%2C with P%3CQ.  %0D%0ALet L%28N%29 be the set of odd natural numbers less than or equal to N.  %0D%0A||65||1
811|0|alexb|02/26/2008|20:20:23|gkvp|elementary counting%2Ftopology problem|The problem is to prove the following observation. %0D%0A%0D%0AObservation%3A The number N%5E2 can be constructed from N lines%2C as follows.  %0D%0A%||63||1
810|0|neat_maths|02/17/2008|19:21:36|neat_maths|Germain Primes|A pair of primes n and p are known as a Sophie Germain Prime Pair if the larger prime%2C p is equal to 1 plus 2%2An%0D%0AFor example%2C %282%2C5%29%2C||85||0
809|0|noggintwisters|02/16/2008|22:37:48|noggintwisters|Noggintwisters|Hello%2C  %0D%0AI think that Cut The Knot is one of the greatest sites on the web%21 And%2C I think that anyone who loves math as much as I do would l||62||0
808|0|gkvp|02/13/2008|08:25:08|gkvp|mathematical games|This is a math game I invented in 1996%2C called %22Differences%22.  It might be a fun way to learn addition and subtraction.%0D%0A%0D%0AThe game star||97||1
807|3|alexb|02/02/2008|13:31:59|Arithmetics|Need help with 2 arithmetic games|Hello%2C%0D%0A%0D%0AThere are 2 arithmetic games which I need to solve but they are too hard. In the first one%2C you need to complete an equation by ||70||1
796|2|Sumanth|02/02/2008|11:48:36|Sumanth|Independent events in probability|Sample Space %3D%7B1%2C2%2C3%2C4%2C5%2C6%2C7%2C8%7D%0D%0AEvent A%3D%7B1%2C3%2C5%2C7%7D%2C Event B %3D %7B7%2C8%7D%2C P%28A%29%3D 1%2F4%2CP%28B%29%3D1%||163||12
805|0|JLSnell|02/01/2008|17:01:15|JLSnell|People%27s thoughts on my means of relating sets of numbers|Hello%2C recently I finished working on this means of relating points. As I initially perceived it such a means could relate points between dimensions||67||0
803|0|alexb|01/04/2008|18:44:54|gkvp|prime number construction|This is not my invention%2C but something I found at%0D%0A%0D%0Ahttp%3A%2F%2Fyoutube.com%2Fwatch%3Fv%3DsbjPwyPT1AI%0D%0A%0D%0AJust search www.youtube.||103||2
801|3|wustvn|12/28/2007|09:12:20|wustvn|Nobody Can Crack This Number Puzzle...%3F%21|Hello to all of you guys here...%0D%0AI%27d like to post a number puzzle%2C which had been brought to many forums%2C but yet nobody can work it out pr||86||0
799|2|panda24|12/22/2007|15:13:19|panda24|Two paradoxes%3A perfect spheres%2C and one is less than one|Two %28apparent%29 paradoxes were given to me by a maths teacher 25 years ago. I%27d like help disproving them.%0D%0A%0D%0AA%0D%0APerfect spheres don%||90||4
800|2|mpdlc|12/18/2007|21:23:13|Bui Quang Tuan|Geometrical Limit Around A Circle|Dear All My Friends%2C%0D%0AGiven one circle %28O%29 and one point P outside this circle. Choose one direction around this circle say d%2C for example||89||7
798|2|Trebawa|12/10/2007|22:42:57|Trebawa|Straightedge construction of angle bisectors|I would like to know if their is any way to construct angle bisectors using intersections between straight lines between corners and midpoints only- n||90||4
797|0|alexb|11/26/2007|15:59:18|K_ling|Coloring Points in a plane|I was reading your proofs of Coloring Points in the Plane%2C and I%27m having trouble understanding the second solution. Why is it that if the circle ||95||1
795|3|Francisco|10/30/2007|07:35:15|Francisco|Imaginary fraction module|Hello%21%21%0D%0AI%B4m Francisco and I%B4m a spanish student who is studying now in the Stuttgart Universit%E4t in Germany%21%0D%0AI%B4m doing my fina||87||2
793|0|alexb|10/15/2007|08:01:13|alexb|Octagon in a parallelogram|Connect the vertices of a parallelogram to the midpoints of the opposing sides. The lines will form an octagon in the middle of the parallelogram. Pro||194||14
794|0|Cliff P|10/11/2007|15:49:49|Cliff P|Hilbert%27s Grand Hotel|Does anyone have a date for when Hilbert proposed his paradox of the grand hotel%3F I believe it is in the 1920s%2C but I%27d love to have a more prec||62||0
791|0|alexb|09/19/2007|13:23:47|sarathian|3 x 3 x 3 strict magic cube - is impossible-but why%3F|A strict 3x3x3 magic cube is one in which the numbers from 1 to 27 are arranged at the 27 matrix points in a 3x3x3 cubical matrix  with integer co-ord||51||1
792|2|alexb|09/19/2007|06:10:10|David Runion|pythagorean theorem question|    I understand that A2%2BB2%3DC2 from the geometry classes I took in high school.  My question is if there is a whole number that can be used for bo||56||1
790|3|mr_homm|09/08/2007|08:14:16|John|Calculating serial number in a permutation|Let%27s say we have to find out what serial number takes a particular combination in an ordered permutation.%0D%0AFor example if we have to choose thr||78||5
786|0|alexb|09/01/2007|16:08:41|Cliff P|Semicubical parabola%2C tautochrone|We read on the web that around 1687%2C Dutch mathematician and physicist Christiaan Huygens %281629 %96  1695%29%2C showed that the semicubical parabo||66||3
789|0|Cliff P.|09/01/2007|08:21:55|Cliff P.|The|Does anyone know the history of the %22Birthday Problem%22 -- e.g. when it might have been first posed and solved%3F  Thanks.%0D%0A%0D%0Ahttp%3A%2F%2F||39||0
788|0|Cliff P.|08/30/2007|08:41:55|Cliff P.|Andrica%27s Conjecture|Do you find %22Andrica%27s Conjecture%22 to be interesting or notable%3F%0D%0A%0D%0Ahttp%3A%2F%2Fen.wikipedia.org%2Fwiki%2FAndrica%27s_conjecture||52||0
787|0|Cliff P.|08/26/2007|14:51:16|Cliff P.|Quadratic reciprocity theorem|Thanks for all the nice feedback in the CTK Exchange forum.%0D%0A%0D%0A%28The symbol %3D below is the congruent symbol.%29%0D%0A%0D%0AI was reading Ha||47||0
785|0|mr_homm|08/25/2007|16:08:41|Cliff P|Descartes%2C Rectification%2C Ellipse|We read below%3A %22Since all attempts to rectify the ellipse and hyperbola%0D%0Ahad been %28necessarily%29 ineffectual%2C it had been supposed that n||51||1
784|0|JJ|08/25/2007|16:08:41|Cliff P|Neile%27s Semi-cubical Parabola|At this page%2C we see two different formulas for %22Neile%27s Semi-cubical%0D%0AParabola%22%0D%0A%0D%0Ay%5E3 %3D a x%5E2%0D%0A%0D%0Aand%0D%0A%0D%0Ax%||52||1
782|0|Cliff P|08/15/2007|21:47:58|Cliff P|Apollonian gasket|Would anyone know a date for the first creation %28or discovery of%29 the Apollonian gasket%3F  Thanks. %0D%0A%0D%0Ahttp%3A%2F%2Fen.wikipedia.org%2Fwi||59||0
780|2|mpdlc|08/12/2007|06:44:37|ociem|product of distances|If you take two fixed points and then plot all the points where the two distances sum to a constant you get an ellipse.  If you do a subtraction%2C yo||67||4
778|0|Al Q|08/09/2007|10:04:27|neat_maths|Sum of three integers|a%2C b and c are integers with no factor in common and none is divisible by an odd prime n. If the sum of a%2C b and c is divisible by n can anyone gi||72||5
779|0|alexb|08/06/2007|20:50:25|Cliff P|Question on Descartes|Gulberg in %22Mathematics From the Birth of Numbers%22 %28p. 367%29 writes of Descartes famous geometry book%3A%0D%0A%0D%0A%22La g%E9om%E9trie does no||59||1
777|2|alexb|08/05/2007|18:58:34|Cliff P.|When Was Viviani%27s Theorem Discovered%2F Published|Hi%2C  %0D%0A%0D%0ADoes anyone know when Viviani%27s Theorem was discovered or published%3F%0D%0A%0D%0ABackground information is here%3A%0D%0A%0D%0Aht||72||1
773|4|Lars|07/24/2007|21:33:53|Lars|smooth surfaces bounded by circle-sections in a cube|Hello%2C %0D%0AI%27ve been thinking about 3D truchet tilings recently%2C as shown on pages like %5Blink%3Alocal.wasp.uwa.edu.au%2F%7Epbourke%2Ftexture||83||7
774|3|alexb|07/23/2007|09:38:53|JE|Triangle%27s area rate of change|I%27m trying to find a relation between the area of an scalene triangle and its obtuse angle while keeping the base constant. So%2C lets say I have a ||80||3
772|2|Ergo|07/04/2007|17:47:15|Dan|Pythagorean Theorem Incomplete%3F|Can someone check this%3F I%27m not very good at cosines and such. I%27d  greatly appreciate it.%0D%0A%0D%0AFor all scalene triangles%3A%0D%0A%0D%0Aif||123||7
771|2|mpdlc|06/17/2007|09:47:01|minus|Squares on a plane|There are N points %28x%2C y%29. Some four points form a square. And there can be a lot of squares. Is there any algorithm which would find out how ma||73||1
757|2|Ib Jørgensen|05/26/2007|14:48:26|zvi|Two envelopes paradox|This is a version of the two envelopes paradox.%0D%0A%0D%0AIn a box there are two envelopes. It is known that with probability 1%2F2%2C one envelope c||129||6
726|0|Chrissy|05/24/2007|19:29:07|dale|Childbirth probability|What is the probability of a woman giving birth to 3 children and all of them born on the same day%2C but different years. So non-twins%2C non induced||157||10
768|0|next_question|05/20/2007|07:18:05|next_question|Hyperbolic Trisection|I%27m wondering if this is something new. It started with the problem of trisecting an angle%2C but led to other interesting discoveries %28or re-disc||76||0
765|0|junglemummy|05/16/2007|08:28:50|junglemummy|one person and 3 light bulbs|Well%2C the 100 prisoners and one light bulb was too hard for me%2C but I was able to solve the following one.  See if you can work it out.%0D%0A%0D%0||54||2
766|2|alexb|05/15/2007|22:25:05|Monty|Modular arithmetic|The definition of mod is%2C I understand%2C%0D%0A    if a %3D b mod n%2C then %28a-b%29 is divisible by n%2C or a-b%3Dkn%2C with    k an integer%0D%0A||41||4
764|2|Neil_Parker|05/07/2007|13:02:45|Neil_Parker|Conjecture|Conjecture%3A sqrt%28%281-t%5E2%29%2F%281%2Bt%5E2%29%29 is irrational for all rational t with 0%3Ct%3C1.%0D%0A%0D%0AIntuitively one senses the conject||41||0
550|0|Jenni|05/03/2007|20:55:08|orion elenzil|triangles solution correct %3F|at http%3A%2F%2Fwww.cut-the-knot.org%2FCurriculum%2FProbability%2FTriProbability.shtml%23Explanation%0D%0A%0D%0Aone scenario is described%3A%0D%0A%5Bi||168||6
763|2|alexb|05/03/2007|06:44:14|Neil_Parker|Another %22t-dious%22 question from Mr Irrational|To prove sqrt%5B%281-t%5E2%29%2F%281%2Bt%5E2%29%5D is irrational for rational t.%0D%0A0%3Ct%3C1.%0D%0A%0D%0AWe would need%3A%0D%0A%0D%0A1 - t%5E2 %3D ||38||1
762|2|alexb|05/01/2007|06:34:19|Neil_Parker|Proving an expression irrational|In the section on irrationality of sqrt 2 it is shown that sqrt%28n%5E2%2B1%29 and sqrt%28n%5E2-1%29 are irrational with n any integer greater than 1.||43||1
761|2|alexb|04/30/2007|06:12:13|Neil_Parker|Solving x%5E2 %2B y%5E2 %3D2|This may sound like a really dumb question but can one prove that x %3D y %3D 1 is the ONLY rational solution to x%5E2 %2B y%5E2 %3D 2 %3F%0D%0ANeil.||58||1
758|0|Neil_Parker|04/29/2007|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||69||4
760|0|alexb|04/26/2007|09:17:56|junglemummy|Find f%28x%29|Could someone please tell me the answer to this%3A%0D%0Aif f%27%28x%29 %3D x%5E%28-1%29 what is f%28x%29%3F%0D%0A%0D%0AI know it is very basic but I c||63||5
759|0|alexb|04/23/2007|09:10:18|Trevor Skeggs|musical math|Hello%2C Alex %0D%0A %0D%0AFrom your excellent website%2C it seems that you may be just the mathematical brain needed to make sense of the following. ||54||1
756|2|mpdlc|04/11/2007|16:12:23|teacher_4400|Cube Root %26 Neusis Construction|Hi all...this is my first time posting and I am completely at a loss.%0D%0A%0D%0AI love doing compass and straightedge constructions and I have done a||66||3
755|0|zcer|03/15/2007|23:31:52|zcer|a possible %28different%29 resolution to Bertrand%27s paradox|Hi%2C I don%27t even consider myself an amateur mathematician%2C so proposing a resolution to Bertrand%27s paradox feels to me quite presumptuous.%0D%||76||0
751|0|alexb|03/06/2007|23:25:34|alexb|Number of cycles in a directed graph|I was approached with the following question by a person who ran into it while working on her Ph.D. thesis in BioInformatics %28years ago we worked on||72||0
750|0|Kenneth Ramsey|02/23/2007|08:59:58|Kenneth Ramsey|11%5E8%2C a Fibonacci problem%21|Problem%3A Use Fibonacci like series %28but not the same starting numbers%29 to prove that there are an infinite number of solutions to 5a%5E2 %2B 5ab||86||1
745|0|Kenneth Ramsey|02/06/2007|18:50:47|Kenneth Ramsey|Wythoff Array%2C Pythagorean Triplets%2C Primes|The Wythoff Array %28http%3A%2F%2Fwww.research.att.com%2F%7Enjas%2Fsequences%2FA035513%29 is a square array of Fibonacci like sequences T%28i%2Cj%29 %||169||5
749|0|alexb|02/04/2007|08:44:22|Major|Re%3A The latest Sangaku|%0D%0A   Hello Alex%2C%0D%0A%0D%0A%0D%0A The important thing first%3A as usual%2C this post is %0D%0A%0D%0A   ABSOLUTELY NOT FOR BROADCAST on the Foru||115||1
746|0|alexb|01/24/2007|17:14:19|herb|Bertrand%27s Paradox and Information theory|%5Bp%5DDoes Information Theory shed any light on Bertrand%27s Paradox%3F %5B%2Fp%5D%0D%0A%0D%0A%5Bp%5DWhether a %22random cord%22 is less or more than||118||3
742|0|Peter Schaefer|01/19/2007|11:05:04|Bent K. Nielsen|RE%3A Probable solution to abhorring math problem|Sorry about this unasked forthcomming if it is of any amusement to you - %0D%0A%0D%0ABut%3A %0D%0A%28I am%3A A Danish philosopher 63%2C currently enga||153||2
747|5|Peter Schäfer|01/18/2007|16:10:47|Peter Schäfer|Towers of hanoi and sierpinski curve|I have made a program which%0D%0A- generates a sierpinski graph using recursive mapping%0D%0A- tags every node with the matching towers of hanoi posit||111||0
730|0|alexb|01/14/2007|22:34:33|alexb|Lasso on an icy cone|Cowboy Joe wants to climb an absolutely slippery glacier of the%0D%0Around conical form. He has a lasso %28with a loop of a fixed size%29 %0D%0Awhich ||287||17
744|3|Frogs and Toads|01/03/2007|14:18:45|Frogs and Toads|Frogs and Toads settings|hello%2C%0D%0AI have been doing a project to Artificial Inteligence course at my school. It should be something with genetics algorithms%2C written in||134||2
683|0|Chelsey|12/13/2006|23:38:48|junglemummy|sudoku|Is sudoku maths%3F||167||7
741|2|newscam9|12/07/2006|07:07:07|newscam9|infinite sets %3A Genie vs Jenny|Hello all%2C%0D%0A%0D%0AI was reading an article on this site about infinite sets and infinite subsets and the curious implication of the property tha||109||7
502|2|alexb|12/04/2006|00:43:01|Paul|A question|Hello everyone.%0D%0A%0D%0AI%27m not a big student of math%2C but ever since I learn that the following number%3A%0D%0A%0D%0A0.123123123...%0D%0A%0D%0||335||31
740|0|sfwc|11/29/2006|16:10:36|Abomb23|Sum of dice Problem|I ran into this next problem and I am having hard time getting a final answer for it for every m %3A%0D%0A%0D%0A%0D%0AA dice is rolled and summed over||83||2
732|3|alexb|11/29/2006|22:25:19|iliaden|math championships|Hi%2C%0D%0A%0D%0AI am looking for ideas on where to look for any preparation for a math championship. I have already solved the problems of the previo||150||5
739|0|Alex|11/16/2006|03:06:07|Alex|Weights and Counterbalances|There is a rock that weights an integer K pounds%2C from 1 to 40 inclusive. You also have a two-sided scale. What is the minimal number n of weights t||131||2
737|0|alexb|11/13/2006|21:25:24|tiusic|area between 3 circles|I came across this very interesting puzzle earlier today and after a little work%2C I think I have the answer %28but it was an open question with no g||137||2
736|0|Curious Lemon|11/12/2006|06:29:22|Curious Lemon|Probability Query|Hello%0D%0A%0D%0ACan anyone suggest the best way to calculate the probability of losing two close relatives %28Father%2FMaternal Grandmother%29in sepa||144||3
738|0|alexb|11/11/2006|21:25:24|Tmalone|Question about the CTK article|http%3A%2F%2Fwww.cut-the-knot.org%2Fpythagoras%2FArchimedes.shtml%0D%0A%0D%0AWhat is the significance of the . in MS.SQ%3F  After googling I found out||155||1
734|0|alexb|11/01/2006|15:32:13|Hugh O'Byrne|Monty Hall|Suppose you%27re on a game show%2C and you%27re given the choice of three doors. Behind one door is a car%2C behind the others%2C goats. You pick a do||194||9
431|0|Mark Huber|10/27/2006|10:31:35|Starlight|4 colour mapping|The problem and answer are both posted on my site%2C http%3A%2F%2Fwww.angelfire.com%2Ftv%2Fdragonbllz%2Fmath.html %2C due to the fact that it is easie||317||7
735|2|alexb|10/18/2006|14:04:17|Abi Kirk|Question on CTK article on Regular Polyhedra|In the cTK article Regular Polyhedra%2C Alexander Bogomolny discusses Euler%27s Formula. He remarkds that it was first proved by Descartes in 1639. I ||104||2
729|4|Rob Fatland|09/29/2006|06:36:23|Joel Shapiro|J. A. H. Hunter%27s %22Fun With Figures%22|When I was a youngster in the 1960%27s%2C our local newspaper published a weekly math puzzle by one J. A. H. Hunter.  Once per month the puzzle was of||128||1
733|0|Pierre Charland|09/25/2006|06:44:25|tushar_kamal84|A math puzzle. can anyone find the solution%3F|hi%0D%0A %0D%0AFind a ten digit number such that the firast two digits are divisible by 2%2Cthe first 3 digits by 3%2Cthe first 4 digits by 4 and so o||137||2
731|2|jpikonen|09/17/2006|22:25:19|jpikonen|Infinite sequences|A hobbyist%27s question%2C not professionally of much value%3A%0D%0A%0D%0AAll infinite sequences%2C like%0D%0A%0D%0A  n_i%2C i%3D1...infinity%2C i%27t||145||0
728|0|Ramsey2879|09/17/2006|08:14:33|ramsey2879|Paired sums using two sets of consecutive integers|Let A%28n%29 %3D %7B1%2C2%2C3%2C4%2C %85 8%7D and B%28n%29 %3D %7B1%2C2%2C3%2C4%2C %85. 16%7D be two sets of%0D%0Aconsecutive integers with no repetit||127||1
667|0|Rob Fatland|09/08/2006|21:35:52|GarpTalk|Difference between Data and Information|What is the difference between data and information%3F  Thank you%2C kindly%2C for your assistance.||137||6
720|2|Pierre Charland|08/07/2006|13:51:35|Zvi|Closed rook tour on a rectangular chessboard|Hi%2C%0D%0A%0D%0AA rook makes a closed tour on a chessboard of m ranks and n files%2C visiting each square once%2C and returning to the starting point||120||1
725|0|alexb|07/25/2006|06:48:10|alexb|spurious math|I have recently come across a shallow equality with a deep appearance and little sense%3A%0D%0A%0D%0A%26%2391%3Be%26%2393%3B%5Bsup%5D%26%2391%3B%26pi%||160||2
723|0|alexb|07/10/2006|15:39:09|Deep G|Geometry - Draw the third circle such that...|Hi%2C%0D%0A%0D%0AI love to sometimes think of how I could construct simple Geometrical figures %28a circle in the following case%29 under different %2||90||1
718|2|Milan|07/10/2006|06:28:33|Milan|Bi-linear transformation|That is in 2D%3A%0D%0A%0D%0AX %3D a %2B b%2Ax %2B c%2Ay %2B d%2Ax%2Ay%0D%0AY %3D e %2B f%2Ax %2B g%2Ay %2B h%2Ax%2Ay%0D%0A%0D%0AAfter finding the eigh||103||2
719|0|alexb|07/07/2006|13:51:35|sfwc|Stones in Cups|I believe there is a flaw in the counterargument on %5Blink%3Awww.cut-the-knot.org%2FCurriculum%2FGames%2FBarryCipra.shtml%7Cthis page%5D.%0D%0A%0D%0A||108||3
722|0|alexb|07/07/2006|07:39:06|sfwc|The MathPro logo.|There doesn%27t seem to be a proof of the result %5Blink%3Awww.cut-the-knot.org%2FCurriculum%2FGeometry%2FMathPro.shtml%7Chere%5D. This seems to do it||81||1
721|2|sfwc|07/07/2006|13:51:35|Zvi|Closed rook tour on a chessboard|A rook makes a closed tour on a chessboard of m ranks and n files%2C visiting each square exactly once and returning to the starting point. The tour c||95||4
714|0|Graham C|06/23/2006|06:28:16|frowdow|Rounding off of numbers|Most computer language compilers %28the oft used ones anyway%29 round off%0D%0Afractions to the floor value viz.%0D%0A%0D%0Ay%2Fx %3D m %2C if y %3D m||90||3
717|0|alexb|06/14/2006|06:28:33|sfwc|Trouble with applet%3F|There appears to be a problem with the applet %5Blink%3Awww.cut-the-knot.org%2FCurriculum%2FCombinatorics%2FPermOnCircle.shtml%7Chere%5D%2C In that it||122||1
716|0|junglemummy|06/07/2006|11:53:48|junglemummy|gifted children|Although it isn%27t specifically about maths%2C I thought I would let everyone know about the following site which provides some useful information fo||133||0
709|0|erszega|06/03/2006|12:35:23|Ramsey2879|Mersenne Primes and Square Triangular Numbers|Let M%28p%29 %3D 2%5E%28p%29-1. These are known as Mersenne Numbers. I checked the%0D%0Afollowing conjecture for values of p between 2 and 27. If and ||163||5
657|2|Dim|05/30/2006|15:35:00|Becky|Palindromes|I have been fascinated by palindromes for quite some time.%0D%0AThe basic form for finding palindromes is n %2B reverse n %3D b%2C i.e. 13 %2B 33 %3D ||146||3
715|0|mr_homm|05/29/2006|23:44:46|mr_homm|Semi-mechanical proof of Euler Line|I just felt like proving something tonight%2C so here it is.%0D%0A%0D%0AHere is a partly geometrical%2C partly mechanical derivation of the collineari||129||2
710|0|neat_maths|05/27/2006|06:46:23|neat_maths|Sum of 3 mutually prime numbers|It seems possible to prove that the sum of 3 mutually prime numbers x%2C y and z cannot contain all the primes contained in each of the pairs %28x%2By||208||9
713|2|Mark Huber|05/25/2006|13:53:27|Ed Schifman|Two parents with both children having same birthday|My daughter was born on the same day that I was and my son was born on the same day that my wife was.  What is the formula and the probablity that thi||177||1
712|0|erszega|05/24/2006|06:22:54|erszega|Bertrand%27s postulate|There is an article proving and generalising on Bertrand%27s Postulate at http%3A%2F%2Fwww.cs.uwaterloo.ca%2Fjournals%2FJIS%2Fgreen.html.%0D%0A%0D%0AI||188||2
711|0|mr_homm|05/22/2006|11:59:48|mr_homm|Rectangle on Chessboard|Recently I was looking at %5Blink%3A%7Cthis%5D page%2C and I think I see a different approach to the proof.%0D%0A%0D%0ATo start with%2C forget about r||147||8
706|0|alexb|05/17/2006|10:25:57|sfwc|The broken chord theorem.|The %5Blink%3Awww.cut-the-knot.org%2FCurriculum%2FGeometry%2FBrokenChordPaperFolding.shtml%7Cproof by paper folding%5D relies only on the fact that CP||165||10
708|0|erszega|05/17/2006|06:41:17|erszega|sum of prime factors and cycles|Let sopfr%28n%29 be the sum of prime factors of n %28see http%3A%2F%2Fmathworld.wolfram.com%2FSumofPrimeFactors.html %29. %0D%0A%0D%0AThere have been ||137||0
707|2|Eddie|05/11/2006|16:14:19|Eddie|Angle Trisection|OK%2C I%27m sure there must be something wrong with this%2C since it is impossible to trisect an angle with only compass and straight edge%2C but what||140||2
703|2|sfwc|04/29/2006|17:08:23|billbranch|Did I solve the Delian problem%3F|I am trying to posy my read-only word document to show that I may have solved the Delian problem.%0D%0A%0D%0ACan anyone let me know how I can post my ||270||15
705|0|alexb|04/21/2006|16:03:42|Eric Yang|Roger Wibberley%27s Delian Problem|What was the error in the proof%3F||152||1
700|0|alexb|04/17/2006|10:41:33|alexb|difficulty of mob cipher|I got a message which I%27d like to respond to%2C but have no idea how. I can imagine that the codes were completely random%2C in which case they coul||87||3
702|3|alexb|04/17/2006|11:15:36|yobi|49er trick|I have to come up with a proof for this trick.  Can anyone help me%3F%0D%0A%0D%0ATo do this trick%2C you%27ll need 2 dice.  Dice are made up so that o||115||1
701|0|alexb|04/13/2006|10:20:35|Robert Dawson|Broken Calculator Applet|A rider%3A is there a way to reach _any_ integer using the broken calculator%3F And how many more keys could break without preventing this%3F%0D%0A%0D||109||1
699|0|Mutley2003|04/11/2006|22:10:38|Mutley2003|Rank order from the min number of paired comparisons|Hi%0D%0AI think this problem has something in common with tournaments%2C but I am not sure quite where to start. Also with binary search%2C perhaps.%0||145||4
698|3|mr_homm|04/07/2006|18:21:52|iliaden|statistics|I have recently bumped into an physics problem. when I was solving it%2C I was unable to find the correct terminology for the following %22mean%22%0D%||152||4
697|0|ricardo|04/03/2006|07:28:21|ricardo|Demonstration for the volume of the pyramid%3F|   For some time I ask myself why the volume of the pyramid is 1%2F3%2AB%2Ah. %0D%0A%0D%0AThat the volume is directly proportional to the Area %22B%22||140||0
696|0|Mr Toad|04/01/2006|06:36:40|guest|dodecahedrons|Can you perfectly fill a 3 dimensional space with dodecahedrons%3F||153||2
694|0|alexb|03/30/2006|14:11:22|Maj. Pestich|Tell Pythagoras that V. Poncelet says %27Hi.%27|  Hello civil%28ian%29  friends%21%0D%0A%0D%0A Let%27s use this time the Poncelet%27s theorem as a starting point.%0D%0A%0D%0A I did not know that thi||155||4
695|0|Maj. Pestich|03/28/2006|14:46:25|Maj. Pestich|Strange %27bedfellows%27 Pythagoras and Napoleon B.|%0D%0A  Hello Alex%2C%0D%0A%0D%0A A short time ago in Mathworld I came across%0D%0A%0D%0A%3E%0D%0AAmazingly%2C the difference between the areas of the||149||1
690|0|alexb|03/28/2006|20:23:56|Maj. Pestich|Euler shakes Pythagoras%27 hand %28Pythagoras Theorem proof%29|   Hello Alex%2C%0D%0A%0D%0A   What do you think about the proof based on Euler%27s identity%3F%0D%0A%0D%0A   Four collinear points A%2CB%2CC%2CD  con||150||13
693|0|mr_homm|03/27/2006|13:29:00|Monty Phister|Post Office|Dear Alex%2C%0D%0A%0D%0A    There is this editor who goes from place to place in times past%2C present%2C and future%2C and not long ago he visited a ||124||7
692|0|Ramsey2879|03/24/2006|08:16:34|erszega|Pythagorean triples and recurrence relations|The values of c in a%5E2 %2B b%5E2 %3D c%5E2 where %7Cb - a%7C %3D 1 and gcd%28a%2Cb%29%3D1 are generated from this recurrence relation%3A%0D%0A%0D%0A||88||1
691|0|HawaiiThad|03/22/2006|06:43:42|HawaiiThad|Pieces on a chess board|In a recent discussion of a variation of chess%2C someone stated to me that it is not possible to calculate the number of legal arrangements of KQP vs||59||0
689|0|enquiry|03/13/2006|08:03:48|enquiry|Global Consciousness Project and September 11 2001|There is a study at http%3A%2F%2Fnoosphere.princeton.edu%2Fterror.html which claims that analysis of random numbers generated continuously shows %22a ||65||0
688|0|alexb|03/12/2006|22:35:09|Nao|9|9%2C and calculations with 9%2C seem to have repeating patterns%2C would you be able to help me with information about 9%2C or links to information ab||60||1
685|2|Frank Bernhart|03/08/2006|14:14:05|Carl Chapman|4 colour problem|I believe I have a proof of the 4 colour theorem that doesn%27t require a computer.  How can I get it checked and reviewed%3F  I know I%27m about the ||85||2
687|0|Tobias Claren|03/08/2006|07:24:32|Tobias Claren|Look for reflector as pointed here|Hello. %0D%0AI found this page%3A http%3A%2F%2Fwww.cut-the-knot.org%2FCurriculum%2FGeometry%2FParabolaMirror.shtml %0D%0AWhere can I buy such a reflec||54||0
686|0|alexb|03/07/2006|20:15:18|aVbH_5|The three glass solution %3D 4|The following is my solution. %0D%0A008%0D%0A053%0D%0A323%0D%0A026%0D%0A206%0D%0A251%0D%0A341%0D%0AIs this the other solution referred to in the expla||59||1
681|0|mr_homm|03/06/2006|19:16:02|mr_homm|Algorithm for 3-color Tower of Hanoi|I promised a few days ago in another thread that I would post this algorithm%2C but then I got very busy for a while.  Here it is%2C finally%3A%0D%0A%||105||11
497|0|neat_maths|03/03/2006|23:33:04|neat_maths|Prime Factors of %28x%5En %2B y%5En%29%2F%28x%2By%29|If integers x%2C y%2C x%2By and n have no common factors and n is prime%2C%0D%0AIt is easy to prove %28x%5En %2B y%5En%29%2F%28x%2By%29 is 1 mod n%0D%||669||57
636|0|momus|03/03/2006|15:25:35|fastguitar|unsolved angle|Hi%2C%0D%0A%0D%0AThe attached geometric problem haven%27t been solved by any one since years. I hope anyone can solve this and send the explanation. Q||210||7
684|2|JJ|02/26/2006|19:01:47|japam|rational function maximus|suppose you have two functions A%28X%29concave%2C and B%28X%29convexe%2Cboth interesect in just 2 points and you want to find the maxim of B%28X%29%2F||107||2
678|2|Roy Avery|02/21/2006|07:28:29|Roy Avery|Maths Puzzel  with Answer|I came across a puzzel the other day which on the face seems easy.%0D%0AThe answer was given later%2C but no explanation as to how it is arrived at. I||139||4
477|0|fadil|02/17/2006|12:53:09|sfwc|Bicolor hanoi.|As I was browsing ctk%2C I happened upon the page www.cut-the-knot.org%2Frecurrence%2FBiColorHanoi.shtml. I don%27t know how general the %27more gener||99||4
673|0|alexb|02/17/2006|16:17:03|sfwc|Two quick comments on recent pages|The theorem at http%3A%2F%2Fwww.cut-the-knot.org%2FCurriculum%2FGeometry%2FThreeConcurrentCircles.shtml is exactly the inverse of the theorem of the S||213||28
680|0|h_alpha|02/09/2006|16:54:56|h_alpha|four travelers alternate%2Fequivalent solution|The 4 Travellers problem is posed at CTK in the %22beautiful %2F elegant proofs%22 part of the manifesto. Taking this problem %27as read%27%3A I came ||78||5
679|0|alexb|02/07/2006|11:54:19|sfwc|Triangle-chopping|At http%3A%2F%2Fwww.cut-the-knot.org%2FCurriculum%2FGeometry%2FDecoSymmetry.shtml in your 4-piece dissection the blue and yellow pieces are adjacent t||66||1
674|0|alex|02/02/2006|07:34:08|alex|very large primes %26 modern cryptography|I read a book about cryptography recently%2C which left a strange catch-22 question in my mind. The book mentions that modern digital cryptography oft||78||2
677|0|alexb|01/31/2006|18:12:58|sfwc|Avoidance of algebra.|At http%3A%2F%2Fwww.cut-the-knot.org%2FCurriculum%2FGeometry%2FRadiusByPaperFolding.shtml %2C we may avoid some of the algebra as follows%3A%0D%0A%0D%||61||1
676|0|sean|01/31/2006|14:10:05|sean|sin%28sin%28sin%28...%29|I recently saw a post on the HP website where someone curiously decided to take the sine of an angle and then take the sine of that and the sine of th||74||0
675|0|alexb|01/27/2006|17:56:53|sfwc|Avoiding algebra.|To see what is going on more easily%2C the algebra may be eliminated from the second proof at http%3A%2F%2Fwww.cut-the-knot.org%2FCurriculum%2FGeometr||66||3
647|0|tony123|01/26/2006|15:55:03|Victor|News aboutFLT|It is common knowledge that if the integers A and B have no common factor and %5Bnobr%5DA %26%2343%3B B%5B%2Fnobr%5D do not divided by simple n then t||172||11
668|2|Pierre Charland|01/12/2006|11:21:01|Lachlan|How can I count the number of chosen options in a matrix%3F|A real life problem in town planning  has come up that I am hoping someone can help us with.%0D%0A%0D%0AWe have generated 9 town planning strategy opt||79||1
670|0|alexb|01/10/2006|23:01:43|neat_maths|Pellian Equations|I understand the solutions to Pellian equations of the type%0D%0A%0D%0Ax%5E2 - n %2A y%5E2 %3D c lie in continued fractions.%0D%0A%0D%0ACan anyone sho||86||7
476|2|jupiter|01/09/2006|10:15:54|JimBrawner|presidential Pythagorean proofs|President James Garfield came up with an elegant proof of the Pythagorean Theorem using a trapezoid%2C which is widely known.  In his book %22Geometry||103||1
671|0|biggestseagull|01/09/2006|20:28:32|biggestseagull|Modified Pigeonholing Problem|Greetings%2C%0D%0A%0D%0AThis problem has been plaguing me right before I go to sleep for a while now%2C please help%21%21%0D%0A%0D%0AMy question is...||71||2
661|4|Pierre Charland|01/06/2006|07:09:20|Pierre Charland|5 circles on 5x5 lattice%2C on nxn|There is a problem asking to find 5 circles going through all points of a 5x5 lattice.%0D%0AA solution can be found in%0D%0A- Ross Honsberger%2C Mathe||140||2
654|0|mpdlc|12/25/2005|18:49:53|Anthony|Holy cube|A cube with width %91x%92 has three circular holes cut from each face to the opposite face. The width of the circles is also x %28assuming you could h||192||9
666|0|jerry|12/23/2005|18:58:57|jerry|monster inequality%2C sequence|Ok find the limit of the sequence%3A%0D%0AC%28n%29 %3D n%21 %2F %28 n%5E%28 n %2B1%2F2%29 %2A e%5E-n %29%0D%0A%0D%0A1. Use the following derived inequ||94||0
664|4|mr_homm|12/19/2005|18:55:57|Alan|Unintuitive result from set theory %28I think%29|I remember reading a while ago about some mathematical result%2C I can%27t remember the name of it. The idea is that it is possible to define a set of||136||11
660|0|Deep G|12/19/2005|03:17:46|Deep G|Physics-based solution to Fermat pt. finding problem.|Hi%2C%0D%0A%0D%0Atie one end of three identical pieces of thread together. That shud loo like -%0D%0A%0D%0A%5C%2A%2A%2A%2A%2A%2A%2F%0D%0A%2A%5C%2A%2A%||124||4
665|0|mr_homm|12/19/2005|20:18:24|neat_maths|Squares and the Pythagorean Equation|It is fairly easy to prove that in the Pythagorean equation%0D%0A%0D%0Ax%5E2 plus y%5E2 %3D z%5E2%0D%0A%0D%0Ai%29 all three x%2C y and z cannot be squ||134||8
656|3|DMays|12/13/2005|22:37:58|DMays|Base 8|I need your help. I was told that this number is in code%2C possibly Base 8. I need to convert this number string to another number that might possibl||131||6
652|0|Alan|12/12/2005|11:14:01|sfwc|counting triangles|At http%3A%2F%2Fwww.cut-the-knot.org%2FCurriculum%2FAlgebra%2FTriangleChain.shtml you ask %22can you construct a chain of adjacent triangles of length||106||8
663|0|snibble|12/11/2005|20:12:52|snibble|Maths refresher - helping to speed up the slow ones|Currently teaching 14 year olds and was looking for a site that gave a fun way to help the %22slower%22 learners and found this one useful %21%0D%0A%0||87||0
662|3|alexb|12/10/2005|07:46:29|blueheron|Uses for pythagorean theorem%3F|I%27m looking for any uses %28technology%2C etc%29 for the pythagorean theorem and really appreciate any input.||89||1
649|0|mr_homm|12/06/2005|07:09:48|Owen|Gift Exchange probability|While reading the %22Plane Problem%22 probability question posed in another thread I was reminded of a probability problem that I%27ve attempted to so||195||11
651|2|Deep G|12/03/2005|10:55:47|Deep G|THe Isosceles Triangle problem|ABC is an isosceles triangle with angles A%2CB and C measuring 20%2C80 and 80 degrees respectively. Two rays BX and CY are drawn such that angle CBX m||184||8
653|0|brac37|11/29/2005|22:46:36|brac37|marriage algorithm|Dear Alexander Bogomolny%2C%0D%0A%0D%0AWhen I searched for an algorithm to determine marriagability%2C google brought me to your page. But I do not un||125||8
659|0|angel_ineed|11/29/2005|07:34:18|angel_ineed|Complex number games|Can anyone recommend a good interactive game involving complex numbers%3F||70||0
658|0|mpdlc|11/28/2005|17:27:46|Deep G|Base 1 %3F%3F%3F|there has been quite some discussion over defining numbers with base n%3E1 and n%3D1.%0D%0A%0D%0AA numbering system%27s basic requirement would be to ||79||1
655|0|Deep G|11/22/2005|16:34:26|Deep G|The pyramid problem|Imagine a square surface ABCD touching a spherical surface with centre O at some point on the plate%28not necessarily the centre of the plate%29. Join||82||2
650|3|iliaden|11/13/2005|15:25:00|Suresh Reddy|Reminder Problem|Hi%2C%0D%0A%0D%0ACan anyone pl try to solve the following problem%3A%0D%0A%0D%0AWhat is the reminder when %28 1%21%2B2%21%2B3%21%2B.....%2B95%21 %29 i||88||5
648|0|mpdlc|11/13/2005|21:59:52|mr_homm|A little circle geometry puzzle|A few days ago%2C my brother brought me a problem that had been passed on  to him by a student in a calculus course.  The problem was supposed to be s||135||10
543|0|eddieboy|10/16/2005|20:08:41|pythagoras|Monty Hall Problem - logic proof|Hi everyone. I have found a simple solution%2Fproof for the Monty Hall problem %28goats behind two doors%2C car behind other%2C etc.%29%0D%0A%0D%0ARat|on|1105||34
644|0|gin&tonic|10/09/2005|06:25:43|gin&tonic|e as the min or max of z%2Alog%28x%2Cz%29|Using the notation log%28x%2Cz%29 as%0D%0Ax%5Elog%28x%2Cz%29 %3D z%2C%0D%0A%0D%0AI think that the minimum value of z%2Alog%28x%2Cz%29 is at z %3D e wh||110||5
641|2|mr_homm|10/06/2005|22:02:18|iliaden|another question about prisonners|I found another problem about prisoners. %0D%0A%0D%0A%5Bi%5D10 people are placed in a row%2C so that every one sees everyone who is in front of him %2||107||5
642|0|alexb|10/04/2005|07:52:59|sfwc|An application of inversion.|This is an alternate proof for the proposition at http%3A%2F%2Fwww.cut-the-knot.org%2FCurriculum%2FGeometry%2FFixedTangentPoint.shtml .  %0D%0A%0D%0AL||88||2
640|0|alexb|10/03/2005|17:49:05|lwn19|Pocket Calculator|How does a pocket calculator %28or a PC for that matter%29supply the value for a trig function or a logarithm%3F  It surely can%27t store all the valu||96||3
498|0|mr_homm|09/19/2005|23:19:19|Maxim|How many roots%3F|Problem 1%3A%0D%0A%0D%0AHow many complex roots does the equation x%5Ee%3De have%3F Here e is of course exp%281%29.%0D%0A%0D%0AProblem 2%3A%0D%0A%0D%0A||207||7
593|0|alexb|09/17/2005|14:27:54|CliveT|Triangle%27s smallest bounding circle|Hi everyone.%0D%0A%0D%0AA few years ago I was faced with the problem of having to find the smallest possible circle which would enclose a triangle.%0D||190||14
639|0|alexb|09/06/2005|10:53:43|bison|a new proof of the pythagorean theorem%3F|I wonder if the following could be considered a new proof of the Pythagorean theorem%2C or is it known%3F     Starting with the familiar 3-4-5 right t||93||3
638|2|alexb|09/02/2005|06:32:39|Tibi|Gaussian factorisation|There is a unique factorisation theorem for Gaussian integers.%0D%0AI factorised 20 in two different ways%3A%0D%0A%0D%0A%281%29 -1%2A%282%2Bi%29%2A%28||74||3
637|0|ak|09/01/2005|15:30:18|ak|Does this series ever sum to an integer%3F|This is a problem I%27ve spent many hours vainly on. If a and d are relatively prime%2C is 1%2F%28a%29 %2B1%2F%28a%2Bd%29 %2B1%2F%28a%2B2d%29...%2B1%2||90||2
635|0|alexb|08/16/2005|14:45:19|sfwc|Hoehn|The theorem at http%3A%2F%2Fwww.cut-the-knot.org%2Fpythagoras%2FHoehn.shtml appears to be simply a restatement of the intersecting chords theorem for ||74||1
627|0|alexb|08/16/2005|00:05:22|mr_homm|On the 4 Pegs Problem|This problem%2C %5Bwww.cut-the-knot.org%2Fproofs%2FPegSquare.shtml%7C4 Pegs%5D has a point in the given solution that I find troublesome.  It is certa||218||21
633|3|Gavin|08/14/2005|09:37:40|Gavin|All numbers equal%3F%3F|I have recently stumbled upon this on a website and%2C along with several of my friends%2C have been trying to figure out if this is indeed valid or i||126||6
625|0|mr_homm|08/10/2005|14:03:53|mr_homm|4 Travelers problem -- a new solution|Looking at this problem recently%2C I decided to try to get a purely geometric solution without going to higher dimensions.  I started from the observ||134||11
632|2|alexb|08/09/2005|19:14:48|japam|dual pappus general|just a few thoughts%0D%0A%0D%0AWhen you look at dual pappus theorem for first time %2C you wonder why this particular points of intersection are choos||97||1
631|0|mr_homm|08/03/2005|00:05:43|mr_homm|moebius strip|Recently I was reading the %5Blink%3Awww.cut-the-knot.org%2Fdo_you_know%2Fmoebius.shtml%7Cmoebius strip%5D section of cut-the-knot%2C and it reminded ||91||2
630|2|mr_homm|08/02/2005|14:53:55|K. Arthur|prime gaps|A005250 in NJAS%27 encyclopedia lists the increasing gaps betwen primes. There is another interesting sequence%2C A063095%2C which is defined as%0D%0A||107||6
626|0|alexb|07/28/2005|10:58:55|mr_homm|Physics based solution to Three Circles Tangents problem|Although there are already very nice proofs for the %5Blink%3Awww.cut-the-knot.org%2Fproofs%2Fthreecircles.shtml%7CThree circles%5D based on a 3D poin||117||5
629|0|Indi|07/27/2005|07:42:52|Indi|continuous interest|Compound interest is described at http%3A%2F%2Fwww.cut-the-knot.org%2Farithmetic%2Finterest.shtml.%0D%0A%0D%0AHowever%2C sometimes continuous interest||99||2
624|0|sfwc|06/30/2005|15:26:57|sfwc|Rectangles on chessboards|At the page about %5Blink%3Awww.cut-the-knot.org%2FCurriculum%2FAlgebra%2FIntegerRectangle.shtml%7Crectangles on chessboards%5D the claim %27A rectang||80||4
623|0|alexb|06/28/2005|08:23:15|sfwc|Theorem of Wilson.|The %5Blink%3Awww.cut-the-knot.org%2Fdo_you_know%2Fgraphs2.shtml%23wilson%7Ctheorem%5D of Wilson generalising the solution to the fifteen puzzle appea||86||1
622|0|alexb|06/27/2005|13:00:20|Gary Bradshaw|Fifteen puzzle and 9-puzzle variant|I%27m having trouble determining whether the 3x3 version of Sam Loyd%27s fifteen puzzle has the same even%2Fodd parity rule that the 4x4 version does%||73||1
621|0|alexb|06/26/2005|17:28:34|Neel|A couple of queries|I have been browsing through the pages of Cut the Knot for a few months now%2C and it%27s been a primary resource of fun and inspiration. Now that I a||89||3
620|3|mpdlc|06/25/2005|17:54:16|nvc102|volume of an arch|could someone please recommend the formula for calculating the volum of an arch%3F%0D%0A%0D%0AThanks%21%21||85||2
619|0|erszega|06/19/2005|14:06:32|Koko|a %2B b divides a%5E3 %2B b%5E3|a and b are integers%0D%0A%0D%0AI found accidentally that a %2B b divides a%5E3 %2B b%5E3. I also know why%3A%0D%0A%0D%0Aa%5E3 %2B b%5E3 %3D %28 a %2B||116||3
383|2|mr_homm|06/13/2005|10:21:39|Panda|Measuring time|Howdy all%2C%0D%0A%0D%0A    A friend recently presented this puzzle and I am completely lost about the solution. There is probably an obvious solution||161||3
612|0|mr_homm|06/13/2005|22:15:18|koko|convergence|It appears that the value of z in %0D%0Az%5En %3D x%5En %2B y%5En%0D%0Aconverges on max%28 x%2C y %29 as n increases.%0D%0ACould somebody please expla||80||6
618|3|ET|06/12/2005|21:03:58|ET|2 x ab x cde %3D fghi| It is an multiplication problem and each of the ten digits are different.%0D%0A%0D%0A2 x ab x cde %3D fghi%0D%0A%0D%0ACan someone help please%3F||60||4
617|0|alexb|06/11/2005|18:07:37|mr_homm|Smooth curve through Fibonacci sequence|Hello all%2C%0D%0A%0D%0AThis is not really a problem or question%2C just an announcement of something you might think is interesting or pretty.  I hav||71||1
614|0|Ramsey2879|06/03/2005|10:34:03|erszega|Three statements re integer sequences|I would be grateful for either proofs or counter-examples %3A%0D%0A%0D%0A%281%29 %0D%0AThe sequence 1%2C 3%2C 17%2C 99%2C 577%2C %85%2C which is A0015||68||3
613|0|Ramsey2879|05/28/2005|23:18:20|Ramsey2879|Recursive Series Problem|T%28n%29 %3D n%28n plus 1%29%2F2 are the well known triangular numbers.%0D%0ALet A%280%29 %3D 2 let A%281%29 %3D 3 A%28n%29 %3D 6%2AA%28n-1%29 -A%28n-||166||0
604|0|Ramsey2879|05/26/2005|06:58:42|erszega|integer sequences and Pythagorean triples|All this is based on the simple observation that 1%2B3 is a square%2C 1%2B3%2B5 is a square%2C 1%2B3%2B5%2B7 is a square%2C etc.%0D%0A%0D%0AI use the ||292||13
306|0|NJZ|08/29/2002|20:15:36|NJZ|Mathematics of General Relativity|Since physics and math are closely tied%2C I felt this question would be appropriate for this message board.  Although I have had no formal schooling ||113||7
283|2|jman_red|07/03/2002|05:17:45|Matt|Probability|Hey. I came across this intersting idea while reading this mathematics book but don%27t seem to understand it. It goes like this%3A A man who travels ||151||3
279|2|jrr7|05/04/2002|11:48:24|Eric|Simultaneous Recurrence%3F|Hi everyone%2C%0D%0A%0D%0AI will be as clear and concise as possible.  I am attempting to model how much dust accumulates on a given surface as a func||89||1
261|2|Rowdy R|03/15/2002|17:39:03|Rowdy Renee|Pythagorean Theorem and the Soul%3F|My instructor has said he can prove we have a soul by using the Pythagorean Theorem.  Any comments%3F||232||7
151|2|Manoj Nair|10/12/2001|13:36:11|Bergerac|number|please can anyone tell me more about the number 011001%0D%0A||74||2
130|0|activeco|07/08/2001|08:18:05|activeco|Bertrand%27s Paradox|%0D%0AI don%27t think there is paradox at all.%0D%0AThose who support first solution %281%2F3%29 should be aware that%0D%0Asuch events happen only 2%2||89||0
4||||||I was wondering if on this website you have anything about rowing shapes%2C as I am having trouble finding anything.%0D%0A %0D%0AGrowing shapes%2C like when you take a square and put another quare on each external edge of it. %0D%0A %0D%0AIf not can you refer me to any other website%3F %0D%0A %0D%0AThanks%2C%0D%0A %0D%0AMark|||75|5.5|1