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Interactive Mathematic Miscellany and Puzzles
Arithmetic and Algebra
17 rooks on an 8×8 chessboard
- 3-Colors Tower of Hanoi [Java]
- 3 glass puzzle [JavaScript]
- 3-Term Arithmetic Progression
- 4x4 coloring problem
- A 49th Degree Challenge
- A Clique of Acquaintances
- A Line in a Square Grid [Java]
- Abacus in Various Number Systems [Java]
- About numbers
- Achieve the Equilibrium [Flash]
- Addition
- Affirmative Action Problem [Java]
- Algorithm for Computing LCM [Java]
- The Aliquot Game [Java]
- Algebraic Structure of Complex Numbers
- Almost every integer has the digit 3 in it
- Almost Integers - Gaussian Integers
- An Application of Mental Arithmetic to Highway Safety
- An Arithmetic Magic Trick [Java]
- An Inequality for Grade 8
- An Inequality With an Infinite Series
- An Interesting Number
- Arithmetic-Geometric Means Inequality
- Arithmetic magic matrix [Java]
- Arithmetic Operations in Various Bases [Java]
- Arithmetic Paradoxes
- A simple integral
- Another simple integral
- Averages, Arithmetic and Harmonic Means [Java]
- Averages in a sequence
- Bachet's Magic Trick [Java]
- Banzhaf Power Index Calculator [Java]
- Barcode Encoding
- Barcode Magic [Java]
- Base Converter [JavaScript]
- Basic Rules of Counting
- Bayes' Theorem
- Beatty Sequences
- Bilateral Diagrams [Java]
- Binary Color Device [Java]
- Binary Euclid's Algorithm
- Binomial Distribution [Java]
- Binomial Theorem\
- Bisector of an imaginary angle may be real
- Boys and Girls Solving Problems
- Breaking Chocolate Bars [Java]
- Broken Calculator [Java]
- Byzantine Basketball
- Calculation of the Digits of pi by the Spigot Algorithm [Java]
- Cantor-Bernstein-Schroeder theorem
- Cardinal Numbers
- Cartesian Coordinate System [Java]
- Caterpillar [Flash]
- Cavalieri's Principle [Java]
- Chameleons of Three Colors
- Chinese Remainder Theorem
- Clifford Algebras
- Collatz Conjecture [Java]
- Coloring a Graph [Java]
- Combinatorial Proofs
- Committee Chairs
- Comparing complex numbers
- Completing a Square and Quadratic Formula
- Complex Numbers: A Dynamic Tool [Java]
- Complex number to a complex power may be real
- Computer As a Magician [Java]
- Constructible Numbers
- Continued fractions
- Countability of Rational Numbers
- Counting: The Beginning of Mathematics [Java]
- Counting Chips On a Circle [Java]
- Counting Squares in a Square [Java]
- Counting Triangles [Java]
- Counting Triangles II [Java]
- Covering A Chessboard With Domino
- Cryptarithms [JavaScript, Frames]
- Cubic Formula [JavaScript]
- Cubics and Bézout's Theorem
- Derivatives without Limits
- Descartes' Rule of Signs
- Distance between the Orthocenter and Circumcenter
- Distance Between Strings [Java]
- Distance From a Point to a Straight Line [Java]
- Distributive Law [Java]
- Dividing Loot Fairly
- Divisibility and Modulo Arithmetic at IMO 2007
- Divisibility by 7
- Divisibility by 9 and 11
- Divisibility by 81
- Divisibility Criteria
- Divisibility by 7, 11, and 13
- Dollars in Pockets
- Dot Patterns and Sierpinski Gasket [Java]
- Dots and fractions [Java]
- Ducci Sequences [Java]
- EAN-13 Encoding [Java]
- Egyptian Multiplication [Java]
- Eigenvectors by Inspection
- Equations of the Staight Line [Java]
- Equivalence Relations
- Euclid's Algorithm
- Euclid's Game [Java]
- Euler’s formula for eiθ
- Euler's Function and Congruence Theorem
- Evolution of Algebraic Symbolism
- Every composite number is the product of some factors and also the sum of the same numbers
- Extension of Euclid's Algorithm
- Factorials and division
- Fair Division: Method of Sealed Bids II [Java]
- Falsity implies anything
- Farey Series
- Fast Arithmetic Tips
- Fermat's Little Theorem
- Fibonacci's Quickies
- First Geometric Interpretation of Complex Numbers [Java]
- Five Methods of Apportionment [Java]
- Five Lattice Points [Java]
- Fleury's Algorithm and Euler's Paths and Cycles [Java]
- Flipping Items Simultaneously [Java]
- Flipping Items Simultaneously II [Java]
- Flipping pancakes [Java]
- Floor Function
- Formal Framework, an example
- Formal Systems - an Example
- Formula for Primes
- Four 3s
- Four 4s
- Four 5s
- Four Hinged Squares: using complex numbers
- Four Pegs That Form a Square
- Four Voting Methods [Java]
- Fraction Comparison [Java]
- Fractions on a Binary Tree
- Fractions on a Binary Tree II
- Frieze Patterns [Java]
- Fun with digits
- Function
- Fundamental Theorem of Algebra
- Funny Arithmetic [JavaScript]
- Gasoline Stations on a Circular Trek
- GCD(M, N) × LCM(M, N) = M × N [Java]
- Generalization That Solves the Problem
- Generating Functions
- Geometric Construction of Roots of Quadratic Equation [Java]
- Geometric view of the Sieve of Eratosthenes [Java]
- Gergonne Magic Trick [Java]
- Gödel's Incompleteness Theorem
- Graph and Roots of a Third Degree Polynomial [Java]
- Graph and Roots of Quadratic Polynomial [Java]
- Graph of a Polynomial [Java]
- Graph of a Polynomial Defined by Its Roots [Java]
- Group multiplication of permutations [Java]
- Guessing Two Consecutive Integers
- Finding Hamilton Paths and Circuits [Java]
- Harmonic Serires And Its Parts
- Heads and Tails [Java]
- Horner's Method [Java]
- Hour glass timing
- How to Ask an Embarrassing Question
- How to define a permutation? [Java]
- How to efficiently defend a castle
- Hyperintegers and Hyperreal Numbers
- Identical Twins Puzzle
- Identities in the Multiplication Table [Java]
- Implementation of Base Conversion
- Impossible Machine
- Importance of the Absolute Value
- Inclusion-Exclusion Principle
- Inequality 1/2·3/4·5/6· ... ·99/100 < 1/10
- Inequality (1 + 1-3)(1 + 2-3)(1 + 2-3)...(1 + n-3) < 3
- Inequality 1 + 2-2 + 3-2 + 4-2 + ... + n-2 < 2.
- Inequality from Math Magazine 2009
- Infinite Discent for x4 + y4 = z4
- Infinitesimals. Non-standard Analysis
- Infinitude of Primes
- Infinity As a Limit
- Inflection Points of Fourth Degree Polynomials [Java]
- Integer Iterations on a Circle [Java]
- Integer Iterations on a Circle III [Java]
- Integer roots of integers are irrational
- Integers and Rectangles [Java]
- Integers and Rectangles: a Proof by Induction [Java]
- Integers and Rectangles: Two Simple Proofs [Java]
- Interest Calculations [Java]
- ISBN Encoding [Java]
- Irrational number to an irrational power may be rational
- Is 0.999... = 1?
- It's All About Powers of 10
- Joachimsthal's Notations
- Jumping Isn't Everything [Java]
- Kaprekar's Iterations and Numbers [Java]
- Lagrange's identity, Proof
- Lagrange interpolation
- Langford and Skolem Sequences [Java]
- Latin Squares [Java]
- Lattice Multiplication [Java]
- Leibniz and Pascal Triangles [Java]
- Lewis Carroll's Game of Logic [Java]
- Light Bulbs in a Circle [Java]
- Lights Out [Java]
- Linear functions
- Linear Programming
- Listing All Combinations [Java]
- Listing all permutations [Java]
- Listing All Permutations: Johnson-Trotter Method [Java]
- Logistic Model applet [Java]
- Long Multiplication [Java]
- Long Runs of Composite Numbers
- Looking your best
- Loop or Halt [Java]
- Lucas' Theorem
- Magic in Square [Java]
- Make An Identity [Java]
- Market Day
- Marriage Theorem
- Marriage Problem, simulation [Java]
- Math Card Trick
- Math Lotto
- Math Telepathy [Java]
- Mathematical Induction
- Mathematical Proof
- Mathematicians Doze Off
- Matrix Groups
- Maximum Volume of a Cut Off Box [Java]
- Means [Java]
- Mediant Fractions
- Method of Markers II [Java]
- Minesweeper Theorem
- Mini Lights Out [Java]
- Minimax Principle [Java]
- Minimax Theorem [Java]
- Minumum Spanning Trees and Kruskal's Algorithm [Java]
- Modular Arithmetic [Java]
- Monotone Convergence Theorem
- Monotone Number Sequences [Java]
- Multiplication
- Napier Bones [Java]
- Napoleon's Relatives [Java]
- Nested Radicals
- Newton's Method [Java]
- Nine Squares [Java]
- Number 8 Is Interesting
- Number Guessing Game [Java]
- Number sequences and Pigeonhole [Java]
- Number System With Base 36
- On the Games of Hex and Y
- One Dimensional Ants
- One Trigonometric Formula and Its Consequences
- Operations on Fractions [Java]
- Order. Well-ordered sets.
- Ordinal Numbers
- Outline Mathematics
- Parity counting [Java]
- Parrondo Paradox Via Simpson Paradox [Java]
- Party Acquaintances [Java]
- Peano axioms
- Peasant Multiplication [Java]
- Pennies in Boxes [Java]
- Percent
- Permutations
- Pigeonhole Principle
- Place Value [Java]
- Probability of Divisibility
- Problem 1 from the IMO 2009
- Problem A1, 69th Putnam Competition
- Problem A2, 69th Putnam Competition
- Problem of Divisibility by 5n
- Product of Diagonals in Regular N-gon
- Product Of Four Consecutive Integers
- Product of Simple Fractions [Java]
- Product of permutations [Java]
- Proizvolov's Identity [Java]
- Proofs Without Words [Java]
- Property of an
- Property of the Powers of 2 [Java]
- Yet Another Puzzle with Hats
- Puzzlist vs. Mathematician: A Practical Arithmetic Problem
- Pythagorean Triples [Java]
- Quasigroups and block designs from triangular grid [Java]
- Ramsey's Theorem
- Recombining Permutations [Java]
- Represent 4 with four digits
- Represent 6 with three digits
- Rectangle on a Chessboard [Java]
- Review of Arithmetic for Parents: A Book for Grownups about Children's Mathematics by R. Aharoni
- Rhind Papyrus
- Riemann Sphere and Möbius Transformation
- Riemann Sums - Function Integration [Java]
- Right Replacement [Java]
- Rolle's and Mean Value Theorems [Java]
- Round Robin Tournament
- Russell's Paradox
- Scheduling and Critical Path Algorithm [Java]
- Scrub Tile Puzzle [Java]
- Self-descriptive Strings [Java]
- Self-reference
- Seven Terms Periodic Sequence
- Shapley-Shubik Power Index [Java]
- Shapley-Shubik Power Index Calculator [Java]
- Ship-Dock Theorem
- Sierpinski Gasket and Tower of Hanoi
- Sierpinski's Gasket and Dihedral Symmetry [Java]
- Sieve of Eratosthenes [Java]
- Sieve of Squares [Java]
- Σ2-n = Σn·2-n
- Signs and Sums in a Sequence [Java]
- Signs in a Matrix [Java]
- Simple Cellular Automaton [Java]
- Simple Graph Practice [Java]
- Simpson Paradox [Java]
- Sine of a Sum Formula, Proof Without Words
- Single formula to express any integer with digits 0-9 each used just once
- Six Balls, Two Weighings
- Slider Puzzles [Java]
- Solitaire in Two Colors [Java]
- Solve xx3 = 3
- Soriteses
- Soroban in Various Number Systems
- Sorting Algorithms
- Sperner's Theorem
- Splitting piles
- Square root of 2 is irrational
- Squares, Circles, and Triangles [Java]
- Steinhaus' Problem [Java]
- Step into the Elliptic Realm
- Stern-Brocot Tree
- Straight Tromino on a Chessboard [Java]
- Structure of Hyperreal Numbers
- Suan Pan in Various Number Systems [Java]
- Subtraction Game [Java]
- Sum without Adding
- Sums and Products [Java]
- Sums of powers of digits [Java]
- Superposition Principle
- Surreal Numbers
- Taking Games Seriously [Java]
- The ass and the mule [Java]
- Three 3s
- Three 4s
- Three 5s
- Tool for Constructing Orthogonal Latin Squares [Java]
- Three Dimensional Cross
- Tower of Hanoi, the Hard Way [Java]
- Transpositions
- Traveling Salesman Problem [Java]
- Triangular numbers that are also square
- Trilateral Diagrams [Java]
- Trinary Tree(s) underlying Primitive Pythagorean Triples
- Twenty five boys and twenty five girls around a table.
- Two Circles and a Limit [Java]
- Two Colors in Two Rows [Java]
- Two Men of Tibet [Java]
- Two Numbers Guessing Game [Java]
- Uncountability of the Reals - via a Game
- Universal Coloring [Java]
- Universal Product Code [Java]
- USA 1975 Problem 3
- Venn Diagrams
- Ways To Count
- Weierstrass Product Inequality
- Weighing 12 coins
- What, how, and the Web [Java]
- What Is Algorithm?
- What Is Fraction?
- What Is Infinity?
- What Is Limit?
- What is so natural about “natural logarithms”?
- WHEN THE COUNTING GETS TOUGH, THE TOUGH COUNT ON MATHEMATICS
- Where To Start? [Java]
- Why 1/3 + 1/4 = 7/12?
- Why 17?
- Wilson's Theorem
- With One 4
- Wolf and Rabbit [Flash]
- Word Problems [Java]
- Zeros and Nines [Java]
Copyright © 1996-2009 Alexander Bogomolny
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