748|0|zain|01/26/2011|14:33:06|zain (Guest)|discrete math|axiam 1%3A every line is a set of points.%0Aaxiam 2%3A for each line %27L%27 there is a point on %27L%27.%0Aaxiam 3%3A there exists at least 2 points.||20||9
747|4|alexb|01/22/2011|11:23:36|dscharpi1 (Guest)|Math proof that sphere has max volume to surface area|I am working with a physician friend on a problem %28we%27re both in our 50%27s and our math is pretty rusty%29 - and was trying to find proof that th||1||1
746|2|alexb|01/20/2011|08:44:00|Jeremy Dunn (Guest)|Regular Polygon problem|In doing some experimental drawing in AutoCAD I ran across what appear to be some interesting relations that appear to be true but which I am unable t||9||2
745|0|alexb|01/15/2011|11:56:05|Anthroxy|Creating a formula|Hi there i saw your post about %22Maximum Volume of a Cut Off Box%22 %28http%3A%2F%2Fwww.cut-the-knot.org%2FCurriculum%2FCalculus%2FBoxVolume.shtml%29||3||1
744|0|hdk |12/14/2010|07:35:02|hdk  (Guest)|Please help%21|A friend of mine created a puzzle that I cannot solve%2C but it somehow relates to Pi.  %0A%0AA %3D  %2C B %3D  %2C C %3D  %2C D %3D  %2C E %3D  %0AF ||0||0
743|0|alexb|11/11/2010|09:44:37|Haim Zamir  (Guest)|glaring apportionment error|Your apportionment computations have  an error%2C in that they ignore the fact that the lower quota is never less than one. According to your site%2C ||1||1
742|0|alexb|10/27/2010|23:28:37|HexyPexy|doll house window|HexyPexy%0A%0AHi - visited a quilter friend the other eve%2C and saw the dollhouse being worked on. There were two windows%2C each with same design%2C||1||1
540|0|HART32Cora|10/04/2010|13:39:42|Maj. Pestich|4 Travellers problem|  Hello Alex%2C%0D%0A%0D%0A  Ca fait longtemps...%0D%0A%0D%0A  I read the solution to 4 travellers by S. Anderson and the %0D%0A  conclusion that they||213||20
725|0|alexb|09/23/2010|19:33:43|Bui Quang Tuan|Concentric Circles In Crossing Circles|Two circles %28O1%29%2C %28O2%29 intersect each other at A%2C B. Two circles %28Oa%29%2C %28Ob%29 centered at any point O%3A %28Oa%29 passing A%2C %28||119||16
740|0|mpdlc|09/09/2010|10:26:39|Bui Quang Tuan|Concurrency With Six Touching Circles|Dear All My Friends%2C%0A%0AGiven six circles %28C1%29%2C C%282%29%2C ... %28C6%29 external touching as following%3A%0A%28C1%29 and C%282%29 are touch||32||1
738|0|alexb|08/26/2010|10:31:41|Bui Quang Tuan|Broken Chord And Pythagorean Theorems|Dear All My Friends%2C%0A%0AThe Broken Chord Theorem is one of very small interesting theorems which credited to Archimedes. There are some proofs for||57||3
741|0|mpdlc|08/21/2010|05:41:50|Bui Quang Tuan|Three Right Triangle Construction Problems|Dear All My Friends%2C%0ATo construct triangle ABC right at C such that altitude length from C is maximal%2C in three cases%3A%0A1. Given a %2B b%0A2.||13||4
736|0|Owen|08/07/2010|16:26:04|Owen|Fermat Point|I don%27t understand the second solution for finding the Fermat point P of a triangle %28P is defined to be the point minimizing the sum AP %2B BP %2B||13||6
739|0|Bui Quang Tuan|08/06/2010|08:28:09|Bui Quang Tuan|Areas Of Two Special Triangles And Pythagorean Theorem|Dear All My Friends%2C%0A%0APlease try one interesting problem%3A first prove following small lemma then use the lemma to prove Pythagorean theorem%21||30||7
735|0|mpdlc|07/30/2010|17:15:42|Bui Quang Tuan|Cyclic Touching Circles Around Triangle|Dear All My Friends%2C%0A%0AIn the triangle ABC we select one direction%2C say A to B to C to A to B... %0AAt vertex A%3A construct a circle %28A1%29 ||77||21
737|0|alexb|07/29/2010|06:35:14|Bui Quang Tuan|H. Eves%27 Tricky Quickie In N-Gon|Dear Alex%2C%0A%0AOther than triangle%2C H. Eves%27 tricky quickie can be used for n gon. I recommend one better geometric inlustration for following ||1||1
734|2|alexb|07/22/2010|15:28:47|PeterB (Guest)|MinMax inequality|On the website http%3A%2F%2Fwww.cut-the-knot.org%2Farithmetic%2FMinMax.shtml%0Athe min-max inequality is shown. However%2C I think that the proof of t||7||3
733|3|alexb|07/11/2010|19:50:10|MikeS (Guest)|Probability|A radio station asks for a caller of a specific year to call. Then the station then spins a %22month%22 wheel for the caller to win a prize if their b||11||8
710|3|Gerenuk|07/10/2010|06:58:40|Manuel Sandoval (Guest)|how do I solve this trigonometric equations system%3F|Hello%3A%0A%0AI am trying to solve this system%3A%0A%0AA%2Acos%28x%29 %2B B%2Asin%28y%29 %3D C%0AD%2Asin%28x%29 %2B E%2Acos%28y%29 %3D F%0A%0AI have t||30||2
732|5|alexb|06/28/2010|07:14:16|Kenneth Ramsey (Guest)|Novel Square Triangular Nos. Generalization%3F|Certain triangular numbers are also square numbers%3A e.g. T%288%29 %3D 36 %3D 6%5E2%2C T%2849%29 %3D 1225 %3D 35%5E2. It is well known that the argum||1||1
656|0|Bui Quang Tuan|06/08/2010|13:29:44|Bui Quang Tuan|Vertex Next Side Midpoint Quadrilateral|Dear All My Friends%2C%0D%0AGiven convex quadrilateral X1X2X3X4.%0D%0AY1%2C Y2%2C Y3%2C Y4 are midpoints of sides X1X2%2C X2X3%2C X3X4%2C X4X1 respect||178||15
731|2|alexb|05/31/2010|18:15:48|Bractals|Vector Sum|The following seems obvious%2C but how do you prove it%3F%0A%0AThe sum of the n vectors that start at the center of a regular n-gon and end at a verte||2||1
730|0|girl_honey|05/22/2010|22:12:34|girl_honey (Guest)|infinite probability|hi i am having trouble with the following question%2C wondering if someone can help me%2C thanks in advance%0A%0AQ. if i have a very large number of p||2||2
729|2|alexb|05/04/2010|12:31:48|Bractals|Compass Alone Constructions|On the page %22Geometric Construction with Compass Alone%22 can the constructions be done with a collapsible compass%3F ||1||1
728|0|alexb|03/17/2010|20:02:25|Ralphbne|Probability%2FStats question|Suppose that I sample from some unknown continuous distribution. I know that the draws are iid%2C but the distribution itself is unknown. However%2C I||3||1
727|0|alexb|03/11/2010|18:26:59|johnm_12|Acute angled triangles|If an acute angled triangle has sides of length x%2C y and z%2C where x%3C%3Dy%3C%3Dz%2C show that the corresponding angles%2C X%2C Y%2C and Z%2C can ||8||3
726|0|alexb|02/15/2010|00:43:39|Ralphbne|Strange question in probability....|Suppose 1%2F2 0. Let sigma%3Dbet%2F%281-delta%29.%0A%0ALet x0%3Dsigma%2F2. %0A%0AWith probability 1%2F2%2C x_%28k%2B1%29%3Dmin%28x%2Fdelta%2C sigma%29||7||1
724|3|Travis|01/27/2010|21:48:19|Travis (Guest)|Probability| The question that I am faced with%2C and am apparently way over my head with is%3A given a spinner numbered 1-10 and assuming that this spinner will ||6||2
723|0|newzad|01/03/2010|00:39:36|newzad|Impossible right triangle%3F%2C newzad%27s theorem|Hi Alexander%2C%0AYour web site is great. %0A%0AMy problem is I want to know that is this right triangle possible%3F %0A http%3A%2F%2Fi47.tinypic.com%||0||0
722|2|alexb|10/26/2009|07:26:41|alan b (Guest)|tractrix|I have a question about the tractrix curve. %0A%0AThe pseudosphere or tractroid surface%2C the surface of revolution based on the tractrix%2C is suppo||2||1
721|2|alexb|09/17/2009|09:06:00|Bractals|Steiner Construction II|Why does the logic of the theorem at%0A%0Ahttp%3A%2F%2Fwww.cut-the-knot.org%2Fimpossible%2Fstraightedge.shtml%0A%0Anot apply to a construction%2C with||8||3
718|0|Peter Scales|08/20/2009|08:58:23|Bui Quang Tuan|Maximal Area Right Triangle In Circular Segment|Dear All My Friend%2C%0A%0AA%2C B are two points on a circle %28O%29. There are two arcs AB and two circular segments AB but we choose the small one.%||31||6
719|0|alexb|08/11/2009|12:19:03|Bractals|Steiner Construction|Given two parallel lines and a line segment.%0A%0AIs it possible to construct the midpoint of the line segment using a straightedge only%3F||21||7
720|0|alexb|08/11/2009|12:06:50|SOL WARDA (Guest)|YOUR PAGE%3A IMPLEMENTATION OF BASE CONVERSION|Hello People%3A%0A%0A  On this page your author is trying to explain how to convert Binary system to Decimal system %26 claims that simple substituion||3||1
717|0|alexb|07/01/2009|18:59:58|Olivier (Guest)|A mistake in Bear Cubs Problem%3F|Dear sir%2C%0A%0AAs a former math researcher turned teacher%2C I enjoy your website tremendously.%0A%0AI may have misunderstood the statement%2C but I||2||1
716|0|alexb|06/10/2009|06:27:49|qassim issa (Guest)|permutations without repetition|hi%2C%0Ado you have a method how to count Permutations  from 1..n that do not%0Ahave the same combination in it%3A like%0Aif we have the numbers 1%2C2||8||9
714|4|alexb|05/22/2009|13:37:11|Creative|A Problem on an Infinite Checkerboard|Hi everyone. I hope i%27m posting this in the right section.%0A%0AOn the website there is A Problem on an Infinite Checkerboard which I have found int||9||5
715|2|alexb|05/22/2009|10:48:13|Bractals|Trig Inequality|How do you prove the following%3F%0A%0AIf A%2C B%2C and C are the interior angles of a triangle%2C then%0A%0AcosA %2B CosB %2B cosC %3C%3D 3%2F2.||3||1
495|2|Ruben Hogenhout|05/16/2009|21:55:11|mr.redpants|can you quinsect%3F|Please relocate if this isn%27t the proper forum.%0D%0A%0D%0AI teach a high school math course and we have been working on fermat primes%2C unmarked s||127||6
713|2|alexb|05/01/2009|20:36:22|ugur (Guest)|complex numbers|Hello%2C i want to ask something about the lemma on this page.%0Ahttp%3A%2F%2Fwww.cut-the-knot.org%2Ffta%2Fvaggione.shtml%0A%0Ahere%2C b is a complex ||1||1
712|2|alexb|04/11/2009|12:19:29|KMGC (Guest)|Conjugate Diameter|In %22 %22%2C conjugate and transverse axes are noted%2C regarding oblate and prolate spheroids%2C which agrees with the definition of  .%0ABut%2C bac||5||1
711|2|Akash Kumar|04/10/2009|23:00:40|Akash Kumar|Puzzle...Recurrence to aid%3F|Demon%27s Dungeon%0A%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%0A%0ASource - I %22did not%22 know the source. At least%2C I did not before I pos||20||8
709|0|alexb|03/13/2009|09:18:04|Bui Quang Tuan|Area Ratio With Vertex Next Side Midpoint Segments|Dear All My Friends%2C%0A%0AGiven convex quadrilateral ABCD%0AE%2C F%2C G%2C H are midpoints of AB%2C BC%2C CD%2C DE%0AM%2C N%2C P%2C Q are midpoints ||14||2
701|0|jay_shark|02/26/2009|12:32:58|jay_shark|disjoint sets|Hey Alex%2C here is an interesting problem taken from 2001 Israel Binational mathematics competition problem 6. %0D%0A%0D%0AYou have 32 natural number||93||12
708|3|George|01/31/2009|11:45:04|George (Guest)|Union of components in Riemann sphere is closed|The following is an exercise from page 32 of the 1952 edition of the book Analytic Functions by Stanislaw Saks and Antoni Zygmund %28it is freely avai||6||2
468|3|alexb|01/28/2009|09:25:05|Michael Klipper|Units in Polynomial Rings|Hello everyone.  I%27ve been rereading one of my algebra textbooks and got stuck on this problem.  I am told to assume that R is a commutative ring wi||221||4
702|2|alexb|01/24/2009|23:17:58|Bryan|Diameter%2Fcircumference ratio on sphere%27s surface|%0D%0AHi%2C%0D%0A%0D%0AAm seeking help towards a problem that has occurred to me but is beyond my current skill-set. %0D%0A%0D%0AOn the Euclidean plan||19||3
707|0|august|01/24/2009|23:11:34|august (Guest)|disproof of a formula|Quoted from Wikipedia%3A %93Kurt G%F6del showed in 1940 that the continuum hypothesis %28CH for short%29 cannot be disproved from the standard Zermelo||0||0
706|0|alexb|01/23/2009|10:34:49|PhilipOakley|Angle as a unit in complex exp%28%29 functions|I am researching the usage and distinction of angular measure from linear measure and how it impacts the complex exponential functions%2C especially f||8||3
705|0|alexb|01/18/2009|18:00:18|Vladimir (Guest)|Sangaku generaization|Sangaku problem at http%3A%2F%2Fwww.cut-the-knot.org%2FCurriculum%2FGeometry%2FInversionInCircleAndIsosceles.shtml %3A%0A%0A%28O%29%2C %28P%29 are cir||4||1
704|3|jay_shark|12/25/2008|10:55:39|FAshepard|probability question|I have a problem understanding this example.  A assuming be is 2%2F11 or .1818 but P%28A%7CB%29 %3D P%28A%26%238745%3BB%29 %2F P%28B%29  hoe do I calc||8||1
525|0|alexb|12/22/2008|07:44:37|mr_homm|K_3%2C3 graph|I was just looking at the %5Blink%3Awww.cut-the-knot.org%2Fdo_you_know%2F3Utilities.shtml%7Cbipartite graph page%5D%2C and I noticed a different way t||99||4
703|0|alexb|12/01/2008|19:44:00|Pierre Charland|Ant on Dicube %28error%3F%29|Problem M19a on p58 and p71 %28in %22The mathemagician and pied puzzler%22 by Elwyn Berlekamp and Tom Rogers%29 ask for the point further away %28on t||10||1
526|0|hs|11/27/2008|22:48:15|tvarhegyi|A geometry problem from N.A. Court|Hello%2C%0D%0AI have found a problem in College Geometry by N.A. Court%2C Page 29.%0D%0Aand making very little progress in solving it. Can someone hel||181||7
698|0|alexb|11/20/2008|12:47:00|Bui Quang Tuan|A Particular Triangle|Dear All My Friends%2C%0D%0AWhat we can say about isosceles triangle ABC %28AB %3D AC%29 in which AD %2B DB %3D BC here D is intersection of side AC a||77||2
700|0|alexb|11/09/2008|18:52:30|WiZaRd|How to prove that the following set is finite%3F|Hello. It is possible to prove that the following set %0D%0A%0D%0AA%3A%3D%7Bx in N %7C 0%3C%3Dx%3C%3Dn%7D%0D%0A%0D%0Ais finite%3F%0D%0A_______________||63||7
699|3|alexb|10/09/2008|12:20:51|Cathy Gordon|Vincenty Formulae %26 Common Tangents to Two Circles|In %3Chttp%3A%2F%2Fwww.cut-the-knot.org%2FCurriculum%2FGeometry%2FTangentTwoCirclesI.shtml%23explanation%3E%2C is it possible to derive point U%2C usi||80||1
697|0|alexb|10/07/2008|21:44:34|shane|how do we construct golden triangles%3F|i find golden triangles interesting. i want to study them closely.%0D%0Asadly%2C i can%27t construct one cause all i know is the angular measurement o||59||1
696|2|alexb|10/01/2008|12:52:38|jack202|Build ABC from OHI|Looking at%0D%0Ahttp%3A%2F%2Fwww.cut-the-knot.org%2Ftriangle%2Findex.shtml%0D%0A%0D%0AI was asking myself how to find the vertices of ABC%2C with%0D%0||102||3
694|0|Bui Quang Tuan|09/16/2008|23:42:43|Bui Quang Tuan|Five Concyclic Points|Dear All My Friends%2C%0D%0AGiven two lines L1%2C L2 intersect each other at X. %0D%0AM%2C N are two points on L1. P%2C Q are two points on L2.%0D%0A%||715||6
695|0|august|09/10/2008|07:23:10|august|function centroid as mean|Prove that%2C assuming that p%28x%29 is continuous and p%28x%29%3E%3D0 for all x%2C%0D%0Aif%0D%0A%2A Integrate%3Cp%28x%29%2C %7Bx%2C-Infinity%2CInfini||226||4
693|3|Pierre Charland|09/05/2008|06:57:30|reidan|difficult mathematics induction proofing|hai%2C i just knew this web yesterday%2C while searching some clue to finish my discrete mathematics homework%2C%2C%0D%0A%0D%0Aand i really need help.||240||2
692|0|Pierre Charland|09/01/2008|06:52:38|WiZaRd|Coxeter Introduction to Geometry|Hello%21%0D%0A%0D%0AI%27ve started to read %22Coxeter - Introduction to Geometry%22 and I%27ve encoutered a problem at page 5 %28link to the book%3A h||287||5
688|0|Bui Quang Tuan|08/21/2008|09:23:35|Bui Quang Tuan|Two Equilateral Triangles - Seven Concyclic Points|Dear All My Friends%2C%0D%0APoint B is on segment AC. Construct two equilaterals triangles XAB%2C YBC on one side of segment AC. Please prove followin||171||9
690|0|Bui Quang Tuan|08/20/2008|08:35:35|Bui Quang Tuan|New Dissection Of Square Into Six Parts %3F|Dear All My Friends%2C%0D%0AI suggest here one Pythagorean theorem proof by dissection of square into six parts. Suppose ABC is right triangle with ri||113||4
691|0|Bui Quang Tuan|08/19/2008|08:17:25|Bui Quang Tuan|Proof Of Pythagorean Theorem By Translation|Dear All My Friends%2C%0D%0ASuppose ABC is right triangle and AB is hypotenuse%2C BC%3C%3DAC. I suggest here one proof of Pythagorean theorem by trans||86||2
689|0|Bui Quang Tuan|08/19/2008|13:53:12|Bui Quang Tuan|New Pythagorean Theorem Proof %3F|Dear All My Friends%2C%0D%0ASuppose ABC is right triangle with side lengths a%2C b%2C c and AB %3D c is hypotenuse. CH is altitude from C to AB. Denot||93||6
687|0|alexb|08/02/2008|09:17:58|Bui Quang Tuan|Ceva Theorem By Signed Circumradii|Dear All My Fiends%2C%0D%0A%0D%0AGiven triangle ABC with side lengths a%2C b%2C c and A%27%2C B%27%2C C%27 are points on sidelines BC%2C CA%2C AB resp||66||1
686|2|alexb|07/22/2008|20:23:32|Manuel|Central Limit Theorem proof problem|Hello%3A%0D%0A%0D%0AI%27m trying to proof the Central Limit Theorem. Unless you have a better suggestion%2C what I%27m doing is show that the moment f||34||1
685|0|JJ|07/14/2008|10:50:29|Pytheus|trisection of an angle|http%3A%2F%2Fuk.youtube.com%2Fresults%3Fsearch_query%3Dtrisecting%26search_type%3D%26aq%3Df%0D%0Ais the link to what seems impossible. Where%27s the c||33||2
684|0|Ralph|07/01/2008|11:26:35|Ralph|Statistical estimation question|Suppose I am sampling from one of two distributions. I know that%2C given a distribution%2C the samples are drawn in an independent way. One of the po||22||2
683|3|alexb|06/27/2008|06:58:55|prathibha|fourier transform|Fourier transform of a function f%28x%29is defined as %0D%0AF%28k%29 %3D Integrate%5B%28 f%28x%29 Exp%28-i k x %29 %29%2C %7Bx%2C -Infinity%2CInfinity||36||2
682|0|alexb|06/03/2008|15:15:10|JoeGoolam|Euclids game|Enjoyed all these interesting games. I have a question regarding Euclid%27s game applet. I am trying to implement the same game using C%2B%2B and was ||31||1
681|0|alexb|06/02/2008|21:41:31|Dad|proof|Let A be a set and let D be the set of all bijections from A to itself.  Define a relation %7E on D by f%7Eg  %3C%3D%3D%3E %26%238707%3Bh%26%238712%3B||37||3
425|0|Pierre Charland|05/26/2008|14:20:20|idavis1|A Riddle|My logic teacher gave our class a riddle and normally I don%27t care much for riddles but I was perplexed and have been tihnnking constantly about it.||678||34
680|2|Manuel S.|05/16/2008|15:55:03|Manuel S.|Need details on a part of Proof of Descartes Sign Rule|Hello%3A%0D%0A%0D%0AIn the article that proves Descartes%27 Rule of Signs%3A%0D%0A%0D%0Ahttp%3A%2F%2Fwww.cut-the-knot.org%2Ffta%2FROS2.shtml%0D%0A%0D%||28||2
679|0|alexb|05/10/2008|11:09:17|ke_45|Deriving functions based on differences|Hi%0D%0A%0D%0AIf I had the following%3A%0D%0A%0D%0A    f%28n%2B1%29 - f%28n%29 %3D %282%B7n - 1%29%B2%0D%0A%0D%0A...what techniques would I use to fig||33||1
677|0|alexb|04/15/2008|21:18:30|Akash Kumar|Nim Games - a query|Hi All%2C%0D%0A%0D%0AI went through the nim games page on this site. I had a recollection of having gone through it before as well.%0D%0A%0D%0AWell%2C||86||1
676|0|gd88|03/29/2008|11:28:10|gd88|Projective Geometry|The Pojective Geometry is a %22Non Euclidean Geometry%22%3F%0D%0AWhen I say %22Non Euclidean Geometry%22 I think Hiperbolic Geometry or Elliptic Geome||60||4
675|0|alexb|03/17/2008|09:28:56|Ralph|Another differential equation|One of my advisors is asking me if I know whether such a differential equation has a closed form solution. %0D%0A%0D%0Ay%26%238242%3B%26%238242%3B%28t||103||1
674|0|alexb|03/07/2008|11:54:23|Bui Quang Tuan|Four%2C Five Then Nine Point Circles|Dear All My Friends%2C%0D%0AIn %22Concyclic Points in a Triangle%22 there are four concyclic points related altitude and angle bisector from vertex A.||124||4
673|3|gd88|03/03/2008|15:30:38|gd88|Induction proof of Cauchy-Schwarz inequality|Good evening.%0D%0AI%27m a new member. I can%27t speak english very well%2C for this reason I write short.%0D%0AI have been looking through the intern||84||3
671|0|alexb|02/17/2008|08:35:14|Bui Quang Tuan|Three Congruent Circles By Reflection In Pedals|Dear All My Friends%2C%0D%0AGiven triangle ABC%2C one any point P with its pedal triangle PaPbPc.%0D%0ABa %3D reflection of B in Pc %28or PPc%29%0D%0A||147||1
462|0|Pierre Charland|02/16/2008|22:38:27|Jeff Jencks|tetrahedron to sphere calculation|My primary question is%3A If you put a tetrahedron inside a sphere in such a way that the four points of the tetrahedron are on the surface of the sph||459||5
666|0|alexb|02/13/2008|11:13:48|Bui Quang Tuan|Two Congruent Circles From Reflections|Dear All My Friends%2C%0D%0AGiven triangle ABC with incenter I and X is any other point.%0D%0ABi %3D reflection of B in AI%0D%0ABx %3D reflection of B||189||11
667|0|alexb|02/03/2008|21:29:58|Greg Markowsky|Hard Geometry problem|Anyone know how to do this one%3F%0D%0A%0D%0Ahttp%3A%2F%2Fwww.geocities.com%2Fgregm112358%2FHard_sudoku.pdf%0D%0A%0D%0AI know how to do it by brute fo||141||1
670|3|alexb|02/03/2008|12:25:15|Kozi12|Triangle 80-80-20|I Need help %21%21 I need some1 who will make for me Triangle 80-80-20 Variant 30-40 %21%21 I CAN%27T do that %3A%28 so some1 can help me %3F%3F||118||1
669|0|Bui Quang Tuan|02/02/2008|08:27:09|Bui Quang Tuan|Infinite Of Congruent Circles From Translations|Dear All My Friends%2C%0D%0AGiven triangle ABC and two different points P%2C Q as a vector v %3D PQ.%0D%0AOa %3D translation of A by vetor v. Similarl||113||0
668|0|Pierre Charland|02/01/2008|21:41:43|Pierre Charland|pi%28x%29 %2C pq%28x%29 %2C %28p%2Cq both primes%29|I%27m looking for info on the distribution of numbers of the form n%3Dpq%2C where p and q are both primes.%0D%0A%0D%0AFor number of the form n%3Dp%2C ||127||1
665|2|mr_homm|01/23/2008|18:38:04|Ralph|Stumped by differential equation|I am assigning an economics problem to my undergrads%2C and I have reduced the problem to a differential equation which I do not know how to solve.  I||182||5
662|0|Pierre Charland|01/20/2008|08:08:04|BenVitale|Discrete logarithm problem|They say that the Discrete logarithm problem is supposed to be very difficult to solve. Here%27s an example%3A %0D%0A%0D%0AGiven the primitive element||159||2
664|3|Pierre Charland|01/19/2008|13:04:55|Marie-Jo W.|Puzzle involving exponential|Dear Puzzle Friends%2C%0D%0A%0D%0AI am not a mathematician but just a math puzzle enthusiast... I placed a month ago an adaptation of an old math prob||175||7
663|3|Paul_B|01/01/2008|18:46:52|Paul_B|Virginia Tech Regional Mathematics Contest|I have been struggling unsuccessfully with problem 5 %28below%29 from the%0D%0A29th Annual Virginia Tech Regional Mathematics Contest October 27%2C 20||121||5
660|0|alexb|12/04/2007|13:18:56|Bui Quang Tuan|Simple Area Facts In Parallelogram And Quadrilateral|Dear All My Friends%2C%0D%0ATwo following triangle area facts in parallelogram and quadrilateral are very simple and equivalent%3A%0D%0A%0D%0A1. Given||115||10
661|0|Bui Quang Tuan|12/02/2007|22:02:26|Bui Quang Tuan|Golden Ratio Hexagon|Dear All My Friends%2C%0D%0ARecently we discuss about Prasolov%27s problem with %22Golden Ratio Pentagon%22. I suggest here one %22Golden Ratio Hexago||58||3
648|2|Bui Quang Tuan|11/29/2007|09:36:01|sarathian|A challenging %27problemuzzle%27 involving a peculiar pentagon.|Let ABCDE be a convex but irregular pentagon such that each of the five peripheral triangles ABC%2C BCD%2C CDE%2C DEA and EAB has equal area %2C say x||144||8
659|0|alexb|11/15/2007|01:14:14|alexb|triangle of minimal area|Among all triangles circumscribed around a given circle the equilateral one has the smallest area.%0D%0A%0D%0AProof%3A%0D%0A%0D%0AWith S - area%2C p -||57||2
657|0|alexb|11/11/2007|01:34:22|Greg Markowsky|Geometry challenge|Here%27s another challenge for those so inclined.%0D%0A%0D%0Ahttp%3A%2F%2Fwww.geocities.com%2Fgregm112358%2FInscribed_circles.pdf||83||2
658|2|alexb|11/10/2007|01:00:41|Ralphbne|Measure theory Q|I seem to remember from a measure theory class a long time ago something about the following result. My memory may be totally wrong.%0D%0A%0D%0AIs it ||56||1
655|0|alexb|11/01/2007|18:14:58|megatron1|related  rates with cone lying on side instead of apex down.|I have an interesting and challenging take on the old related rates problem involving a cone being filled with water. %0D%0A%0D%0ASuppose a cone with ||46||1
651|0|alexb|10/30/2007|20:12:27|Greg Markowsky|Geometry challenge|Anyone who would like to do a Euclidean geometry problem%2C please look at the following link and let me know what you think.%0D%0A%0D%0Ahttp%3A%2F%2F||208||27
653|0|sbjnyc|10/30/2007|08:11:46|Akash Kumar|Rational and Irrational - Continued fractions|Hello everybody%2C%0D%0A%0D%0AFor quite a long time i did not know how to untie the definition of rational and irrational numbers from base 10.%0D%0A%||61||2
654|2|alexb|10/27/2007|18:14:54|fasttalkerchat|intersection of sinA and xsinA|i was woindering how it is possible to find the points of intersection of Sin%28theta%29 and 12Sin%28theta%29.%0D%0APlz help%21||59||1
652|0|Bui Quang Tuan|10/15/2007|13:49:12|Bractals|Semiperimeter and Circumradius Inequality|I have checked this out with Sketchpad%2C but I%27m stumped on how to prove it.%0D%0A%0D%0AFor an acute triangle%2C s %3E 2R.%0D%0A%0D%0AAny help will||73||3
650|0|The Mask|10/09/2007|09:02:49|The Mask|Recreational Combinatorics|There is a wire stretching infinitely long in both directions. And there two species of birds - yellow and green- who happen to sit on it.%0D%0A%0D%0A||68||3
396|2|alexb|09/24/2007|11:35:42|ossipoff|Brief elllipse%2Fconic section proof%3F|%0D%0AI%27ve seen the proof%2C using 2 inscribed spheres%2C that when a plane intersects a cone in a way that the intersection is a closed curve%2C th||180||4
649|0|alexb|09/23/2007|08:50:17|Akash Kumar|The revenge of the Birthday Paradox|I dont know whether the title i chose for this subject sounds right to you or not but i am absolutely convinced that it sounds right to me. %0D%0A%0D%||65||1
647|0|Akash Kumar|09/07/2007|09:34:49|Akash|Recursion - or no recursion|The problem below was on IBM ponder this challenge in August..Now that they have posted the solution%2C i feel it is not wrong posting this problem he||70||2
646|0|Bui Quang Tuan|09/04/2007|08:41:31|Bui Quang Tuan|Six Concyclic Orthocenters|Dear All My Friends%2C%0D%0AGiven triangle ABC and one point P with pedal triangle PaPbPc.%0D%0AAp%2C Bp%2C Cp are reflections of P in BC%2C CA%2C AB ||48||1
643|0|alexb|08/24/2007|07:13:20|Akash|The amazing book of squares|The following is a puzzle from the book of squares authored by fibonacci somewhere in 1200%27s...Though it has gone old%2C it still has its power.%0D%||50||1
641|0|MichaelD|08/20/2007|23:34:42|MichaelD|Geometry article illustrating discovery function of proof|My homepage has been updated with the following article of mine %22A hexagon result %26 its generalization via proof%22%2C The Montana Mathematics Ent||35||1
642|2|alexb|08/20/2007|07:49:41|stu|Continuous function differentiable at its end points%3F|Let a function from %5B0%2C1%5D %28closed interval%29 to R be defined as f%28x%29%3Dx. Nothing else is mentioned. The function is clearly differentiab||40||1
634|0|alexb|08/15/2007|22:26:21|Bui Quang Tuan|A Present For Archimedes|Dear All My Friends%2C%0D%0AIt is very well known that after discover of a method to determine the purity of new gold crown for King Hieron%2C Archime||189||18
640|0|mpdlc|08/08/2007|19:53:57|Jeremy|Toroidal Helix Problems|It is an unfortunate fact for me that I am far better at posing interesting problems than I am at solving them. So I hope that one of you whiz-bang pe||63||8
639|2|Bractals|07/25/2007|20:00:08|Bractals|Intersecting tangent circles|Given the following four circles%5Bpre%5D%0D%0A  %28x-a%29%5Bsup%5D2%5B%2Fsup%5D %2B y%5Bsup%5D2%5B%2Fsup%5D %3D a%5Bsup%5D2%5B%2Fsup%5D%0D%0A%0D%0A  ||54||2
637|3|mpdlc|07/23/2007|23:05:52|jason z|programmatically find eqns of tangent lines to 2 circles|In reference to this page%3A%0D%0A%0D%0Ahttp%3A%2F%2Fwww.cut-the-knot.org%2FCurriculum%2FGeometry%2FTangentTwoCirclesII.shtml%0D%0A%0D%0A%0D%0AI%27d l||56||10
638|2|alexb|07/23/2007|07:55:46|Oystein|Voting power of a player in a weighted voting system|Dear all%2C%0D%0A%0D%0ASometimes I work with joint ventures and voting rules. There has been many discussions on how to change the voting rules when a||38||1
635|3|alexb|07/12/2007|14:57:44|Gina|Ptolmey%27s theorem|Why when proving this theorem do you add the two identies together%3F||50||1
632|2|Greg Markowsky|06/26/2007|07:25:07|Greg Markowsky|Credit to Archimedes|Hello%2C%0D%0A%0D%0AI%27ve seen on this site and in other places various things attributed to Archimedes%28e.g. Stewart%27s Theorem%2C Broken Chord Th||72||2
633|0|alexb|06/24/2007|08:07:18|Bui Quang Tuan|Generalization Of Interesting Lemma|Dear Alex%2C%0D%0A%0D%0AThank you very much for very interesting remark about %22Generalization Of Van Schooten%27s Theorem%22. It is not easy to iden||105||8
622|0|alexb|06/22/2007|22:06:36|Greg Markowsky|Challenge problems|Hi all%2C%0D%0A%0D%0AI made up a couple of problems. If anyone wants to try them%2C check out%3A%0D%0A%0D%0Ahttp%3A%2F%2Fwww.umcs.maine.edu%2F%7Emarko||260||21
631|2|alexb|06/16/2007|16:23:54|tonytb|Construct a tangent to an ellipse%3F|A recently mailing from MAA asked about showing the origin-focus distance was the geometric mean of lengths of the tangent to the major axis and the  ||62||1
630|0|Bractals|06/13/2007|17:59:40|Bractals|Questions about real numbers|Real numbers are defined as the limits of convergent series of rational numbers.%0D%0A%0D%0A   A %3D lim%28n-%3Eoo%29%7Bsum%28i%3D1%2Cn%2Ca_i%2F10%5Ei||60||2
627|0|melefthe|06/11/2007|15:49:30|melefthe|Probability|Astronomers reckon that%2C say%2C 1.000 stars in the visible universe are capable of carrying life on them. They randomly selected 50 stars %28without||90||2
612|0|Pierre Charland|05/27/2007|19:21:30|melefthe|Mahavira%27s formula for cyclic quadrilaterals|Does anyone know the proof of Mahavira%27s formulae for the calculation of the inner diagonals of the cyclic quadrilaterals%3F Presumably%2C they must||108||6
628|0|alexb|05/20/2007|14:34:05|Bill McEachen|http%3A%2F%2Fwww.cut-the-knot.org%2Fdo_you_know%2FProductAndSum.shtml|I definitely could be wrong%2C but doesn%27t the stronger statement apply for summing%3A%0D%0Aevery composite can be expressed as the sum of a lone pr||53||1
613|2|JJ|05/09/2007|06:01:26|Alan|infinite sum over rational function|Is there any sort of general method for evaluating an infinite sum of an arbitrary rational function%3F For example%2C sum 1%2Fn diverges%2C but the a||76||2
619|2|TefJLives|05/07/2007|17:47:33|Greg Markowsky|Pictures on this site|Hello%2C%0D%0A%0D%0AHey%2C great site. I would like to ask the moderator what software he uses to draw the pictures on this site%2C as they look a lot||43||2
616|3|alexb|05/07/2007|19:21:07|Cory H|Incredibly lost in Mathematical Induction|ok so I feel completely stupid about this%2C but I am far beyond conventionally lost. I have two questions %28at least one of them using Mathematical ||68||1
611|0|alexb|05/07/2007|06:34:35|Catalin Mates|Nim on a sequence of cells|  Hello%2C can anybody tell me how cand this game be reduced to the classical Nim game%3F%0D%0A  We have an array with K cells. We also have N black p||51||1
618|0|nkumar|05/07/2007|09:36:44|nkumar|A %27conjecture%27 on partitioning convex polygons|Hi%2C%0D%0A%0D%0AWe have neither a proof nor a counter example for the following claim.%0D%0A---------%0D%0A%22For N any positive integer%2C any conve||53||0
610|0|mr_homm|03/29/2007|20:06:13|james3760|Converting Base Numbers|I%27m lost.%0D%0A%0D%0AI%27m trying to reverse convert two numbers to figure out what the base conversions are and frankly I%27m lost.%0D%0A%0D%0AI ha||43||2
604|0|Sumudu|03/26/2007|06:36:23|melefthe|Fagnano%27s formula for %F0|Has anyone seen the proof of Fagnano%27s formula for pi%3F It%27s so bizarre yet so beautiful. %D0%3D2ilog%5B%281-i%29%2F%281%2Bi%29%5D. How did he th||81||2
609|3|alexb|03/23/2007|23:04:15|maaranda|MATH|I have a questions with item %238 on this website %28Reflection in line%29.%0D%0A%0D%0A%238 states%3A%0D%0A%0D%0AThe order of reflection matters%2C tw||34||1
602|0|alexb|03/13/2007|23:25:35|melefthe|A %28Comprehensible%29 Proof of Descartes Theorem|Has anyone ever thought of the Descartes problem rediscovered by F. Soddy%3F Given three mutually tangent circles there is a smaller internal fourth c||126||5
607|0|mr_homm|03/05/2007|15:17:10|Jim|Expectation of a function|Hi%2C%0D%0A%0D%0AI am looking at the following problem.%0D%0A%0D%0AE%5B 1%2F%28x%5ET A x%29 %5D%0D%0A%0D%0AA is diagonal N%2AN%0D%0Ax is a column vect||61||1
605|0|alexb|02/26/2007|12:26:34|Kenneth Ramsey|Coaxial Polygons of the same area|If a coaxial regular n%2B1 sided polygon overlies a regular n-sided polygon of the same area%2C would a rotation of one about its center change the ar||61||1
603|2|alexb|02/25/2007|08:09:44|generic name|Standard notation for the set of nonnegative reals|It struck me that while R%2B is very commonly used for the positive reals - see%2C e.g.%2C http%3A%2F%2Fmathworld.wolfram.com%2FR-Plus.html - I%27m le||64||1
601|0|alexb|02/15/2007|06:46:24|student|Isoperimetric Theorem|The nice article on %22Isoperimetric Theorem%22%0D%0A%0D%0A     http%3A%2F%2Fwww.cut-the-knot.org%2Fdo_you_know%2Fisoperimetric.shtml%0D%0A%0D%0Aprove||79||1
378|3|alexb|02/11/2007|23:48:33|Jodi|Pythagoras theory|Hi there I just dropped by to ask if you can tell me please%3A%0D%0A%0D%0ACan you use Pythagoras theory to create a triangle with a perfect right angl||260||8
455|3|DHiersekorn|02/03/2007|13:40:45|Sam|Birds on a Wire|The Birds on a Wire question you have on this site is quite amazing%2C and the applet you have set up does a really good job of arriving at the answer||657||25
435|3|alexb|01/28/2007|23:40:38|Renee Lon|1-1 corrrespondence|I have been working on the poem the ten weary travelers.  I believe that you use a 1-1 correspondence to solve it%2C but I am not sure I have it exact||147||3
600|2|Pierre Charland|01/18/2007|11:50:23|xs|are there Alexander polynomials %3F|Hello%2C%0D%0A%0D%0AAre there Alexander polynomials for knots besides the trefoil and four knot%0D%0A%0D%0AFor the trefoil it is x%5E2-x%2B1%0D%0A%0D%||56||2
559|0|Pierre Charland|12/29/2006|18:53:11|alan|trig values|I%27m trying to figure out how to solve the 5th problem of the week from Purdue University %28http%3A%2F%2Fwww.math.purdue.edu%2Fpow%2F%29%2C and I ca||161||5
598|0|Pierre Charland|12/23/2006|08:06:40|Prav|Regarding Monty Hall Problem|I do not agree with the solution provided by Marilyn vos Savant.%0D%0A%0D%0AThe problem is such that the event has already occured%2C ie the door with||66||1
555|3|Pierre Charland|12/19/2006|18:03:27|Kathy|math|trying to solve a problem...%0D%0A%0D%0Ahow do you get the numbers..%0D%0A%0D%0A%0D%0A17%2C14%2C9%2C4%2C2%0D%0A%0D%0Ato equal 2%0D%0A%0D%0Aonly using ||137||5
596|0|oniwaka|12/13/2006|15:16:51|oniwaka|a %3D sin%28f%28x%29 %2A n%29%3B n %3D %3F%3F%3F|I%27m being haunted by this problem%21  My only solution at this point is the dirtiest of programmers tricks%28the lookup table%29%2C which is workabl||72||2
583|5|alexb|11/24/2006|06:40:42|VENKAT RAMAYYA|GEOMETRY|PLEASE KINDLY THROW SOME LIGHT ON THE BASIC PRINCIPLE INVOLVED IN INSCRIBING AN ELLIPSE INSIDE A REACTANGLE USING OBLONG METHOD.||116||3
594|5|MichaelD|10/29/2006|23:22:03|MichaelD|A Generalization of Spieker circle %26 Nagel line|Some here may be interested in the update of p. 4 of my Homepage at%0D%0Ahttp%3A%2Fmysite.mweb.co.za%2Fresidents%2Fprofmd%2Fhomepage4.html with an%0D%||51||0
591|3|alexb|10/24/2006|06:37:29|Vatanden|Trying to understand the Blithe 12 proof|The Blithe 12 proof on this site %28http%3A%2F%2Fwww.cut-the-knot.org%2Fdo_you_know%2Fblithe12_proof.shtml%29 fascinates me%2C but there is one measly||78||5
590|2|alexb|10/18/2006|14:03:42|Hunter101|Dominos and Nim Values|How can I work out the Nim values of the starting positions in the following domino game%3F  I have no idea where to start.%0D%0A%0D%0AThe game board ||52||1
589|0|a3t|10/11/2006|13:58:55|a3t|Matrix of Weingarten map%3F|Hey guys%2C %0D%0A%0D%0ASay I have a map S from R%5E2 -%3E R%5E3 defined by %0D%0Af%28u%2Cv%29%3D%28u.cos%28v%29%2C u.sin%28v%29%29 %0D%0A%0D%0AHow do||57||0
588|0|alexb|10/04/2006|16:07:49|Venkat Ramayya|CONICS|I have a doubt.%0D%0A%0D%0AIs it possible to get rectangular hyperbola when we cut a cone with a section plane parallel to axis of the cone with any d||79||4
587|0|alexb|09/17/2006|08:53:31|crewman1973|Two 3%27s|i HAVE A PUZZLE i NEED SOME HELP ON.  PLEASE HELP%21  hERE IS THE QUESTION%3A%0D%0A%0D%0AONLY USING TWO 3%27S%2C HOW DO YOU GET A TOTAL OF 20%3F aNY M||107||1
586|2|Fernando Sanz|08/30/2006|19:33:32|Fernando Sanz|non-bandlimited interpolation|Hello.%0D%0A%0D%0AI have been looking for a result on interpolation of non-bandlimited signals.%0D%0A%0D%0AIt is well known the WKS sampling theorem w||64||0
584|4|DK|08/28/2006|22:05:55|Dean|Bend tube to specific angle|I%27m looking for a formula where I can insert different numbers for diameter of a tube and angle needed but don%27t know what this is catagorized as ||75||2
585|4|mr_homm|08/27/2006|22:25:53|jellul|Using Spectral Analysis to update a PDF|Hi%2C%0D%0A%0D%0AI am currently investigating environmental time series and algorithms to  determine when an %27unexpected%27 event has occured in the||66||1
581|0|alexb|07/20/2006|15:17:43|calculus|is taylor series always accurate%3F|Taylor Series for f%28x%2Ba%29 is given by%0D%0A%0D%0Af%28x%2Ba%29%3Df%28a%29%2Bf%27%28a%29x%2Bf%22%28a%29%28x%5E2%29%2B.....%0D%0A%0D%0A%0D%0ANow con||99||1
580|0|mr_homm|07/20/2006|08:46:31|alan|spatial rotational dynamics|I%27m trying to learn about the dynamics of a body rotating in space about an arbitrary axis%2C which itself may also be rotating. Rotation about an a||81||2
578|3|alexb|07/19/2006|08:48:25|rahool|basic concepts of trignometry in brief|please explain the trignometry in brief as my foundatuon is not perfect||80||1
579|0|mr_homm|07/17/2006|09:01:23|Calculus|second derivative for maxima%2Fminima|hi everybody%2C%0D%0A%0D%0AI know that the second derivative should be checked for determining whether the point of inflection is maxima or minima. Ho||78||1
577|0|Jim|07/09/2006|20:22:18|Jim|matrix algebra|I am trying to solve a matrix optimization problem.%0D%0ACan anyone help in solving this%3F%0D%0A%0D%0AI need to maximize %7CAZB%7C%5E2%2B%7CAZC%7C%5E||115||3
576|4|Bractals|07/06/2006|20:01:39|Bractals|Circumcircle%2FIncircle Question|I%27m looking for a synthetic proof for the following.%0D%0A%0D%0ALet P and Q be the circumcircle and incircle respectively of an arbitrary triangle. ||86||2
575|2|Bractals|06/13/2006|06:40:25|Bractals|Is there a name%3F|Is there a specific name for the five triangles that have integer sides and whose area and perimeter have the same integer value%3F||101||3
404|3|alexb|06/12/2006|15:05:35|Jon|Levenshtein Distance|Hi%2C I%27m taking a look at Levenshtein distance for comparing two strings%2C and was wondering if %28and how%21%29 we can prove that it satisfies th||197||5
574|2|Bractals|05/22/2006|13:24:37|Bractals|Distance between circumcenter and incenter|Where would you find a proof that the distance d between the circumcenter and the incenter%2C the circumradius R%2C and the inradius r are related by ||86||2
573|0|alan|05/09/2006|13:12:25|alan|polynomial coefficients|I was trying to read through this%3A http%3A%2F%2Fwww.math.purdue.edu%2Fpow%2Fspring2006%2Fpdf%2Fsolution14.pdf and I don%27t understand where some of||88||2
572|0|mr_homm|05/07/2006|06:00:00|alan|torus-ray intersection|I%27m looking for information about finding the intersection point between a torus and a ray. Starting off its easy enough%2C substitute a ray equatio||71||3
558|2|DWCantrell|04/30/2006|15:18:52|Jupiter  |divergent series|The series  1 %2B 1%2F2 %2B 1%2F3 %2B 1%2F4 %2B  etc. is known to diverge very slowly.  I believe to get a sum of 10 you need close to 12%2C360 terms.||159||5
568|0|mr_homm|04/25/2006|15:38:00|Ignorant|Linear MMSE|Suppose%0D%0AY%3DAX%2BB%0D%0A%0D%0AY%2C B  M x 1 vector%0D%0AX     N x 1 vector%0D%0AA     M x N  Matrix%0D%0A%0D%0A%0D%0AX and B are random vectors o||82||1
570|3|mr_homm|04/25/2006|21:55:42|Jorge Zehl|Convolution|How does one prove that if f is in Lp%28Rn%29 %28the lebesgue space of order p%29 and g is in L1%28Rn%29 %28that is%2C g is integrable%29 then the p-t||62||1
571|2|Mark Huber|04/21/2006|07:12:13|houseoflogic|pieces of paper%2C probablity of largest in subset|You have a set of real numbers written on pieces of paper in a hat%2C all mixed up. You know how many pieces of paper there are %28call it N%29. You l||61||1
569|3|alexb|04/11/2006|19:44:53|MathGirl|Topology|Let p be a metric on a non -empty set X.%0D%0AShow that the function f defined by f%28a%2Cb%29%3D min%7B1%2Cd%28a%2Cb%29%7Dwhere a%2Cb is an element X||71||1
567|2|Mr Toad|04/09/2006|16:10:18|Jupiter|Mersenne numbers|I have been compiling a list of the Mersenne numbers %28all primes%29 as they are discovered. My list is a bit out of date%2C the last entry being M37||62||1
566|2|annie|04/05/2006|18:17:03|annie|Binomial Theorem and Prob%2FStats|Hi Ya%27ll%2C %0D%0A%0D%0AI%27m taking a self paced class through the mail.  I%27m working on a rough draft of this topic%3A %22Identify three roles t||70||0
565|2|Just curious|03/31/2006|11:02:53|Just curious|Different Gaussian %28normal function%29|Long time ago I wondered about the normal distribtion. Since it%27s based%0D%0Aon standard deviation as a measure of dispersion %2C can%27t a similar ||82||0
564|0|mr_homm|03/29/2006|19:25:52|jim|calculus of variations|Can anyone suggest a book for problems in calculus of variations.%0D%0APrecisely I would like to solve problem of following structure.%0D%0A%0D%0AMaxi||143||5
563|0|iliaden|03/26/2006|20:23:29|Teresa|Solution needed for a Logic Problem|Would you be able to tell me if you have the solution to this Logic Problem.%0D%0A%0D%0A%22Billy is twice as old as Sally was when Billy was as old as||110||2
561|3|Jim|03/26/2006|22:20:24|linda1x4x3|Functions of more than two varaibles|Suppose that f%28x%2Cy%2Cz%29 %3D 2x%5E3 %2B2y%5E2 %2B z%0D%0ACompute %0D%0Af%28x%2Bh%2C y%2Bk%2C z%2Bt%29 - f%28x%2Cy%2Cz%29%0D%0AThe answer is 6x%5E||103||4
562|0|mr_homm|03/13/2006|18:04:52|alan|spectral analysis question|I%27m trying to teach myself a little bit about fourier series and spectral analysis. I%27m using matlab to create a plot of the power spectrum of a s||111||8
560|2|mpdlc|03/06/2006|10:13:44|bob|density question|a straight road goes through the center of a circular city of radius 5km.  the density of the population at a distance r %28in km%29 from this road is||98||3
557|3|College101|02/02/2006|16:27:02|College101|Bases%2F Engineering Codes|I%27m having problems with a question on a study guide.%0D%0A%0D%0AA number%28xyz%29 in base 7 if expressed in base 9 becomes%28zyx%29. What is the he||92||2
553|0|mr_homm|01/29/2006|12:00:27|jupiter|probability|I am thinking of our UK bank credit-card PINs%2C which have 4 digits.%0D%0AObviously many PINs are repeated.  Say a bank has a million customers%0D%0A||146||5
556|0|alexb|01/26/2006|07:30:25|Richard Smith|Vector Cross Product - Associative Law|Suggestion that %28AxB%29XC %3D AX%28BXC%29 for 3 dimensional vectors A%2C B%2C C %28http%3A%2F%2Fwww.cut-the-knot.org%2Fdo_you_know%2Fmul_vec.shtml%2||82||1
546|0|mr_homm|01/23/2006|00:46:30|tommy|difficult sequence%2C areas partitioned in circle %2C|THe question is the opposite of the famous one.%0D%0ATake a circle%2C put on the inside of the  circle %28not on the circumference%29 any n points no ||166||15
554|2|mr_homm|01/06/2006|12:36:26|Terry|Best connection linking random event|A device with two light bulbs. Suppose you are allowed to combine N such devices. Everytime when a switch is pressed%2C each device has one of these t||79||1
552|0|John|12/23/2005|09:05:35|benyamin|limit of a sequence %28stirling approximation%29|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 ineq||92||1
550|3|alexb|12/13/2005|22:51:24|hippothal|Chebychev%27s Inequality|I have tried to figure this one out to no avail%3A%0D%0A%0D%0AP%28xbar- mu %E2%89%A4 %CF%83%2F4%29%E2%89%A5.99%0D%0A%0D%0AI think to solve this inqeua||116||2
549|0|alexb|12/12/2005|17:57:22|Ralph Boles|Integration question|Is there a closed form solution for integrals from minus infinity to infinity of e to a polynomials of degree three or higher%3F i.e.%0D%0A%0D%0Ainteg||105||1
548|0|Gil Wolff|12/09/2005|19:06:56|Gil Wolff|12 coins Problem%3A a possible solution|I propose the following solution to the %5BLink%3Awww.cut-the-knot.org%2Fblue%2Fweight1.shtml%7C12 coins Problem%5D%3A%0D%0A%0D%0Aweigh 4 coins agains||113||0
545|0|JJ|12/09/2005|17:44:24|sean|integration problem|I am trying to integrate the following function f%28x%29%3D%281%2Bx%5E3%29%5E%28-1%2F3%29 w.r.t. x.  I am pretty sure that I have gone astray as my so||157||4
547|2|alexb|12/08/2005|19:18:08|Jackie|Two Coins Problem|I am currently doing a project on epicycloids for Mathematics Research.  I came upon the %22Two Coins%22 problem posted on this website and I%27m seek||128||1
541|0|alexb|12/04/2005|20:29:12|Ellehuny|Geometry Construction HELP%21|I have to construct from two given circles%2C a common internal tangent.  Problem is%2C I have no idea how to do this...  its driving me crazy... geez||131||5
544|3|alexb|12/04/2005|19:11:47|Bractals|Crux Converse|This problem is a converse to one that I found in the journal %22Crux Mathematicorum with Mathematical Mayhem%22 published by the Canadian Mathematica||121||1
543|2|Bractals|12/04/2005|20:13:03|Bractals|Volume Question|Can somebody help me with this problem%3A%0D%0A%0D%0ALet A%2C B%2C and C be points on a sphere with center O and radius r.%0D%0AAngles AOB%2C BOC%2C a||114||5
511|2|Bractals|11/29/2005|12:55:54|Bractals|A Parallel Question|Let ABC be a triangle with angle C equal to 60 degrees and %7CAC%7C %3C %7CBC%7C. Let point D be on line segment BC such that %7CBD%7C %3D %7CAC%7C. L||134||8
520|2|Deep G|11/26/2005|14:23:28|H1|Most probable score|There are an infinite number of balls of four colors.  Red gets 1 point%2C blue gets 2%2C yellow gets 3 and green gets 4.  There are 6 bins into which||106||5
490|0|Daryl Williams|11/21/2005|23:41:50|everythingflows|Multigral Calculus|Hi Everyone%21%0D%0A%0D%0AHas anybody wondered if you could have an infinitesimal calculus based on the limit of PRODUCTS rather than series%3F %0D%0A||143||2
539|0|Owen|11/14/2005|01:53:05|Owen|Complex number solutions|I am searching for a set of geometry problems %28at the undergraduate level%29 that can be solved using complex numbers.  I found one such problem on ||96||2
538|0|Madan|10/30/2005|06:34:40|Madan|A new group for statisticians has formed. Request to join|Hi%2C%0D%0A %0D%0AI have  started a new group name %22Statisticians_group%22 in the yahoo group for statisticians or the persons who are interested in||104||0
528|3|Owen|10/27/2005|08:58:59|rama1977|An Interesting Property of Ellipse|I found one onteresting property of Ellipse. Let P%28x.y%29 be the any point on ellipse. Let C %26 D be the endpoints of Minor axis. Then the product ||197||6
536|0|mr_homm|10/22/2005|21:06:36|eric99gt|Rearranging Equation|Alright I%27m going absolutely nuts here. It%27s a simple matter of rearranging an equation and for the life of me I can%27t do it. I%27ve been workin||163||8
537|3|alexb|10/21/2005|06:41:48|cleodsc|Probability Question|Ok I have an issue I need to prove the following %28in notation%29%3A P%28A%29%2BP%28B%29-2P%28AB%29%3D %28Ac U B%29 U %28Bc U A%29%0D%0A%0D%0AI know ||153||1
533|2|alexb|10/16/2005|16:09:22|Bractals|Product of Chords|Let there be n%3E2 equally spaced points on a circle of radius one %28the vertices of a regular n-gon%29. Pick any point and draw the n-1 chords from ||186||7
534|3|sfwc|10/14/2005|08:41:26|Gotti|Inverse to an eisenstein-related function|%28since it seems%2Cthat the plus-sign disappears in postings and I do not realize how to keep them I use the %23 sign in the following%29%0D%0A%0D%0A||173||1
531|2|Owen|10/06/2005|14:25:13|Naveed Aslam|Proof of Vectors|Hi%3A%0D%0A%0D%0ADoes anybody know how I can Prove that the area of the triangle contained betewen vectors a and b is half of the absolute value of ve||218||1
530|3|alexb|09/20/2005|06:20:05|noorine|zeno%27s paradox|Hi i was wondering if i could get help on zeno%27s paradoxes. i have a presentation at the end of this month in college and i think all the informatio||222||1
522|0|alexb|09/13/2005|07:40:57|bitrak|Shortest distance A-B|Have we proof that shortest distance between two points in the plan is a straight line AB or maybe this is axiom%3FIs it same in the 3- dimensional sp||141||4
529|0|alexb|09/07/2005|10:43:37|Josh|Three Circle Thereom|I know that they%27ve got this proof of the three circle thereom %28common chords of three circles are concurrent%29 at this url%3A%0D%0Ahttp%3A%2F%2F||104||1
527|0|delta59|08/29/2005|19:40:43|Ganitopasak|Focus of parabola.|Hello%2C%0D%0A%0D%0AHow to calculate the focus of parabola given by%3A%0D%0A%0D%0A%28x %96 3%29%5E2  %3D %28y %2B 1%29%0D%0A%0D%0AThanks for any help.||81||1
524|2|mr_homm|08/10/2005|14:20:05|Bractals|Soddy Hexlet|Does anybody know a proof for why the centers of the spheres making up a Soddy hexlet lie in a plane%3F Also%2C is the plane determined by the specifi||102||5
523|0|alexb|08/06/2005|06:34:13|M&M|Motion or Mapping%3F Rigid Transformations|Hello Everybody%2C%0D%0AI am interested in rigid geometric transformations and I have a few questions regarding the plane.%0D%0A%0D%0A1- In the litera||80||1
516|0|mpdlc|07/31/2005|16:49:13|Ralph Boles|Recomb. Binom. Tree|Hello everyone%3B%0D%0A%0D%0AI am wondering about the following issue.  I am working with a binomial tree model for a valuation.  Basically v1%3D1%2C ||102||4
521|2|David Radcliffe|07/28/2005|07:06:18|Bractals|Function Name|Is there a common mathematical name for the following function%3F%0D%0A%0D%0Af%3A%7B2%2C4%2C6%2C8%2C...%7D --%3E %7B1%2C3%2C5%2C7%2C...%7D%0D%0A%0D%0A||114||2
519|3|mpdlc|07/11/2005|16:09:20|Grant|Spherical integration of any triangular pyramid|I am trying to develop an algorithm to find the volume of any triangular pyramid by spherical integration using the apex of the pyramid as the origin.||102||1
515|0|alexb|06/30/2005|17:28:11|Neel|The so-called plane problem|Hello everyone%2C %0D%0A%0D%0AThis is one of my first posts at the CTK exchange%2C so I hope I am doing this right...  A couple of months ago%2C I cam||122||6
514|3|alexb|06/27/2005|09:24:34|CSpeed0001|Calculus of Variations%3A Shape of a Hanging Cable|Just for fun%2C I%27m trying to figure out a function to describe the shape that a cable takes when suspended between two walls.  I just recently lear||114||8
513|0|MichaelD|05/30/2005|06:23:29|MichaelD|An Extended Classification of Quadrilaterals|Of interest to some here may be an extended classification of 26 quadrilaterals%2Cincluding concave %26 crossed quadrilaterals%2C which can be downloa||72||0
512|2|Kris|05/27/2005|22:14:33|Oskar|Diophantine equation|I friend told me about this problem %28which kinda looks like a special case of Fermat%27s last theorem%29. Solve this equation in the positive intege||75||1
510|0|sfwc|05/12/2005|10:21:06|Ganitopasak|Closed curve|What is the criteria to decide a curve is%0D%0A%0D%0A1%29 Closed%0D%0A%0D%0A2%29 Non-self intersecting%3F%0D%0A%0D%0AThanks for any help%0D%0A%3D%3D%3||71||3
508|3|alexb|05/10/2005|07:14:52|Ganitopasak|Combined scaling and rotation|Hello%2C %0D%0A%0D%0AI am trying to study combined point transformation. %0D%0A%0D%0AI tried to rotate and then scale a point about origin in a cad pa||65||3
507|3|alexb|05/07/2005|22:03:22|Maggie|Probability|Testing for HIV%3A%0D%0AAn article in New York Times some time ago reported that college students are beginning to routinly ask to be tested for the A||81||1
506|0|Ramsey2879|05/02/2005|09:10:14|Ramsey2879|Triangular a%28a%2B1%29%2F2 as products of two sequence terms|Let T%28a%29%3Da%28a%2B%2B1%29%2F2. I found that there are interdependent arithmetic%0D%0Asequences%3A%0D%0AA%2An%2B%2BB%2C C%2An%2B%2BD%2C and E%2An%||67||1
505|2|MPC|04/18/2005|07:11:38|srh44612|Interest in Joint Measure|Hi%2C%0D%0A %0D%0AI am reviewing the college and university rankings guide publication %28US News and World Report%29%2C which lists both a freshman r||58||1
504|3|alexb|04/07/2005|17:19:39|Edward Smart|Absolute flatness|Let A be a commutative ring with identity and let R be its nilradical. We define a module of said ring to be flat if%2C on taking an exact sequence of||63||1
503|0|Fernando|03/26/2005|20:25:54|Fernando|Double Fourier Series|Hello.%0D%0A%0D%0AI was wondering if anyone could provide me with the proof of the pointwise convergence theorem on double fourier series. Namely%3A%0||61||0
500|2|alexb|03/18/2005|07:46:26|Bractals|Complex Numbers|If A%2C B%2C and C are non-collinear complex numbers and x%2C y%2C and z are real%2C then clearly x %3D y %3D z %3D 1%2F2 is a solution to the followi||207||26
501|3|CJ|03/07/2005|13:08:04|CJ|Combinatorics using interger partitions|I have two questions. Is there any easy way to fill in the P%28m%2Cn%29 table all the way up to m and n equal to 10%3F Here is what I have based on wh||67||0
499|0|alexb|02/20/2005|19:19:12|Ralph Boles|USC correspondence| am working on a proof to present to a reading group I am in%2C that relies on the following proposition%2C  which I am having trouble proving.  Perha||86||1
497|0|CSpeed0001|02/07/2005|17:44:57|CSpeed0001|shortest distance between curves|A friend of mine is in a calculus 4 class%2C and shwas asked to find the shortest distance between two curves %28a line and a parabola%29.  She asked ||88||4
498|2|sfwc|02/03/2005|20:24:07|Amanda|Cannot Find A Proof|No one%2C not even my Geometry professor can find the prrof for the following theorem%3A%0D%0AIf two lines are cut by a transversal so that the exteri||102||1
496|3|alexb|01/29/2005|01:18:36|Sheniqua|divisibility proofs|%0D%0A%0D%0AHi I would really appreciate it if you could help me.%0D%0A%0D%0AI really do not know what to do for this question%3A%0D%0A%0D%0AShow that||85||1
486|0|alexb|01/25/2005|10:16:52|constantxarax|triangle construction%3A| By the meeting points of the meridians with the circumcircle.%0D%0A In general%2C by the meeting points of triangle special lines with triangles spec||106||1
494|3|MHTSOS|01/20/2005|20:36:22|troubled @ ucsc|Counterfit coins...|The famous 12 counterfit coin problem can be solved using 3 weighings.  If youre not familiar with this problem its on the site. %0D%0AAlso if you wan||69||1
493|2|Jeremy|01/17/2005|14:35:40|Jeremy|Pseudo Cardioid Curve|Suppose we have a unit radius circle with center A. We pick a point B on the circumference. We call the intersection of the X-axis on the circumferenc||78||4
491|2|alexb|12/24/2004|00:32:08|revicamc|Shapley-Shubik Power Index|On webpage -%0D%0A%0D%0Ahttp%3A%2F%2Fwww.cut-the-knot.org%2FCurriculum%2FSocialScience%2FPowerIndices.shtml%0D%0A%0D%0AI was amused a the speed at whi||71||1
489|2|maladjusted|12/18/2004|18:29:04|Quintopia|Vector in Null Space|Given an integer matrix A%2C what is the simplest way to find a rational vector in Nul A%3F  Is there anyway to do it without finding the null basis%3||108||8
410|0|Graham C|11/24/2004|17:14:19|nbro0|Optimization mod problem|Folks%2C%0D%0A%0D%0AI came across this problem studying for GRE.  Seems like a possibility for a mod-based solution.%0D%0A%0D%0AAn airline passenger i||152||2
466|2|Jachson|11/13/2004|20:06:05|ricardo|Area|%0D%0AThe area below the sine function from 0 to Pi%2F2 is 1 an exact number so I thought it could have an elementary demonstration%28not using calcul||166||1
483|0|Ramsey_KJ|11/13/2004|10:38:04|Ramsey_KJ|Recursive Series|This problem appears in the yahoo groups IntermediateNumberTheory%0D%0AGroup.%0D%0AThe following concerns the set of recursive series%3A R_0 %3D 0%2C ||96||0
470|0|Fendetestas|11/03/2004|20:06:05|userofmath|Is this possible%3F|Replace %22%3F%22 with either %22%2B%22 or %22-%22%0D%0AYou can not shuffle numbers.%0D%0AEvery %22%3F%22 must be replaced with a %22%2B%22 or %22-%22||169||2
481|3|alexb|10/28/2004|06:50:18|Nico Achtsis|Binomial theorem problem|I found this in a book%3A%0D%0A%0D%0AQ%3A if n is a positive integer%2C find the coefficient of x%5Er in the expansion of %281%2Bx%29%281-x%29%5En as ||145||1
476|0|alexb|10/14/2004|19:44:21|Fernando|Coordinate Systems|When I read the definition of %22Cartesian coordinate system%22 I read once and again that it is the system in which every point is represented by mea||121||1
474|2|alexb|10/04/2004|21:44:14|peterash|pigeonhole sequence problem|I%27m looking for applications of the pigeonhole principle that would be good for a freshman-level course in mathematical problem solving that I am te||179||4
469|3|sfwc|10/01/2004|20:06:05|4878bayley|modulus arithmetic|hi and good morning %0D%0A%0D%0Ai am a new member.  i have read a few of the recent messages and they all seem to contain information at a more advanc||209||2
472|3|Bractals|09/16/2004|18:26:42|Bractals|Seemingly simple problem|Here is a problem that I found in the September issue of Crux Mathematicorum. I thought it would be simple when I first read it%2C but I seem to have ||284||8
471|3|alexb|08/30/2004|17:07:03|Gwen Johnson|other bases|Does anyone know where I can find info about representing DECIMALS in other bases or can you give me an example of how to do it%3F||124||1
467|3|stlag37|08/13/2004|20:06:05|stlag37|Probability question|On a manufacturing line moving uni-directionally at 60rpm %28about 825 continers filled per minute%29 a bolt%2Fnut has been observed in the bottom of ||104||0
442|4|Oskar|08/01/2004|16:08:03|Kyle|Mathmatical Shorthand Notation|In my calculus III class%2C the instuctor sometimes uses a %22shorthand%22%2C like instead of therefore%2C he uses three dots %282 on bottom%2C1 on to||226||2
463|3|alexb|07/12/2004|10:54:09|Azzi Jang|Remainder Theorem|%28Confusing%7E%7E%29%0D%0A%0D%0AWhen you have P%28x%29 %3D X%5E%5E3 %2B X %2B 42%2C%0D%0Ayou are trying to test if P%28x%29 is factorized by%0D%0AX %||111||1
458|3|jmitchem|06/16/2004|14:00:16|jmitchem|Scheduling Algorithm|As seen on%3A%0D%0Ahttp%3A%2F%2Fwww.cut-the-knot.org%2FCurriculum%2FCombinatorics%2FCriticalPath.shtml%0D%0A%0D%0AThere is an applet which determines ||126||2
443|2|Tony|05/30/2004|07:11:26|Rob|Ratio of even and odd numbers|I was given this question for bonus and I%27m trying to figure it out.%0D%0A%0D%0AThe natural numbers%2C N%2C consist of the set %7B1%2C2%2C3%2C4....%||294||14
454|0|av8bricky|05/20/2004|18:09:49|av8bricky|Liberal Arts Math|I thought this was kind of funny. %0D%0A%0D%0AOn the applet about discontinuous functions%3A%0D%0A%0D%0A%22Naturally Discontinuous Functions%0D%0AMost||115||0
450|0|Fernando|05/02/2004|08:51:06|Fernando|Wiener-Kinchin theorem|Does anyone know where can I find the proof of Wiener-Kinchine theorem%3F%0D%0A%0D%0AIt states that the power spectral density %28PSD%29 of a stochast||141||0
449|2|Ron Olszewski|04/26/2004|10:30:51|Ron Olszewski|Pascal%27s Theorem|I%27ve been examining this page%3A %0D%0Ahttp%3A%2F%2Fwww.cut-the-knot.org%2FCurriculum%2FGeometry%2FPascal.shtml%0D%0A%0D%0AI understand most of the ||174||2
448|3|alexb|04/25/2004|12:44:21|Matt|perp diagonals in bicentric quad|Does bicentric quadrilaterals %28tangent.-chord. quadr.%29have perpendicular diagonals%3F I%27m certain they do but I cant find proof. Does anyone hav||127||1
446|0|bmclean|04/21/2004|21:11:27|bmclean|simplification of a sine series|I am familiar with the trig identity%0D%0A%0D%0Asum%7Bn%3D0-%3EN%7D sin%28nx%29 %3D %7Bsin%28Nx%2F2%29.sin%28%28N%2B1%29x%2F2%29%7D%2Fsin%28x%2F2%29%0||172||1
445|2|alexb|04/20/2004|07:50:08|Don|Trig%2FDensity Questions|After searching this site %28to no avail%29%2C does there exist a way to show %22the derivative of the sine is the cosine%22 that doesn%27t rely on al||235||1
444|2|alexb|04/18/2004|22:25:14|Fernando|Separation of Variables Method|In many physical and engineering problems invloving differential equations in a function F%28x%2Cy%2Cz%29%2C we search the solutions by asuming that F||195||5
440|0|Graham C|04/14/2004|09:03:02|Graham C|Weakest link|This is a computational problem%2C not a theoretical one%2C and is a sense may therefore be dull%2C and of course a simulation program could %27solve%||234||6
441|0|alexb|04/08/2004|21:03:31|Raelynn|Geometry|Evaluate 3bc -2a to the second power when a%3D2%2C b%3D3 and c%3D4%0D%0A%0D%0A           3abc-2a to the second power%0D%0A         3 %283%29%284%29- 2||185||1
415|0|darij|04/06/2004|20:15:30|darij|Synthetic proof of CB%27s Conjecture|%5Bfont size%3D%223%22%5D%0D%0A%0D%0A%0D%0A%0D%0A%5Bfont color%3D%22%23FF0000%22 size%3D%223%22%5D%5Bstrong%5D%5Bu%5DSynthetic proof of%0D%0AChristoph||324||6
438|4|alexb|04/05/2004|12:04:32|Marcos Mothé|Esponential Proof|Someone knows how could I proof that only the exponential function follows that f%28a%2Bb%29%3Df%28a%29%2Af%28b%29%3F  ||129||1
433|2|Bractals|03/17/2004|21:19:49|Bractals|Geometry and Vectors|Hi%2C%0D%0A%0D%0AI enjoy applying vector analysis and complex numbers to geometry problems where possible. I think the following combines the chord%2C||221||2
430|2|Ralph Boles|03/14/2004|18:56:39|rossnoe|Composite question|I%27m taking a number theory course to complete my undergraduate math degree. I want to know if my approach to solving this problem is correct%3A%0D%0||278||7
296|3|Soroban|09/16/2002|05:41:29|math_freak|Mathematical Induction and powers|Hi%2C%0D%0A%0D%0AI have to prove by MI that%2Cx%5E5-1 is a multiple of 5.%0D%0AMy analysis is as follows%3A%0D%0A%0D%0A1.If some no say x has to be a ||47||4
283|0|Michael Klipper|08/11/2002|22:02:34|sirelfman|Draft Lottery%2FProbability|I have been working on this several weeks now. Here%27s the setup.%0D%0A%0D%0AIn a 10 team league%2C the draft order is chosen by weighted lottery. Th||42||2
286|2|Samuele|08/08/2002|19:46:54|Samuele|Farey series|Hi%21 I%27m an Italian student. I found on Cut-the-knot and on %22The book of Numbers%22%2C  by Conway-Guy%2C something about the Farey series%2C but ||38||0
229|4|Michael Klipper|08/03/2002|14:15:50|wjn|napier logs|If someone knows where to find it %21%21%0D%0A%0D%0ALong time ago%2C when i was at college%2C an uncle showed me how Napier get to the number %22e%22 ||155||4
265|3|Michael Klipper|07/27/2002|14:46:54|William|Prove that e is irrational|Prove that e-%281%2B1%2F1%21%2B1%2F2%21%2B1%2F3%21%2B.......%2B1%2Fn%21%29%3C1%2F%28n%21n%29 for all natural number n.%0D%0A%0D%0AHence prove that e i||121||4
256|2|John A. Velling|05/01/2002|05:18:22|John A. Velling|degenerate case of Pascal%27s theorem|Consider the degenerate case of Pascal%27s theorem when vertices A and B%2C and vertices D and E%2C respectively%2C merge.  The figure from the proof ||60||0
208|3|Sumudu|03/25/2002|16:22:36|Proof Pudding|Prove n choose r|Hi all%2C I have been ask to look at the problem of proving by induction that n C r %3D %28n%21%29%2F%28%28n-r%29%21r%21%29 %2C %0D%0A0%3C%3D r %3C%3D||118||2
144|3|EdSmart|11/06/2001|00:52:51|RLCohen@POL.NET|Volume|What is the equation to find the VOLUME of a SPHERE.||29||1
120|2|Whymme|10/27/2001|12:53:30|mohr35|18 %25 shortcut|This may be an easy question -- I%27m not sure.%0D%0A%0D%0AAt any rate%2C does anyone know an easy trick or some sort of a quick shortcut to figure ou||60||2
130|3|Bubis|10/16/2001|06:11:15|Bubis|Galios field|If I am given k%60 the inverse of a number k modulo m%2C How would I find the inverse of the same number k modulo m in the galios field GF%282%5E8%29%||52||2
6|0|Greg Viers (Guest)|08/15/2001|23:01:04|tle|counting|How many integers n are there such that 1000%3C%3Dn%3C%3D9000 and %0D%0A%28a%29the 4 digits in n are nonincreasing %28as in 7330%29%3F%0D%0A%28b%29the||313|5.52671755725191|2
55|0|Marvin  Chang (Guest)|08/12/2001|09:04:20|andrew glenville (Guest)|point on a graph|this is probably fairly basic%2C but i was never particularly gifted in the matamatical arena%21 ......on a downward curving graph%2C what is the poin||345|5.49664429530201|3
65|0|Marvin Chang (Guest)|08/12/2001|12:30:02|Pitball|MAPPING AND MATRICES|I have a few things I need defining. I%27m studying a Computing degree and therefore not a mathmetician although it%27s part of our course.%0D%0A%0D%0||207|5.5|2
13||||||What does it mean to be %22degenerate%22 in a mathmatical sense%3F  |||4|10|1