| Mathematics_in_Art_and_Architecture An interdisciplinary course on mathematics in art and architecture. |
| Mathematics_Museum_(Japan) At Mathematics Museum (Japan) you would be surprised how interesting mathematics is. You will find exhibition rooms produced by Japanese researchers and educators. |
| Mathematik Individual pages on different topics in Mathematics. Examples : group theory, dynamical systems theory, geometry or number theory. |
| Mathematische_Basteleien Topics include Flexagon, Soma Cube, Pentominos, Cube-it, Rubik's Cube, Froebel's Star, Tangram, House of Santa Claus, Chronogram, Numeric Palindromes, Latticework of Letters. English/German. |
| Mathematrix Devoted to exploring the more entertaining (and generally lesser known) areas of mathematics. Can be enjoyed by anyone, from individuals with little or no math background to professors of the subject. |
| Mathmos Includes puzzles, jokes, quotations, poetry, and FAQs. |
| Maze_Classification_and_Algorithms A short description of mazes and how to create them. Definition of different mazetypes and their algorithms. |
| Mudd_Math_Fun_Facts An archive of interesting math facts for use in the classroom or just for fun. Browse by subject, difficulty, keywords, or try the "random" feature. Based at Harvey Mudd College. |
| Narcissistic_Numbers Those that are representable, in some way, by mathematically manipulating the digits of the numbers themselves. |
| The_Nine_Digits_Page Puzzles and problems connected with numbers using the digits 1-9. |
| Number_Recreations_by_Shyam_Sunder_Gupta Features interesting facts about different numbers. Includes favorite related links. |
| On_the_Puzzles_with_Polyhedra_and_Numbers This is an article on a set of didactical games edited by the Portuguese Mathematical Society (SPM). |
| One_Metaphor_Fits_All Explains Conway's audioactive decay that is generated by a particular kind of sequence. Includes illustrations and related resources. |
| Properties_of_Dice Polyhedral dice and their properties. |
| Recmath Includes pages on magic squares and polyomino patterns and contains related java applets. |
| Recreational_and_Educational_Computing A newsletter with programs, including optional supplemental PC disk. All back issues are available. Topics include puzzles and teasers, BASIC programming, letters, graphics, fractals, challenges, r |
| Recreational_Mathematics Links collected at CAMEL, the Canadian Mathematical Society website. |
| Recreational_Mathematics_(David_Eppstein) An extensive list of web resources for recreational math. |
| Recreational_Mathematics_Forum A forum for posting messages about math recreations. Hosted at Delphi. |
| Recreational_Mathematics_Topics By Steven Dutch. Symmetry, Crystals, Polyhedra and Tilings; Pythagorean triplets and other things about sums of powers; Geometry Classics. |
| Roman_Numerals Contains a introduction to Roman numerals including a translation of the digits used and a converter which can convert decimal to Roman numerals and vice versa. |
| Rubik\'s_Cube_Lecture_Notes Notes on the mathematics of the Rubik's cube. |
| SimonSingh_net Home of Simon Singh: author, journalist and TV producer, specialising in science and mathematics. Cryptography is one of his specialties, and his site has a lot of educational and fun content about c |
| Sir_Roger_Penrose A article about him and his interests and contributions to recreational mathematics. |
| Skytopia_-_Super_Magnet A colourful world built entirely using mathematical atoms and molecules. Pictures and animations demonstrate structures colliding and interacting. Animated GIF demonstrations. |
| The_Sound_of_Mathematics Algorithmic music determined by mathematics and by the musical preferences of a human. General MIDI files. |
| Spirocharts A windows application that creates mathematically precise spirograph drawings; savable as images. |
| Spirograph A java applet for creating Spirograph images. |
| Sportlab Combines high school and college math topics into sports applications. |
| Stunning_Friends_with_Math_Magic A collection of card tricks, number guessing games, paper and glue magic, and other math exercises. |
| Table_of_Numbers_Problem Given a m * n rectangle, place all numbers from 1 to mn that minimizes the sum of the products of rows and columns (both in Spanish and English). |
| Treasure_Troves___Book_List Book list including titles, authors, publishers, prices, page count and some have links to Amazon.com. |
| Wade_Edward_Philpott Profile and description of his mathematical games and puzzles. |
| Wade_Edward_Philpott_Collection A special collection at the University of Calgary Library. |
| Who_Can_Name_the_Bigger_Number? An essay by Scott Aaronson on the quest for ever-bigger numbers, from exponentials to Busy Beavers. |
| Australian_Map_Circle The Australian Map Circle (AMC) is a national group of map producers, users and curators, which acts as a medium of communication for all those interested in maps. |
| The_British_Cartographic_Society an association of individuals and organisations dedicated to exploring and developing the world of maps |
| International_Map_Trade_Association_(IMTA) IMTA members are the companies that create and sell the maps, atlases and map-related products you use. Find information on maps, geography and mapping technology. |
| MapHist_Discussion_Group MapHist, the Map History Discussion List, is an e-mail discussion group whose primary focus is historical maps, atlases, globes and other cartographic documents. |
| Mt__Diablo_Surveyors_Historical_Society Society of Land Surveyors interested in tne history of Mount Diablo, Northern California, and the establishment of the Mt. Diablo meridian and initial point. |
Problems :: PDF format :: Naoki Sato's solutions PDF:: Naoki Sato's info:: Spanish Version:: Contact Math Links :: A Catalog ofMathematics Resources:: Art of Problem Solving :: Interactive MathematicsMiscellany and Puzzles :: MathematicalProblems - Problem Solving :: MathematicsArchives :: Mathematics WWWVirtual Library :: NRICH: MathematicsEnrichment :: Number TheoryResources :: OpenDirectory (Mathematical Recreations) :: The Math Forum :: The Prime Puzzles andProblems Connection Mathematical Induction A page of uncommon problems, most closely connected with number theory. Some properties may be proved in different ways.For more exercises, problems, puzzles, games, math riddles, brain teasers, etc. to see the site : Art of Problem Solving New Problems Let p be an odd prime and let d be a divisor of p-1, it is known that the congruence ad ≡ 1 ( mod p) has exactly d distinct solutions.Let a1,a2,...,ad those solutions.Prove that ∑ i=1d ain ≡ cn d ( mod p) where cn=1 if nis divisible by d and 0 otherwise. See solutionComment:Another solution is using thefollowing property:the number of integers between 1 and p-1 which haveorder d is phi(d). Prove or disprove the following property: given the statement of Problem 23 andlet f(n) be: a(p-1)n+4+b(p-1)n+4+(a+b)(p-1)n+4 . Then:12f(n)≡ ((n-3)(n-4)f(0)) ( mod p3) for all integers n ≥0 . See Naoki Sato's solution (Problem 32)Comment: Using Naoki Sato's formula for gk(x) I can to prove that the propery is true for n=0 , n=6and n=12.Hence using the result of Problem 27 , theproperty is true for all n ≥ 0. An alternative for thefinal part of Naoki Sato's proof.Let p > 3 be a prime dividing x2+x+1 (1,x relatively prime).Let f(n) be (1+x){(p-1)n+1}-x{(p-1)n+1}-1 then:6f(n)≡n(n-1)x(x+1)((x2+x+1)2)mod p3 for all n ≥ 0.Hint:Let gk(x) be (1+x)(6k+1)-x(6k+1)-1 thengk(x) = Qk(x)x(x+1)(x2+x+1)3 + k(6k+1)x(x+1)(x2+x+1)2where Qk(x) is a polynomial with integer coefficients.Link of interest:Sums of Powers in Terms of Symmetric Functions Interactive Induction See PHP Script for Problem 21. Contact Email Form 