Interactive Mathematics Miscellany and Puzzles

Interactive Mathematics Miscellany and Puzzles

Interactive Mathematics Miscellany and Puzzles

Interactive Mathematics Miscellany and Puzzles

What has changed?

What has changed?

|Contents|

|Contents|

|Front page|

|Front page|

Index page

Index page

CTK wiki-math

CTK wiki-math

Privacy policy

Privacy policy

Help with math

Help with math

Arithmetic

Arithmetic

Algebra

Algebra

And much much more ...

And much much more ...

Probability

Probability

Trigonometry

Trigonometry

Visual illusions

Visual illusions

Cut the knot!

Cut the knot!

What is what?

What is what?

Manifesto

Manifesto

Eye Opener Series

Eye Opener Series

Math as language

Math as language

CTK Insights blog

CTK Insights blog

Problem solving

Problem solving

Outline mathematics

Outline mathematics

Book reviews

Book reviews

Interactive activities

Interactive activities

Did you know?

Did you know?

Eye opener

Eye opener

Draw Ellipse

Draw Ellipse

Math Olympiads

Math Olympiads

Proofs in mathematics

Proofs in mathematics

Things impossible

Things impossible

Index/Glossary

Index/Glossary

Fast Arithmetic Tips

Fast Arithmetic Tips

Stories for young

Stories for young

Word problems

Word problems

Mathematics Games %26 Puzzles

Mathematics Games %26 Puzzles

Our logo

Our logo

Make an Identity

Make an Identity

Elementary geometry

Elementary geometry

CutTheKnotMath facebook page

CutTheKnotMath facebook page

Tell a friend

Tell a friend

Talk about it

Talk about it

Twitter

Twitter

Facebook

Facebook

Base Conversion

Base Conversion

Divisibility Criteria

Divisibility Criteria

Euclid's Game

Euclid's Game

Hour glass timing

Hour glass timing

Magic in Square

Magic in Square

Napier Bones

Napier Bones

Number Guessing Game

Number Guessing Game

Arithmetic Word Problems

Arithmetic Word Problems

Online practice

Online practice

Three Jugs Problem

Three Jugs Problem

Box Labels

Box Labels

Fish Soup game

Fish Soup game

Goat, Cabbage and Wolf

Goat, Cabbage and Wolf

Josephus Flavius' problem

Josephus Flavius' problem

Mastermind Variants

Mastermind Variants

Peg Solitaire

Peg Solitaire

Scoring

Scoring

Toads And Frogs Puzzle

Toads And Frogs Puzzle

Toads And Frogs in 2D

Toads And Frogs in 2D

Tower of Hanoi

Tower of Hanoi

Tromino Puzzle

Tromino Puzzle

And much much more ...

And much much more ...

Lewis Carroll's Logic Game

Lewis Carroll's Logic Game

Venn Diagrams

Venn Diagrams

Logic Word Problems

Logic Word Problems

And more ...

And more ...

Fractals %26 Chaos

Fractals %26 Chaos

Color Cycling on Mandelbrot

Color Cycling on Mandelbrot

Emergence of Chaos

Emergence of Chaos

All Peano Curves

All Peano Curves

Cantor sets

Cantor sets

Pascal Triangle

Pascal Triangle

Fractal Curves and Dimension

Fractal Curves and Dimension

Iterated Function Systems

Iterated Function Systems

Iterations in Mandelbrot Set

Iterations in Mandelbrot Set

Julia Sets

Julia Sets

Logistic Model

Logistic Model

Plane Filling Curves

Plane Filling Curves

Sierpinski Gasket

Sierpinski Gasket

Toying with Tremas

Toying with Tremas

Fallacies

Fallacies

Curry's Paradox

Curry's Paradox

Delian Problem Solved

Delian Problem Solved

A Faulty Dissection

A Faulty Dissection

Langman's Paradox

Langman's Paradox

Sam Loyd's Son's Dissection

Sam Loyd's Son's Dissection

Rouse Ball's Fallacy

Rouse Ball's Fallacy

Calculus

Calculus

Equations of the Straight Line

Equations of the Straight Line

Function, Derivative and Integral

Function, Derivative and Integral

Lagrange Interpolation

Lagrange Interpolation

Riemann Sums

Riemann Sums

Rolle's and Mean Value

Rolle's and Mean Value

Taylor Series for Cosine

Taylor Series for Cosine

Combinatorial Games

Combinatorial Games

Date Game

Date Game

Grundy's Game

Grundy's Game

Kayles

Kayles

Nimble

Nimble

Northcott's game

Northcott's game

One Pile

One Pile

Plainim Mis%26#232;re

Plainim Mis%26#232;re

Subtraction Game

Subtraction Game

Take-Away Games

Take-Away Games

Turning Turtles

Turning Turtles

Wythoff's Nim

Wythoff's Nim

And much more ...

And much more ...

3-Term Arithmetic Series

3-Term Arithmetic Series

Binary Color Device

Binary Color Device

Candy Game

Candy Game

Chebyshev polynomials

Chebyshev polynomials

Counting Triangles

Counting Triangles

Averages

Averages

Heads and Tails

Heads and Tails

Multiplication Table

Multiplication Table

Interest Calculations

Interest Calculations

Letter Counting

Letter Counting

Merlin's Magic Squares

Merlin's Magic Squares

Proizvolov's Identity

Proizvolov's Identity

Pythagorean Triples

Pythagorean Triples

Self-documenting Sentences

Self-documenting Sentences

What's next?

What's next?

Word Problems

Word Problems

Online practice

Online practice

Visual Illusions

Visual Illusions

Balls and Shadows Illusion

Balls and Shadows Illusion

Bulging lines illusion

Bulging lines illusion

Gerbino's Illusion

Gerbino's Illusion

Heaver: A Visual Illusion

Heaver: A Visual Illusion

Hering Illusion

Hering Illusion

Judd Illusion

Judd Illusion

Kanizsa Triangle

Kanizsa Triangle

M%26#252;ller-Lyer Illusion

M%26#252;ller-Lyer Illusion

Necker Cube

Necker Cube

Perspective Illusion

Perspective Illusion

Poggendorff Illusion II

Poggendorff Illusion II

Ponzo Illusion

Ponzo Illusion

Revolving Circles Illusion

Revolving Circles Illusion

Twisted Cord Illusion

Twisted Cord Illusion

Wundt Block Illusion

Wundt Block Illusion

Z%26#246;llner's Illusion

Z%26#246;llner's Illusion

And much much more ...

And much much more ...

Birds On a Wire

Birds On a Wire

Buffon's Noodle

Buffon's Noodle

Misuse of Statistics

Misuse of Statistics

Monty Hall Dilemma

Monty Hall Dilemma

Parrondo's Paradox

Parrondo's Paradox

Probability and Infinity

Probability and Infinity

Computer Math Magic

Computer Math Magic

Arithmetic magic matrix

Arithmetic magic matrix

Bachet's Magic Trick

Bachet's Magic Trick

Calendar Magic

Calendar Magic

Gergonne's Magic Trick

Gergonne's Magic Trick

Hummer's Mind Reader

Hummer's Mind Reader

Magic in Square

Magic in Square

Number Guessing Game

Number Guessing Game

Guessing Two Numbers

Guessing Two Numbers

Combinatorics

Combinatorics

Bicolor Tower of Hanoi

Bicolor Tower of Hanoi

Art Gallery Theorem

Art Gallery Theorem

Coin change

Coin change

Critical Path

Critical Path

Latin Squares

Latin Squares

Listing all permutations

Listing all permutations

Mazes

Mazes

Monotone Sequences

Monotone Sequences

A Pigeonhole Problem

A Pigeonhole Problem

Project Scheduling

Project Scheduling

Scrub Tile Puzzle

Scrub Tile Puzzle

Shuttle Puzzle

Shuttle Puzzle

Mathematics Miscellany

Mathematics Miscellany

Disappearing Rectangles

Disappearing Rectangles

Genetic Algorithm

Genetic Algorithm

Impossible Fork

Impossible Fork

Projectile Trajectory

Projectile Trajectory

Random Dot Stereograms

Random Dot Stereograms

Ratchet Effect

Ratchet Effect

3 Utilities Puzzle

3 Utilities Puzzle

All About Altitudes

All About Altitudes

Angle Bisectors

Angle Bisectors

Area of Parallelogram

Area of Parallelogram

Asymmetric Propeller

Asymmetric Propeller

Butterfly Theorem

Butterfly Theorem

Sangaku: Thoughts %26 Problems

Sangaku: Thoughts %26 Problems

Fagnano's problem

Fagnano's problem

Inversion: Reflection in Circle

Inversion: Reflection in Circle

Mathematics in Pizzeria

Mathematics in Pizzeria

Morley's Miracle

Morley's Miracle

Outline Solutions

Outline Solutions

Poles and Polars

Poles and Polars

Pythagorean Theorem (122 proofs)

Pythagorean Theorem (122 proofs)

Reflection in Line

Reflection in Line

Translation Transform

Translation Transform

Triangle geometry

Triangle geometry

Breaking Chocolate Bars

Breaking Chocolate Bars

Farmer and Wife

Farmer and Wife

Make Your Move, Kid!

Make Your Move, Kid!

Solitaire on the Circle

Solitaire on the Circle

Two Butterflies Theorem

Two Butterflies Theorem

Mathematics in Social Science

Mathematics in Social Science

Method of Markers

Method of Markers

Method of Sealed Bids

Method of Sealed Bids

Fast Power Indices

Fast Power Indices

Hamilton's Apportionment

Hamilton's Apportionment

Huntington-Hill Apportionment

Huntington-Hill Apportionment

Social Choice

Social Choice

And much much more ...

And much much more ...

Mathematical Droodles

Mathematical Droodles

Circle Chains

Circle Chains

Diagonal Count

Diagonal Count

Directly Similar Figures

Directly Similar Figures

Equal Incircles Theorem

Equal Incircles Theorem

Eyeball Theorem

Eyeball Theorem

Fagnano's problem

Fagnano's problem

Maxwell's Theorem

Maxwell's Theorem

Poncelet's Porism

Poncelet's Porism

Shape of Constant Width

Shape of Constant Width

Squinting Eyes Theorem

Squinting Eyes Theorem

Angle Trisector

Angle Trisector

Broken Calculator

Broken Calculator

Cycloids

Cycloids

Ellipse and Other Curves

Ellipse and Other Curves

Geoboard

Geoboard

Peaucellier Linkage

Peaucellier Linkage

Pythagorean Theorem

Pythagorean Theorem

And more ...

And more ...

|Contact|

|Contact|

Alexander Bogomolny

Alexander Bogomolny

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