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Manifesto: what CTK is about Buying a book is a commitment to learning Table of content Things you can find on CTK Chronology of updates Email to Cut The Knot Recommend this page

Interactive Mathematic Miscellany and Puzzles

Arithmetic and Algebra

What Is Arithmetic?
What Is Algebra?
Mental Calculations

  1. 3-Colors Tower of Hanoi [Java]
  2. 3 glass puzzle [JavaScript]
  3. 3-Term Arithmetic Progression
  4. 4x4 coloring problem
  5. A 49th Degree Challenge
  6. A Clique of Acquaintances
  7. A Line in a Square Grid [Java]
  8. Abacus in Various Number Systems [Java]
  9. About numbers
  10. Achieve the Equilibrium [Flash]
  11. Addition
  12. Affirmative Action Problem [Java]
  13. Algorithm for Computing LCM [Java]
  14. The Aliquot Game [Java]
  15. Algebraic Structure of Complex Numbers
  16. Almost every integer has the digit 3 in it
  17. Almost Integers - Gaussian Integers
  18. An Application of Mental Arithmetic to Highway Safety
  19. An Arithmetic Magic Trick [Java]
  20. An Inequality for Grade 8
  21. An Inequality With an Infinite Series
  22. An Interesting Number
  23. Arithmetic-Geometric Means Inequality
  24. Arithmetic magic matrix [Java]
  25. Arithmetic Operations in Various Bases [Java]
  26. Arithmetic Paradoxes
  27. A simple integral
  28. Another simple integral
  29. Averages, Arithmetic and Harmonic Means [Java]
  30. Averages in a sequence
  31. Bachet's Magic Trick [Java]
  32. Barcode Encoding
  33. Barcode Magic [Java]
  34. Base Converter [JavaScript]
  35. Basic Rules of Counting
  36. Bayes' Theorem
  37. Beatty Sequences
  38. Bilateral Diagrams [Java]
  39. Binary Color Device [Java]
  40. Binary Euclid's Algorithm
  41. Binomial Distribution [Java]
  42. Binomial Theorem\
  43. Bisector of an imaginary angle may be real
  44. Boys and Girls Solving Problems
  45. Breaking Chocolate Bars [Java]
  46. Broken Calculator [Java]
  47. Byzantine Basketball
  48. Calculation of the Digits of pi by the Spigot Algorithm [Java]
  49. Cantor-Bernstein-Schroeder theorem
  50. Cardinal Numbers
  51. Cartesian Coordinate System [Java]
  52. Caterpillar [Flash]
  53. Chameleons of Three Colors
  54. Chinese Remainder Theorem
  55. Clifford Algebras
  56. Collatz Conjecture [Java]
  57. Coloring a Graph [Java]
  58. Combinatorial Proofs
  59. Committee Chairs
  60. Comparing complex numbers
  61. Completing a Square and Quadratic Formula
  62. Complex Numbers: A Dynamic Tool [Java]
  63. Complex number to a complex power may be real
  64. Computer As a Magician [Java]
  65. Constructible Numbers
  66. Continued fractions
  67. Countability of Rational Numbers
  68. Counting: The Beginning of Mathematics [Java]
  69. Counting Chips On a Circle [Java]
  70. Counting Squares in a Square [Java]
  71. Counting Triangles [Java]
  72. Counting Triangles II [Java]
  73. Covering A Chessboard With Domino
  74. Cryptarithms [JavaScript, Frames]
  75. Cubic Formula [JavaScript]
  76. Cubics and Bézout's Theorem
  77. Derivatives without Limits
  78. Descartes' Rule of Signs
  79. Distance Between Strings [Java]
  80. Distance From a Point to a Straight Line [Java]
  81. Distributive Law [Java]
  82. Dividing Loot Fairly
  83. Divisibility and Modulo Arithmetic at IMO 2007
  84. Divisibility by 7
  85. Divisibility by 9 and 11
  86. Divisibility by 81
  87. Divisibility Criteria
  88. Divisibility by 7, 11, and 13
  89. Dollars in Pockets
  90. Dot Patterns and Sierpinski Gasket [Java]
  91. Dots and fractions [Java]
  92. Ducci Sequences [Java]
  93. EAN-13 Encoding [Java]
  94. Egyptian Multiplication [Java]
  95. Eigenvectors by Inspection
  96. Equations of the Staight Line [Java]
  97. Equivalence Relations
  98. Euclid's Algorithm
  99. Euclid's Game [Java]
  100. Euler’s formula for e
  101. Euler's Function and Congruence Theorem
  102. Evolution of Algebraic Symbolism
  103. Every composite number is the product of some factors and also the sum of the same numbers
  104. Extension of Euclid's Algorithm
  105. Factorials and division
  106. Falsity implies anything
  107. Farey Series
  108. Fast Arithmetic Tips
  109. Fermat's Little Theorem
  110. Fibonacci's Quickies
  111. First Geometric Interpretation of Complex Numbers [Java]
  112. Five Lattice Points [Java]
  113. Flipping Items Simultaneously [Java]
  114. Flipping Items Simultaneously II [Java]
  115. Flipping pancakes [Java]
  116. Floor Function
  117. Formal Framework, an example
  118. Formal Systems - an Example
  119. Formula for Primes
  120. Four 3s
  121. Four 4s
  122. Four 5s
  123. Four Hinged Squares: using complex numbers
  124. Four Pegs That Form a Square
  125. Fraction Comparison [Java]
  126. Fractions on a Binary Tree
  127. Fractions on a Binary Tree II
  128. Frieze Patterns [Java]
  129. Fun with digits
  130. Function
  131. Fundamental Theorem of Algebra
  132. Funny Arithmetic [JavaScript]
  133. Gasoline Stations on a Circular Trek
  134. GCD(M, N) × LCM(M, N) = M × N [Java]
  135. Generalization That Solves the Problem
  136. Generating Functions
  137. Geometric Construction of Roots of Quadratic Equation [Java]
  138. Geometric view of the Sieve of Eratosthenes [Java]
  139. Gergonne Magic Trick [Java]
  140. Gödel's Incompleteness Theorem
  141. Graph and Roots of a Third Degree Polynomial [Java]
  142. Graph and Roots of Quadratic Polynomial [Java]
  143. Graph of a Polynomial [Java]
  144. Graph of a Polynomial Defined by Its Roots [Java]
  145. Group multiplication of permutations [Java]
  146. Guessing Two Consecutive Integers
  147. Harmonic Serires And Its Parts
  148. Heads and Tails [Java]
  149. Horner's Method [Java]
  150. Hour glass timing
  151. How to Ask an Embarrassing Question
  152. How to define a permutation? [Java]
  153. How to efficiently defend a castle
  154. Hyperintegers and Hyperreal Numbers
  155. Identical Twins Puzzle
  156. Identities in the Multiplication Table [Java]
  157. Implementation of Base Conversion
  158. Impossible Machine
  159. Inclusion-Exclusion Principle
  160. Inequality 1/2·3/4·5/6· ... ·99/100 < 1/10
  161. Inequality (1 + 1-3)(1 + 2-3)(1 + 2-3)...(1 + n-3) < 3
  162. Inequality 1 + 2-2 + 3-2 + 4-2 + ... + n-2 < 2.
  163. Infinite Discent for x4 + y4 = z4
  164. Infinitesimals. Non-standard Analysis
  165. Infinitude of Primes
  166. Infinity As a Limit
  167. Inflection Points of Fourth Degree Polynomials [Java]
  168. Integer Iterations on a Circle [Java]
  169. Integer roots of integers are irrational
  170. Integers and Rectangles [Java]
  171. Integers and Rectangles: a Proof by Induction [Java]
  172. Integers and Rectangles: Two Simple Proofs [Java]
  173. Interest Calculations [Java]
  174. ISBN Encoding [Java]
  175. Irrational number to an irrational power may be rational
  176. Is 0.999... = 1?
  177. It's All About Powers of 10
  178. Joachimsthal's Notations
  179. Jumping Isn't Everything [Java]
  180. Kaprekar's Iterations and Numbers [Java]
  181. Lagrange interpolation
  182. Langford and Skolem Sequences [Java]
  183. Latin Squares [Java]
  184. Lattice Multiplication [Java]
  185. Leibniz and Pascal Triangles [Java]
  186. Lewis Carroll's Game of Logic [Java]
  187. Light Bulbs in a Circle [Java]
  188. Lights Out [Java]
  189. Linear functions
  190. Linear Programming
  191. Listing All Combinations [Java]
  192. Listing all permutations [Java]
  193. Listing All Permutations: Johnson-Trotter Method [Java]
  194. Logistic Model applet [Java]
  195. Long Multiplication [Java]
  196. Long Runs of Composite Numbers
  197. Looking your best
  198. Loop or Halt [Java]
  199. Lucas' Theorem
  200. Magic in Square [Java]
  201. Make An Identity [Java]
  202. Market Day
  203. Marriage Theorem
  204. Marriage Problem, simulation [Java]
  205. Math Card Trick
  206. Math Lotto
  207. Math Telepathy [Java]
  208. Mathematical Induction
  209. Mathematical Proof
  210. Mathematicians Doze Off
  211. Matrix Groups
  212. Maximum Volume of a Cut Off Box [Java]
  213. Means [Java]
  214. Mediant Fractions
  215. Minesweeper Theorem
  216. Mini Lights Out [Java]
  217. Minimax Principle [Java]
  218. Minimax Theorem [Java]
  219. Modular Arithmetic [Java]
  220. Monotone Convergence Theorem
  221. Monotone Number Sequences [Java]
  222. Multiplication
  223. Napier Bones [Java]
  224. Nested Radicals
  225. Newton's Method [Java]
  226. Nine Squares [Java]
  227. Number 8 Is Interesting
  228. Number Guessing Game [Java]
  229. Number sequences and Pigeonhole [Java]
  230. Number System With Base 36
  231. On the Games of Hex and Y
  232. One Dimensional Ants
  233. One Trigonometric Formula and Its Consequences
  234. Operations on Fractions [Java]
  235. Order. Well-ordered sets.
  236. Ordinal Numbers
  237. Outline Mathematics
  238. Parity counting [Java]
  239. Parrondo Paradox Via Simpson Paradox [Java]
  240. Party Acquaintances [Java]
  241. Peano axioms
  242. Peasant Multiplication [Java]
  243. Pennies in Boxes [Java]
  244. Percent
  245. Permutations
  246. Pigeonhole Principle
  247. Place Value [Java]
  248. Probability of Divisibility
  249. Problem of Divisibility by 5n
  250. Product of Diagonals in Regular N-gon
  251. Product Of Four Consecutive Integers
  252. Product of Simple Fractions [Java]
  253. Product of permutations [Java]
  254. Proizvolov's Identity [Java]
  255. Proofs Without Words [Java]
  256. Property of an
  257. Property of the Powers of 2 [Java]
  258. Puzzlist vs. Mathematician: A Practical Arithmetic Problem
  259. Pythagorean Triples [Java]
  260. Quasigroups and block designs from triangular grid [Java]
  261. Ramsey's Theorem
  262. Recombining Permutations [Java]
  263. Represent 4 with four digits
  264. Represent 6 with three digits
  265. Rectangle on a Chessboard [Java]
  266. Review of Arithmetic for Parents: A Book for Grownups about Children's Mathematics by R. Aharoni
  267. Rhind Papyrus
  268. Riemann Sphere and Möbius Transformation
  269. Riemann Sums - Function Integration [Java]
  270. Right Replacement [Java]
  271. Rolle's and Mean Value Theorems [Java]
  272. Round Robin Tournament
  273. Russell's Paradox
  274. Scrub Tile Puzzle [Java]
  275. Self-descriptive Strings [Java]
  276. Self-reference
  277. Seven Terms Periodic Sequence
  278. Shapley-Shubik Power Index [Java]
  279. Ship-Dock Theorem
  280. Sierpinski Gasket and Tower of Hanoi
  281. Sierpinski's Gasket and Dihedral Symmetry [Java]
  282. Sieve of Eratosthenes [Java]
  283. Sieve of Squares [Java]
  284. Σ2-n = Σn·2-n
  285. Signs and Sums in a Sequence [Java]
  286. Signs in a Matrix [Java]
  287. Simple Cellular Automaton [Java]
  288. Simpson Paradox [Java]
  289. Single formula to express any integer with digits 0-9 each used just once
  290. Six Balls, Two Weighings
  291. Slider Puzzles [Java]
  292. Solitaire in Two Colors [Java]
  293. Solve xx3 = 3
  294. Soriteses
  295. Soroban in Various Number Systems
  296. Sorting Algorithms
  297. Sperner's Theorem
  298. Splitting piles
  299. Square root of 2 is irrational
  300. Squares, Circles, and Triangles [Java]
  301. Steinhaus' Problem [Java]
  302. Step into the Elliptic Realm
  303. Stern-Brocot Tree
  304. Straight Tromino on a Chessboard [Java]
  305. Structure of Hyperreal Numbers
  306. Suan Pan in Various Number Systems [Java]
  307. Subtraction Game [Java]
  308. Sum without Adding
  309. Sums and Products [Java]
  310. Sums of powers of digits [Java]
  311. Superposition Principle
  312. Surreal Numbers
  313. Taking Games Seriously [Java]
  314. The ass and the mule [Java]
  315. Three 3s
  316. Three 4s
  317. Three 5s
  318. Tool for Constructing Orthogonal Latin Squares [Java]
  319. Tower of Hanoi, the Hard Way [Java]
  320. Transpositions
  321. Triangular numbers that are also square
  322. Trilateral Diagrams [Java]
  323. Trinary Tree(s) underlying Primitive Pythagorean Triples
  324. Twenty five boys and twenty five girls around a table.
  325. Two Circles and a Limit [Java]
  326. Two Colors in Two Rows [Java]
  327. Two Men of Tibet [Java]
  328. Two Numbers Guessing Game [Java]
  329. Universal Coloring [Java]
  330. Universal Product Code [Java]
  331. Venn Diagrams
  332. Ways To Count
  333. Weierstrass Product Inequality
  334. Weighing 12 coins
  335. What, how, and the Web [Java]
  336. What Is Algorithm?
  337. What Is Fraction?
  338. What Is Infinity?
  339. What Is Limit?
  340. What is so natural about “natural logarithms”?
  341. WHEN THE COUNTING GETS TOUGH, THE TOUGH COUNT ON MATHEMATICS
  342. Where To Start? [Java]
  343. Why 1/3 + 1/4 = 7/12?
  344. Why 17?
  345. Wilson's Theorem
  346. With One 4
  347. Wolf and Rabbit [Flash]
  348. Word Problems [Java]
  349. Zeros and Nines [Java]

Copyright © 1996-2009 Alexander Bogomolny

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