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Recommended Print E-mail
Wednesday, 01 December 2004

The following sites are all highly recommended as sources of mathematical inspiration, enlightenment, ideas and information:

Thanks to Interactive Mathematics for these
This site relies heavily on Java applets if you do not have Java then download it here

 

Memory and Matching

  1. Match answers
  2. Memory - Easy
  3. Memory - Medium
  4. Memory - Hard

Arithmetic

  1. 2 Pails Puzzle
  2. 3 Jugs Puzzle
  3. 3 Jugs Puzzle in Barycentric Coordinates
  4. Abacus in Various Number Systems
  5. Aliquot Game
  6. Arithmetic Operations in Various Bases
  7. Broken Calculator
  8. Collatz Conjecture
  9. Counting and Grouping
  10. Equivalent Fractions
  11. Even, Odd and Total Number of Digits
  12. Euclid's Game
  13. Farey Fractions
  14. Less, Equal, More
  15. Napier Bones
  16. Plain Multiplication table up to 20×20
  17. Sums and Products
  18. Sums of Powers of Digits
  19. Two Simple Equations

Algebra

  1. Binary Color Device
  2. Breaking Chocolate Bars
  3. Candy Game: Integer Iterations on a Circle
  4. Chebyshev polynomials
  5. Divisibility Problem
  6. Dots and Fractions
  7. Frieze Patterns
  8. Heads and Tails (counting, invariance)
  9. Identities in the Multiplication Table
  10. Integer Iterations on a Circle II (superposition principle)
  11. Interest Calculations
  12. Letter Count in a Sentence
  13. Logistic Model
  14. Mean Values
  15. Merlin's Magic Squares (modular arithmetic, boolean and linear algebra)
  16. Minimax Principle
  17. Modular Arithmetic
  18. Parrondo Paradox Via Simpson Paradox
  19. Plus or Minus (parity, invariance)
  20. PolygonalNumbers
  21. Pythagorean Triples
  22. Self-documenting Sentences
  23. Simpson Paradox
  24. Squares and Circles (parity, invariance)
  25. Squares, Circles, and Triangles (modular arithmetic, invariance)
  26. Sum of Consecutive Integers is Triangular
  27. Sum of Consecutive Odd Numbers is Square
  28. Sum of Consecutive Triangular Numbers is Square
  29. Toads And Frogs Puzzle (counting, logic, problem solving)
  30. What's next?
  31. Word Problems

Logic

  1. Lewis Carroll's Bilateral Diagrams
  2. Lewis Carroll's Trilateral Diagrams
  3. Lewis Carroll's Logic Game

Geometry

  1. 2N-Wing Butterfly Theorem
  2. Addition of Radius-Vectors
  3. An Isoperimetric Theorem
  4. Angle Bisector
  5. Angle Preservation Property
  6. Angle Trisection by Archimedes
  7. Angle Trisectors on Circumcircle
  8. Area of Parallelogram
  9. Areas in Triangle
  10. Areas in Triangle II
  11. Bride's Chair
  12. Butterfly Problem
  13. Cardioid As Envelope of Circles
  14. Cardioid As Epicycloid
  15. Ceva's Theorem
  16. Chain of Inscribed Circles
  17. Chords in Cardioid
  18. Circumcevian Triangle
  19. Complete Quadrilateral
  20. Concurrency in Analytic Geometry
  21. Concyclic Circumcenters: A Dynamic View
  22. Delian Problem Solved
  23. Desargues' Theorem
  24. Douglas' Theorem (complex variables, linear algebra)
  25. Dynamic Construction of Ellipse and Other Curves
  26. Ellipse, how to draw
  27. Equichordal Curves
  28. Equilateral Triangle: A Criterion in Complex Variables
  29. Fagnano's Problem, Third Solution
  30. Fagnano's Problem in Reverse
  31. Fibonacci Bamboozlement
  32. First Vecten Point
  33. Five Cardioids
  34. Fixed point on a rod rotating around a triangle
  35. Friendly Kiepert's Perspectors
  36. Geoboard
  37. Golomb's inductive proof of a tromino theorem
  38. Grebe's Theorem
  39. Harmonic Ratio
  40. Hexagon Parallel to Medial Triangle
  41. Hexagon Parallel to Orthic Triangle
  42. Hofstadter Triangles and Points
  43. Hypocycloid Families
  44. Incident Center Circles and Cardioid
  45. Inversion Tool
  46. Iterations in Geometry, an example
  47. Lighthouse Curves
  48. Mathematics in Pizzeria
  49. Menelaus and Ceva Theorems
  50. Menelaus From Ceva
  51. Minkowski's addition of convex shapes
  52. Miquel's Point of a 4-line Via Spiral Similarity
  53. Morley Constellation
  54. Morley's Theorem
  55. Napoleon Theorem by Plane Tesselation
  56. Nine Point Circle
  57. Non-classic Way To Draw Cardioid
  58. One Sided Surface in 4D
  59. Pascal Lines: Steiner and Kirkman Theorems
  60. Pascal Lines: Steiner and Kirkman Theorems II
  61. Peaucellier Linkage
  62. Poles and Polars
  63. Poles, Polars and Quadrilaterals
  64. Polygon from midpoints of its sides
  65. Polygon Metamorphosis
  66. Problem of polygon construction
  67. Proof Without Words for the Pythagorean Theorem
  68. Pythagorean Theorem By Euclid
  69. Pythagorean Theorem By Hexagonal Tessellation
  70. Pythagorean Theorem By Shearing and Rotations I
  71. Pythagorean Theorem By Shearing and Rotations II
  72. Quest for Paragon
  73. Rotation Transform
  74. Simson Line From Isogonal Perspective
  75. Spira Mirabilis - Wonderful Spiral
  76. Star Construction of Shapes of Constant Width
  77. Steiner's porism
  78. Straight Edge Construction of Polar
  79. Tesseract
  80. Triangle and Segment Count in a Polygon
  81. Two Proofs of MenelausTheorem
  82. Triangle Geometry
  83. Triangular Billiard
  84. Trigonometric Form of Ceva's Theorem (a tool for discovery of trigonometric identities and other problems)
  85. Tucker Circles Through Homothety
  86. Vecten's Theorem
  87. When a Triangle is Equilateral
  88. What does one see inside a spherical mirror?

Fractals

  1. All Peano Curves
  2. Apollonian Gasket
  3. Cantor sets
  4. Dot Patterns, Pascal Triangle and Lucas Theorem
  5. Emergence of Chaos
  6. Fractal Curves and Dimension
  7. Iterated Function Systems
  8. Iterations in the Mandelbrot Set
  9. Mandelbrot Set and Indexing of Julia Sets
  10. Plane Filling Curves: Hilbert's and Moore's
  11. Plane Filling Curves: Peano's and Wunderlich's
  12. Sierpinski Gasket by Trema Removal

Probability

  1. Bertrand's Paradox
  2. Birds On Wire
  3. Buffon's Noodle
  4. Family Statistics
  5. Lewis Carroll's pillow problem
  6. Monty Hall Dilemma
  7. Parrondo Paradox
  8. Random Clock Hands
  9. Three pancakes

Visual Illusions

  1. Assimilation Illusion
  2. Balls and Shadows Illusion
  3. Bulging lines illusion
  4. Circular Poggendorff Illusion
  5. Continuous Line Illusion
  6. Day's Sine Illusion
  7. Delboeuf Illusion
  8. Distorted Lines Illusion
  9. Gerbino's Illusion
  10. Heaver: A Visual Illusion
  11. Height/Width Interplay Illusion
  12. Hering Illusion
  13. Hermann Grid Illusion
  14. Judd Illusion
  15. Kanizsa Triangle
  16. Müller-Lyer Illusion
  17. Necker Cube
  18. Orbison Illusion
  19. Perspective Illusion
  20. Poggendorff Illusion
  21. Ponzo Illusion
  22. Ponzo Illusion II
  23. Revolving Circles Illusion
  24. Scintillating Grid Illusion
  25. Shimmer Illusion
  26. Simultaneous Contrast Illusion
  27. Simultaneous Contrast Illusion II
  28. Twisted Cord Illusion
  29. Zöllner's Illusion

Calculus

  1. Derivative of Sine and Cosine
  2. Equations of the Staight Line
  3. Function, Derivative and Integral
  4. Graph of a Polynomial
  5. Lagrange Interpolation
  6. Naturally Discontinuous Functions
  7. Riemann Sums - Function Integration
  8. Taylor Series Approximation to Cosine


Combinatorics

  1. Bicolor Tower of Hanoi
  2. Blithe 12
  3. Cheapest Link & Kruskal's Algorithms - skill practice
  4. Coin change
  5. Critical Path in a Weighted Digraph
  6. de Bruijn Cycle
  7. Euler & Hamilton Paths - skill practice
  8. Flipping pancakes
  9. Gray Codes
  10. Group multiplication of permutations
  11. Happy 8
  12. How to define a permutation
  13. Infinite Latin Square
  14. Latin Squares
  15. Leibniz and Pascal Triangles
  16. Listing all permutations
  17. Lucky 7
  18. Make Your Move, Kid!
  19. Number sequences and Pigeonhole
  20. Project Scheduling
  21. Sam Loyd's Fifteen
  22. Scrub Tile Puzzle
  23. Shuttle Puzzle
  24. Simple Graphs
  25. Sliders (slider games on torus, Moebius strip, projective plane, permutations, cycles)
  26. Tower of Hanoi

Mathematical Droodles

  1. 3 Isosceles Trapezoids
  2. 5-Star and A Circle
  3. 9-point Circle as a Locus of Concurrency
  4. A Famous Theorem
  5. Angle Bisectors in a Quadrilateral
  6. Apollonius Problem
  7. An Application of Ceva's Theorem
  8. A problem with equilateral triangles
  9. Arithmetic in Disguise
  10. Asymmetric Propeller I
  11. Asymmetric Propeller II
  12. Asymmetric Propeller III
  13. Bottema's Theorem
  14. Brahmagupta's Theorem
  15. Brianchon's Theorem
  16. Cantor's Theorem
  17. Carnot's Theorem
  18. Center Circles and Their Chains
  19. Centroids in a Polygon
  20. Ceva and Menelaus Theorems for Angle Bisectors
  21. Ceva's Theorem
  22. Circle and Hyperbola as Lighthouse Curves
  23. Circle Chains and Inscribed Angles
  24. Circle Crosses Triangle
  25. Circle Inscribed in a Circular Segment
  26. Circles and Reflections in a Triangle
  27. Circles in Morley's Triangles
  28. Clifford Chain
  29. Clifford's Lemma
  30. Conway's Circle
  31. Copernicus' Theorem
  32. Copernicus' Theorem II
  33. Cycloids
  34. Cyclic Incenters
  35. Diagonal Count
  36. Dual to Pappus' Theorem
  37. Easy Construction of Bicentric Quadrilateral
  38. Easy Construction of Bicentric Quadrilateral II
  39. Eight Point Circle
  40. Equal Incircles Theorem
  41. Euler Line Cuts Off Equilateral Triangle
  42. Eyeball Theorem
  43. Fagnano's problem
  44. Fagnano's problem II
  45. Feuerbach's theorem
  46. Five Incircles Theorem
  47. Five Lattice Points
  48. Four Concurrent Lines in a Cyclic Quadrilateral
  49. Four Touching Circles
  50. Fundamental Theorem of 3-Bar Motion
  51. Heron's Problem
  52. Hinged Squares
  53. Incenters in Cyclic Quadrilateral
  54. Incircles, Circumcircles and Inscribed Angles
  55. Inversion: Reflection in a Circle
  56. Inversion with Negative Power
  57. Isogonal Concurrency
  58. Isogonal image of the circumcircle
  59. Iterations on Euler Lines
  60. Kiepert's Theorem
  61. Law of Cosines
  62. La Hire's Theorem
  63. La Hire's Theorem, a Variant
  64. Maxwell's Theorem
  65. Medians in a Quadrilateral
  66. Miquel's Point
  67. Morley's Theorem
  68. Newton's Theorem
  69. Optimization Problem in Acute Angle
  70. Orthopole
  71. Pairs of Incircles in a Quadrilateral
  72. Pappus' Theorem
  73. Paragon
  74. Parahexagon
  75. Parallel Lines and Similar Triangles
  76. Pascal's Theorem
  77. Pivot Theorem
  78. Point common to two similar rectangles
  79. Poncelet's Porism
  80. Poncelet's Theorem
  81. Problem in Three Squares
  82. Projective Collinearity in a Quadrilateral
  83. Property of Circumscribed Quadrilaterals
  84. Property of Points Where In- and Excircles Touch a Triangle
  85. Pythagorean Theorem By Dissection
  86. Pythagorean Theorem By Dissection II
  87. Pythagorean Theorem By Dissection III
  88. Pythagorean Theorem By Rearrangement
  89. Radical Axis of Circles Inscribed in a Circular Segment
  90. Remarkable Line in Cyclic Quadrilateral
  91. Rusty Compass Construction of Equilateral Triangle
  92. Salinon: from Archimedes Book of Lemmas
  93. Shape of Constant Width
  94. Siamese Triangles
  95. Siamese Triangles II
  96. Simson Line
  97. Simson Lines Of Diametrically Opposite Points
  98. Simsons and 9-Point Circles in Cyclic Quadrilateral
  99. sin(N)
  100. Soddy Circles and David Eppstein's Centers
  101. Sperner's Lemma
  102. Square Inscribed in Triangle
  103. Squares on Sides of a Quadrilateral
  104. Squinting Eyes Theorem
  105. Steiner's Chain
  106. Thébault's Problem I
  107. Thébault's Problem II
  108. Thébault's Problem III
  109. Theorem of Complete Quadrilateral
  110. Three Incircles in a Triangle
  111. Three Similar Triangles
  112. Tucker Circles
  113. Two Butterflies Theorem
  114. Two Circles in a Square
  115. Two Quadrilaterals
  116. Two Triples of Similar Triangles
  117. Varignon Parallelogram
  118. Wittenbauer's Parallelogram
  119. Zaslavsky's theorem

Puzzles & Games

  1. Changing Colors (combinatorics, invariance)
  2. Computer Mastermind (logic and problem solving)
  3. Farmer and Wife To Catch Rooster and Hen (invariance, city block distance)
  4. Fif (multiple representations)
  5. Fill a Hexagonal Grid (space visualization)
  6. Fish Soup Game (multiple representations)
  7. Four Knights (multiple representations)
  8. Goat, Cabbage and Wolf to move across a river (multiple representations)
  9. Jam (multiple representations)
  10. Looping Chips (multiple representations)
  11. Mastermind (logic and problem solving)
  12. Mastermind Variants (logic and problem solving)
  13. Peg Solitaire (logic, problem solving, subproblems)
  14. Pick A Label (logic, problem solving)
  15. Reverse Solitaire (logic, problem solving, subproblems)
  16. Sending scouts into the desert (algebra, geometric series, problem solving)
  17. Seven Coins Puzzle (multiple representations)
  18. Solitaire on a Circle (iterations, invariance)
  19. Toads And Frogs in 2 dimensions (repeated application of same idea)

Combinatorial Games

  1. Date Game (impartial game)
  2. Fraction Game (partisan game)
  3. Kayles (impartial game)
  4. Nim (impartial game)
  5. Nimble (impartial game)
  6. Northcott's game (impartial game)
  7. One Pile (impartial game)
  8. Plainim (impartial game)
  9. Scoring (impartial game)
  10. Silver Dollar Game (impartial game)
  11. Silver Dollar Game With No Silver Dollar (impartial game)
  12. Subtraction Game (impartial game)
  13. Take-Away Games (impartial game)
  14. Turning Turtles (impartial game)
  15. Wythoff's Nim (impartial game)

Social Science

  1. Adams' Apportionment Method
  2. Fair Division: Method of Lone Divider
  3. Fair Division: Method of Markers
  4. Fair Division: Method of Sealed Bids
  5. Fast Power Indices
  6. Hamilton's Apportionment Method
  7. Huntington-Hill Apportionment Method
  8. Jefferson's Apportionment Method
  9. Social Choice
  10. Webster's Apportionment Method
  11. Weighted Voting and Power Indices

Math Magic

  1. Arithmetic magic matrix
  2. Bachet's Magic Trick
  3. Calendar Magic
  4. Gergonne's Magic Trick
  5. Magic in Square
  6. Number Guessing Game
  7. Two Numbers Guessing Game

Miscellaneous Demonstrations

  1. Disappearing Lines
  2. Disappearing Rectangles
  3. Experimentation with Dynamic Geometry Software: An Example
  4. Genetic Algorithm Solves the Toads and Frogs Puzzle
  5. Impossible Fork
  6. Mazes
  7. Popping A Square
  8. Random Dot Stereograms
  9. Ratchet Effect
  10. Sorting Algorithms

Last Updated ( Monday, 04 July 2005 )
 
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