Fun maths facts

153 entries

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• The Diagonal of a Regular Pentagon
  • Published in 2026
  • Added on 2026-10-18
• Inevitable Dottie Number. Iterals of cosine and sine
  • Published in 2012
  • Added on 2026-10-14
• An arborist's guide to the rationals
  • Published in 2014
  • Added on 2026-06-23
• Consecutive Integers and the Collatz Conjecture
  • Published in 2015
  • Added on 2026-06-18
• A non-involutory selfduality
  • Published in 1989
  • Added on 2026-04-27
• All knots are trivial: a "proof" by sleight of hand
  • Published in 2026
  • Added on 2026-04-27
• The first 50 million prime numbers
  • Published in 1977
  • Added on 2026-04-10
• Braids in trivial braid diagrams
  • Published in 2003
  • Added on 2026-04-10
• How to cage an egg
  • Published in 1992
  • Added on 2026-03-14
• What Type of Apollonian Circle Packing Will Appear
  • Published in 2021
  • Added on 2026-02-26
• The Extraordinary Power of Division in Straight Line Programs
  • Published in 2012
  • Added on 2026-02-06
• A formula for any real number, maybe
  • Published in 2026
  • Added on 2026-02-05
• On Formulae for the Nth Prime Number
  • Published in 1964
  • Added on 2026-01-12
• Magic Triangles
  • Published in 2022
  • Added on 2026-01-12
• On the existence of numbers with matching continued fraction and decimal expansions
  • Published in 2021
  • Added on 2025-12-18
• A Theorem On Repeating Decimals
  • Published in 1967
  • Added on 2025-08-28
• The Rubik's Cube Perfect Scramble
  • Published in 2025
  • Added on 2025-08-20
• The Paradox of Anti-Inductive Dice
  • Published in 2025
  • Added on 2025-05-23
• A robot that unknots knots
  • Published in 2025
  • Added on 2025-05-03
• On the Traveling Fly Problem
  • Published in 1996
  • Added on 2025-04-22
• Squaring the Plane
  • Published in 2020
  • Added on 2025-01-07
• Hamiltonian Cycles on Ammann-Beenker Tilings
  • Published in 2024
  • Added on 2024-12-02
• Tiling with Three Polygons is Undecidable
  • Published in 2024
  • Added on 2024-12-02
• Ropes, fractions, and moduli spaces
  • Published in 2023
  • Added on 2024-09-30
• Look, There's More to Say about Conway's Look and Say Sequence
  • Published in 2024
  • Added on 2024-09-05
• Tumbling Downhill along a Given Curve
  • Published in 2024
  • Added on 2024-07-24
• Normal Numbers are Normal
  • Published in 2006
  • Added on 2024-07-11
• Integers that are not the sum of positive powers
  • Published in 2024
  • Added on 2024-06-21
• Iterated failures of choice
  • Published in 2019
  • Added on 2024-06-10
• Sur la loi de répartition du k-ième facteur premier d'un entier
  • Published in 2002
  • Added on 2024-05-24
• How big a table do you need for your jigsaw puzzle?
  • Published in 2023
  • Added on 2024-01-15
• The Sine of a Single Degree
  • Published in 2017
  • Added on 2024-01-15
• When Can You Tile an Integer Rectangle with Integer Squares?
  • Published in 2023
  • Added on 2023-10-09
• Conway and Doyle Can Divide by Three, But I Can't
  • Published in 2023
  • Added on 2023-09-29
• Distant decimals of $π$
  • Published in 2017
  • Added on 2023-08-14
• Wallpaper Functions
  • Published in 2002
  • Added on 2023-06-20
• A curious result related to Kempner's series
  • Published in 2008
  • Added on 2023-02-27
• The Packing Chromatic Number of the Infinite Square Grid is 15
  • Published in 2023
  • Added on 2023-01-26
• Maclaurin Integration: A Weapon Against Infamous Integrals
  • Published in 2022
  • Added on 2022-10-08
• Euclidean traveller in hyperbolic worlds
  • Published in 2022
  • Added on 2022-09-09
• Stuttering look and say sequences and a challenger to Conway's most complicated algebraic number from the silliest source
  • Published in 2022
  • Added on 2022-07-08
• On The Euclidean Algorithm: Rhythm Without Recursion
  • Published in 2022
  • Added on 2022-07-08
• The Strong Law of Small Numbers
  • Published in 1988
  • Added on 2022-07-05
• Filling space with hypercubes of two sizes -- The pythagorean tiling in higher dimensions
  • Published in 2022
  • Added on 2022-05-13
• A simple mnemonic to compute sums of powers
  • Published in 2022
  • Added on 2022-04-24
• Convex Equipartitions: The Spicy Chicken Theorem
  • Published in 2013
  • Added on 2022-04-24
• Descending Dungeons and Iterated Base-Changing
  • Published in 2006
  • Added on 2022-02-28
• Easy Proof of Three Recursive $π$-Algorithms -- Einfacher Beweis dreier rekursiver $π$-Algorithmen
  • Published in 2019
  • Added on 2022-02-25
• Tiling with arbitrary tiles
  • Published in 2015
  • Added on 2022-02-23
• Check Digits
  • Published in 1999
  • Added on 2022-01-18
• On Kaprekar's Junction Numbers
  • Published in 2021
  • Added on 2022-01-10
• Bell-ringing methods as polyhedra
  • Published in 2015
  • Added on 2021-11-20
• Yet another Proof of an old Hat
  • Published in 2021
  • Added on 2021-11-20
• A Self-Referential Property of Zimin Words
  • Published in 2016
  • Added on 2021-03-31
• The cocked hat
  • Published in 2020
  • Added on 2021-03-23
• Maximum overhang
  • Published in 2007
  • Added on 2021-03-15
• The Amazing $3^n$ Theorem and its even more Amazing Proof [Discovered by Xavier G. Viennot and his École Bordelaise gang]
  • Published in 2012
  • Added on 2021-03-15
• Pythagorean Triples, Complex Numbers, Abelian Groups and Prime Numbers
  • Published in 2021
  • Added on 2021-02-12
• Braids which can be plaited with their threads tied together at each end
  • Published in 1962
  • Added on 2021-02-12
• Hilbert 13: Are there any genuine continuous multivariate real-valued functions?
  • Published in 2021
  • Added on 2021-02-02
• Are There More Finite Rings than Finite Groups?
  • Published in 2020
  • Added on 2021-01-06
• Envelopes are solving machines for quadratics and cubics and certain polynomials of arbitrary degree
  • Published in 2020
  • Added on 2021-01-06
• "Match-Stick" Geometry
  • Published in 1939
  • Added on 2020-12-20
• A Prime-Representing Constant
  • Published in 2020
  • Added on 2020-11-06
• Least Significant Non-Zero Digit of n!
  • Published in 2000
  • Added on 2020-10-22
• World's shortest explanation of Gödel's theorem
  • Published in 2009
  • Added on 2020-10-16
• An Interesting Serendipitous Real Number
  • Published in 2000
  • Added on 2020-09-21
• Plane-filling curves on all uniform grids
  • Published in 2016
  • Added on 2020-09-21
• An Optimal Solution for the Muffin Problem
  • Published in 2019
  • Added on 2020-08-17
• Some Doubly Exponential Sequences
  • Published in 1970
  • Added on 2020-07-13
• Goldbug Variations
  • Published in 2005
  • Added on 2020-06-12
• Indigenous perspectives in maths: Understanding Gurruṯu
  • Published in 2020
  • Added on 2020-06-08
• Gergonne's Card Trick, Positional Notation, and Radix Sort
  • Published in 2017
  • Added on 2020-05-30
• Infinitude of Primes Using Formal Language Theory
  • Published in 2020
  • Added on 2020-05-25
• Word calculus in the fundamental group of the Menger curve
  • Published in 2013
  • Added on 2020-05-02
• Four Pages Are Indeed Necessary for Planar Graphs
  • Published in 2020
  • Added on 2020-04-19
• Conway's Tiling Groups on JSTOR
  • Published in 1990
  • Added on 2020-04-15
• Knots and links in spatial graphs
  • Published in 1983
  • Added on 2020-04-12
• On Some two way Classifications of Integers
  • Published in 1959
  • Added on 2020-03-13
• The no-three-in-line problem on a torus
  • Published in 2012
  • Added on 2019-12-10
• A unique pair of triangles
  • Published in 2018
  • Added on 2019-12-10
• Palindromes in Different Bases: A Conjecture of J. Ernest Wilkins
  • Published in 2009
  • Added on 2019-09-14
• Fractal Sequences
  • Published in 1999
  • Added on 2019-08-21
• Chords of an ellipse, Lucas polynomials, and cubic equations
  • Published in 2018
  • Added on 2019-06-30
• Brainfilling Curves - a Fractal Bestiary
  • Published in 2012
  • Added on 2019-05-09
• Planar Hypohamiltonian Graphs on 40 Vertices
  • Published in 2013
  • Added on 2019-05-09
• A universal differential equation
  • Published in 1981
  • Added on 2019-05-09
• Brazilian Primes Which Are Also Sophie Germain Primes
  • Published in 2019
  • Added on 2019-03-13
• The Takagi Function and Its Properties
  • Published in 2011
  • Added on 2019-03-04
• Yet Another Single Law for Lattices
  • Published in 2003
  • Added on 2019-03-02
• The Instructor's Guide to Real Induction
  • Published in 2012
  • Added on 2019-03-02
• Amusing Permutation Representations of Group Extensions
  • Published in 2018
  • Added on 2019-01-01
• Mathematics applied to dressmaking
  • Published in 1994
  • Added on 2018-11-29
• Seven Trees in One
  • Published in 1994
  • Added on 2018-11-26
• Prime Number Races
  • Published in 2004
  • Added on 2018-11-12
• Conway's doughnuts
  • Published in 2018
  • Added on 2018-11-04
• The largest small hexagon
  • Published in 1975
  • Added on 2018-09-22
• How to hear the shape of a billiard table
  • Published in 2018
  • Added on 2018-06-27
• Proof without Words: Fair Allocation of a Pizza
  • Published in 1994
  • Added on 2018-06-26
• When are Multiples of Polygonal Numbers again Polygonal Numbers?
  • Published in 2018
  • Added on 2018-06-25
• One parameter is always enough
  • Published in 2018
  • Added on 2018-06-06
• Any Monotone Boolean Function Can Be Realized by Interlocked Polygons
  • Published in 2010
  • Added on 2018-01-08
• Every positive integer is a sum of three palindromes
  • Published in 2016
  • Added on 2017-06-21
• Best Laid Plans of Lions and Men
  • Published in 2017
  • Added on 2017-03-22
• On the Existence of Ordinary Triangles
  • Published in 2017
  • Added on 2017-02-06
• Rules for Folding Polyminoes from One Level to Two Levels
  • Published in 2017
  • Added on 2017-01-16
• Two short proofs of the Perfect Forest Theorem
  • Published in 2016
  • Added on 2016-12-18
• Every natural number is the sum of forty-nine palindromes
  • Published in 2015
  • Added on 2016-12-17
• On the interval containing at least one prime number
  • Published in 1952
  • Added on 2016-11-14
• On subsets with intersections of even cardinality
  • Published in 1969
  • Added on 2016-11-01
• A Discrete and Bounded Envy-Free Cake Cutting Protocol for Any Number of Agents
  • Published in 2016
  • Added on 2016-10-13
• Searching for generalized binary number systems
  • Published in 2017
  • Added on 2016-08-22
• Rational Polynomials That Take Integer Values at the Fibonacci Numbers
  • Published in 2016
  • Added on 2016-08-02
• On the Cookie Monster Problem
  • Published in 2013
  • Added on 2016-05-19
• Prime numbers in certain arithmetic progressions
  • Published in 2001
  • Added on 2016-05-07
• Planar graph is on fire
  • Published in 2015
  • Added on 2015-12-02
• Denser Egyptian Fractions
  • Published in 1998
  • Added on 2015-07-23
• A combinatorial theorem in plane geometry
  • Published in 1975
  • Added on 2015-02-23
• Efficient Algorithms for Zeckendorf Arithmetic
  • Published in 2012
  • Added on 2015-02-16
• Bells, Motels and Permutation Groups
  • Published in 2012
  • Added on 2014-12-17
• Irrationality From The Book
  • Published in 2009
  • Added on 2014-12-01
• Division by three
  • Published in 2006
  • Added on 2014-11-17
• Solving Triangular Peg Solitaire
  • Published in 2007
  • Added on 2014-11-10
• A number system with an irrational base
  • Published in 1957
  • Added on 2014-03-12
• Playing pool with $\pi$ (the number $\pi$ from a billiard point of view)
  • Published in 2003
  • Added on 2013-11-14
• The Ubiquitous Thue-Morse Sequence
  • Published in 2006
  • Added on 2013-10-21
• An Infinite Set of Heron Triangles with Two Rational Medians
  • Published in 2013
  • Added on 2013-10-09
• The Strange and Surprising Saga of the Somos Sequences
  • Published in 1991
  • Added on 2013-10-09
• Half of a coin: negative probabilities
  • Published in 2005
  • Added on 2013-07-17
• On a problem of Störmer
  • Published in 1964
  • Added on 2013-07-11
• The Ubiquitous Pi
  • Published in 2013
  • Added on 2013-06-11
• Six Ways to Sum a Series
  • Published in 1994
  • Added on 2013-06-10
• Embedding countable groups in 2-generator groups
  • Published in 1993
  • Added on 2013-02-19
• Conway's Rational Tangles
  • Published in 2012
  • Added on 2013-02-06
• Biologically Unavoidable Sequences
  • Published in 2012
  • Added on 2012-12-16
• On sphere-filling ropes
  • Published in 2010
  • Added on 2012-10-29
• A Hamiltonian circuit for Rubik's Cube
  • Published in 2012
  • Added on 2012-09-04
• Equilibrium solution to the lowest unique positive integer game
  • Published in 2010
  • Added on 2012-06-22
• The wobbly garden table
  • Published in 2001
  • Added on 2012-06-17
• Topology Explains Why Automobile Sunshades Fold Oddly
  • Published in 2012
  • Added on 2012-05-23
• The mate-in-n problem of infinite chess is decidable
  • Published in 2012
  • Added on 2012-03-28
• Orange Peels and Fresnel Integrals
  • Published in 2012
  • Added on 2012-02-15
• Fibonacci determinants-a combinatorial approach
  • Published in 2007
  • Added on 2012-02-08
• The Collatz Fractal
  • Published in 2012
  • Added on 2012-01-15
• Laying train tracks
  • Published in 2011
  • Added on 2011-12-03
• Cool irrational numbers and their rather cool rational approximations
  • Published in 2003
  • Added on 2011-10-13
• Gödel's Second Incompleteness Theorem Explained in Words of One Syllable
  • Published in 1994
  • Added on 2011-09-24
• Gödel's incompleteness theorem
  • Published in 1994
  • Added on 2011-06-01
• An example of a computable absolutely normal number
  • Published in 2002
  • Added on 2011-03-28
• On a curious property of 3435
  • Published in 2009
  • Added on 2011-02-02
• Can One Hear the Shape of a Drum?
  • Published in 1966
  • Added on 2011-01-12
• A combinatorial approach to sums of two squares and related problems
  • Published in 2002
  • Added on 2010-07-16
• Unbounded spigot algorithms for the digits of pi
  • Published in 2006
  • Added on 2010-01-05