| Geometric_Packing_Problems By Joseph Malkevitch: "Given one shape X how and when can one pack identical copies of this shape into another shape Y?" |
| HAKMEM A collection of problems from MIT. Work reported herein was conducted at the Artificial Intelligence Laboratory, a Massachusetts Institute of Technology research program. |
| How_To_Manually_Find_A_Square_Root The way to do find a square root without a calculator. |
| Iamond A page on polyiamond puzzles. Includes many pages on tessellation. |
| Jlpe\'s_Number_Recreations_Page Features original number recreations by the author, such as generalized perfect numbers, digital diversions, diophantine equations, didactic numbers, and number theory. |
| Look_and_Say_Sequence_Generator Creates a special kind of summation formula created by John Conway. |
| MAA_Library_List_in_Recreational_Mathematics Book list split into categories. Includes title, author, publisher and date information about each book. |
| MAT_007_I_News A newsletter edited by undergraduates of the Department of Mathematics at the University of Toronto. Includes some online copies. |
| Math_Forum__2001_Mathematics_Game A contest that asks to write all integers from 1 to 100 using only the digits 2,0,0,1 and arithmetic operations. |
| Math_Forum__2002_Mathematics_Game A contest where the contestants have to write all integers from 1 to 100 using only the digits 2,0,0,2 and arithmetic operations. |
| Math_Forum__Algebra_Problem_of_the_Week View this week's algebra problem or those of previous weeks. |
| Math_in_the_Movies A guide to major motion pictures with scenes of real mathematics. |
| Math_Magic_By_Computer Interactive java puzzles and activities in different mathematical topics. |
| Mathematical_Diversions Mostly original diversions in mathematics and word play. |
| Mathematical_Fiction A list of mathematical fictional movies, books, stories, plays and shows. Split into categories including children's books. Can be sorted by mathematical content and literary quality. |
| Mathematical_Induction A page of uncommon problems, most closely connected with number theory. |
| Mathematical_Lego_Sculptures Designed and built by Andrew Lipson. Images and LDraw files. |
| Mathematical_Problems_-_Problem_Solving Mathematics Hots (Problems) by Bruno Kevius |
| Mathematical_Quotation_Server Furman University Mathematical Quotation Server - random or searchable math quotes. |
| Mathematical_Quotation_Server A collection of mathematical quotations culled from many sources. You may conduct a keyword search through the quotation database. |
| Mathematical_Spectrum Mathematical Spectrum is a magazine for students and teachers of mathematics in universities, colleges and schools worldwide. It may be read by anybody interested in mathematics as a recreation. |
| A__Mathematician\'s_Aesthetics In his classic A Mathematician's Apology, G. H. Hardy likened mathematics to poetry and painting. This site elaborates on Hardy's remark with quotations from Stevens, Klee, Fry, and Focillon. Links to |
| 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. |
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Odds of a dimpled die, out of 10,000 tosses, using a Markov Chain model
This page contains a complete list of all possible Fair Dice. First
off, objects which are ISOHEDRAL are fair. To be isohedral, each
face must have the same relationship with all other faces, and each face
must have the same relationship with the center of gravity. Thus,
each object has a Group structure (a Group Theory topic). Using Group
Theory and Euler's formula (Vertices + Faces - Edges = 2), it can be proven
that the following list contains all possible isohedra. An interactive
version of this page is at the CRC
Concise Encyclopedia of Mathematics. A good explanation of the
math behind all this can be found at Klaus
Æ. Mogensen's website.
Regular Tetrahedron
Isosceles Tetrahedron
Scalene Tetrahedron
Cube
Octahedron
Regular Dodecahedron
Octahedral Pentagonal Dodecahedron
Tetragonal Pentagonal Dodecahedron
Rhombic Dodecahedron
Trapezoidal Dodecahedron
Triakis Tetrahedron
Regular Icosahedron
Hexakis Tetrahedron
Tetrakis Hexahedron
Triakis Octahedron
Trapezoidal Icositetrahedron
Pentagonal Icositetrahedron
Dyakis Dodecahedron
Rhombic Triacontahedron
Hexakis Octahedron
Triakis Icosahedron
Pentakis Dodecahedron
Trapezoidal Hexecontahedron
Pentagonal Hexecontahedron
Hexakis Icosahedron
120 sides
Triangular Dihedron
Move points up/down - 4N sides
Basic Triangular Dihedron
2N sides
Trigonal Trapezohedron
Asymmetrical sides -- 2N Sides
Basic Trigonal Trapezohedron
Sides have symmetry -- 2N Sides
Triangular Dihedron
Move points in/out - 4N sides
Note to gaming companies: I'd love to see someone make the exotic
dice in the list above.
Can a non-isohedral fair die exist? Consider a pyramid
made from 4 isosceles triangles and a square. If the pyramid is short
and fat, the square face will be landed upon more than a fifth of the time.
If the pyramid is tall and thin the square face will be landed upon less
than a fifth of the time. Is there a height where the square face
will be landed upon exactly one fifth of the time???
Yes, for a given set of conditions. If you knew
the height, force, elasticity, and throwing method, you could find the
right height. However, once the conditions changed, the die would
no longer be fair. (NOTE: I have a strong argument for this,
but no proof.)
If you find the polyhedrons above interesting, you're bound to enjoy
the Pavilion of Polyhedreality
by George Hart.
There are 6 regular 4-dimensional object. Peek
is a fascinating and very pretty piece of software that allows looking
at 3-D cross-sections of complex 4-D objects. The pictures are beautiful!
geovisit();
