Interactive Mathematics Miscellany
and Puzzles
[画像:Alex]
Back in 1996, Alexander Bogomolny started making the internet math-friendly by creating thousands of images, pages, and programs for this website, right up to his last update on July 6, 2018. Hours later on July 7th he passed away. His friend Nassim Taleb announced the devastating news. "He was of the few saints you meet in life: he gave more, much more than he took." Alex's family and friends have asked the Wolfram Foundation to serve as a steward for continuing maintenance and updates to the site, more details to come.
Twitter, Facebook
Twitter, Facebook
book
Cut the Knot is a book of probability riddles curated to challenge the mind and expand mathematical and logical thinking skills. First housed on cut-the-knot.org, these puzzles and their solutions represent the efforts of great minds around the world. Follow along as Alexander Bogomolny presents these selected riddles by topical progression. Try them for yourself before reading their solutions. Just like it was for Alexander the Great, the non-trivial, unexpected solution might be exactly the one you need.
Buy on Amazon
This commemorative book was produced in collaboration with STEM Academic Press and Wolfram Media. Published on November 17, 2020 all proceeds from sale go to Alexander's family. For more info on the book and its release see Nassim Nicholas Taleb's post.
Buy on Amazon
This commemorative book was produced in collaboration with STEM Academic Press and Wolfram Media. Published on November 17, 2020 all proceeds from sale go to Alexander's family. For more info on the book and its release see Nassim Nicholas Taleb's post.
Arithmetic
Base Conversion
Divisibility Criteria
Euclid's Game
Fast Arithmetic Tips
Hour glass timing
Magic in Square
Make an Identity
Napier Bones
Number Guessing Game
Arithmetic Word Problems
Online practice
And much much more ...
Base Conversion
Divisibility Criteria
Euclid's Game
Fast Arithmetic Tips
Hour glass timing
Magic in Square
Make an Identity
Napier Bones
Number Guessing Game
Arithmetic Word Problems
Online practice
And much much more ...
Mathematics Games & Puzzles
Three Jugs Problem
Box Labels
Fish Soup game
Goat, Cabbage and Wolf
Josephus Flavius' problem
Mastermind Variants
Peg Solitaire
Scoring
Toads And Frogs Puzzle
Toads And Frogs in 2D
Tower of Hanoi
Tromino Puzzle
And much much more ...
Three Jugs Problem
Box Labels
Fish Soup game
Goat, Cabbage and Wolf
Josephus Flavius' problem
Mastermind Variants
Peg Solitaire
Scoring
Toads And Frogs Puzzle
Toads And Frogs in 2D
Tower of Hanoi
Tromino Puzzle
And much much more ...
Fractals
& Chaos
Color Cycling on Mandelbrot
Emergence of Chaos
All Peano Curves
Cantor sets
Pascal Triangle
Fractal Curves and Dimension
Iterated Function Systems
Iterations in Mandelbrot Set
Julia Sets
Logistic Model
Plane Filling Curves
Sierpinski Gasket
Toying with Tremas
And more ...
Color Cycling on Mandelbrot
Emergence of Chaos
All Peano Curves
Cantor sets
Pascal Triangle
Fractal Curves and Dimension
Iterated Function Systems
Iterations in Mandelbrot Set
Julia Sets
Logistic Model
Plane Filling Curves
Sierpinski Gasket
Toying with Tremas
And more ...
Fallacies
Curry's Paradox
Delian Problem Solved
A Faulty Dissection
Langman's Paradox
Sam Loyd's Son's Dissection
Rouse Ball's Fallacy
And more ...
Curry's Paradox
Delian Problem Solved
A Faulty Dissection
Langman's Paradox
Sam Loyd's Son's Dissection
Rouse Ball's Fallacy
And more ...
Calculus
Equations of the Straight Line
Function, Derivative and Integral
Lagrange Interpolation
Riemann Sums
Rolle's and Mean Value
Taylor Series for Cosine
And more ...
Equations of the Straight Line
Function, Derivative and Integral
Lagrange Interpolation
Riemann Sums
Rolle's and Mean Value
Taylor Series for Cosine
And more ...
Combinatorial Games
Date Game
Grundy's Game
Kayles
Nim
Nimble
Northcott's game
One Pile
Plainim Misère
Subtraction Game
Take-Away Games
Turning Turtles
Wythoff's Nim
And much more ...
Date Game
Grundy's Game
Kayles
Nim
Nimble
Northcott's game
One Pile
Plainim Misère
Subtraction Game
Take-Away Games
Turning Turtles
Wythoff's Nim
And much more ...
Algebra
3-Term Arithmetic Series
Binary Color Device
Candy Game
Chebyshev polynomials
Counting Triangles
Averages
Heads and Tails
Multiplication Table
Interest Calculations
Letter Counting
Merlin's Magic Squares
Proizvolov's Identity
Pythagorean Triples
Self-documenting Sentences
What's next?
Word Problems
Online practice
And much more ...
3-Term Arithmetic Series
Binary Color Device
Candy Game
Chebyshev polynomials
Counting Triangles
Averages
Heads and Tails
Multiplication Table
Interest Calculations
Letter Counting
Merlin's Magic Squares
Proizvolov's Identity
Pythagorean Triples
Self-documenting Sentences
What's next?
Word Problems
Online practice
And much more ...
Visual Illusions
Balls and Shadows Illusion
Bulging lines illusion
Gerbino's Illusion
Heaver: A Visual Illusion
Hering Illusion
Judd Illusion
Kanizsa Triangle
Müller-Lyer Illusion
Necker Cube
Perspective Illusion
Poggendorff Illusion II
Ponzo Illusion
Revolving Circles Illusion
Twisted Cord Illusion
Wundt Block Illusion
Zöllner's Illusion
And much much more ...
Balls and Shadows Illusion
Bulging lines illusion
Gerbino's Illusion
Heaver: A Visual Illusion
Hering Illusion
Judd Illusion
Kanizsa Triangle
Müller-Lyer Illusion
Necker Cube
Perspective Illusion
Poggendorff Illusion II
Ponzo Illusion
Revolving Circles Illusion
Twisted Cord Illusion
Wundt Block Illusion
Zöllner's Illusion
And much much more ...
Probability
Birds On a Wire
Buffon's Noodle
Misuse of Statistics
Monty Hall Dilemma
Parrondo's Paradox
Probability and Infinity
And much more ...
Birds On a Wire
Buffon's Noodle
Misuse of Statistics
Monty Hall Dilemma
Parrondo's Paradox
Probability and Infinity
And much more ...
Computer Math Magic
Arithmetic magic matrix
Bachet's Magic Trick
Calendar Magic
Gergonne's Magic Trick
Hummer's Mind Reader
Magic in Square
Number Guessing Game
Guessing Two Numbers
Arithmetic magic matrix
Bachet's Magic Trick
Calendar Magic
Gergonne's Magic Trick
Hummer's Mind Reader
Magic in Square
Number Guessing Game
Guessing Two Numbers
Combinatorics
Bicolor Tower of Hanoi
Art Gallery Theorem
Coin change
Critical Path
Latin Squares
Listing all permutations
Mazes
Monotone Sequences
A Pigeonhole Problem
Project Scheduling
Scrub Tile Puzzle
Shuttle Puzzle
Tower of Hanoi
And much more ...
Bicolor Tower of Hanoi
Art Gallery Theorem
Coin change
Critical Path
Latin Squares
Listing all permutations
Mazes
Monotone Sequences
A Pigeonhole Problem
Project Scheduling
Scrub Tile Puzzle
Shuttle Puzzle
Tower of Hanoi
And much more ...
Mathematics Miscellany
Disappearing Rectangles
Genetic Algorithm
Impossible Fork
Projectile Trajectory
Random Dot Stereograms
Ratchet Effect
And more ...
Disappearing Rectangles
Genetic Algorithm
Impossible Fork
Projectile Trajectory
Random Dot Stereograms
Ratchet Effect
And more ...
Geometry
3 Utilities Puzzle
All About Altitudes
Angle Bisectors
Area of Parallelogram
Asymmetric Propeller
Butterfly Theorem
Sangaku: Thoughts & Problems
Fagnano's problem
Inversion: Reflection in Circle
Mathematics in Pizzeria
Morley's Miracle
Outline Solutions
Poles and Polars
Pythagorean Theorem (122 proofs)
Reflection in Line
Translation Transform
Triangle geometry
And much much more ...
3 Utilities Puzzle
All About Altitudes
Angle Bisectors
Area of Parallelogram
Asymmetric Propeller
Butterfly Theorem
Sangaku: Thoughts & Problems
Fagnano's problem
Inversion: Reflection in Circle
Mathematics in Pizzeria
Morley's Miracle
Outline Solutions
Poles and Polars
Pythagorean Theorem (122 proofs)
Reflection in Line
Translation Transform
Triangle geometry
And much much more ...
Eye Opener Series
Breaking Chocolate Bars
Farmer and Wife
Make Your Move, Kid!
Solitaire on the Circle
Two Butterflies Theorem
And much more ...
Breaking Chocolate Bars
Farmer and Wife
Make Your Move, Kid!
Solitaire on the Circle
Two Butterflies Theorem
And much more ...
Mathematics in Social Science
Method of Markers
Method of Sealed Bids
Fast Power Indices
Hamilton's Apportionment
Huntington-Hill Apportionment
Social Choice
And much much more ...
Method of Markers
Method of Sealed Bids
Fast Power Indices
Hamilton's Apportionment
Huntington-Hill Apportionment
Social Choice
And much much more ...