The Erdos Distinct Distances Problem
Problem summary
Research progress
Student research
Graph theory links:
Peña and Touchette soccer graphs
The Konigsberg bridge problem
The number of graphs
The Icosian Game
William Rowan Hamilton
Bob Bosch's Hamiltonian art
Ramsey Theory
The Planarity game
The Four-Color Theorem
The proof of the four color theorem part 1 and part 2
Residency matching
Prime number links:
Transport Layer Security
Large prime numbers
from the Great Internet Mersenne Prime Search.
Matt Parker on the prime from 2016
EFF Cooperative Computing Awards
The Prime Number Theorem graphs
Hilbert's Problems
The Clay Millenium Problems
Primality tests and the AKS Primality test
Prime cicada life cycles
Fermat's Last Theorem Nova episode
Is this prime? the game
Fibonacci number links:
Hemachandra / Virahanka / Pingala sequence
The Fibonacci Association and Fibonacci Quarterly
An application of Fibonacci numbers to quantum computing
Tiling links:
Pentagonal tilings and the 15th tiling
Hexagonal city plans
MC Escher tilings
Design your own Escher tilings here.
Penrose tilings
Pinwheel tiling and Federation Square architecture
Crystals and more examples.
Parquet deformations
Madonna Yoder's fabric tilings
Wallpaper groups
Wallpaper group flow chart
Homepage of the hat tiling including an interactive demo.
Symmetry and group theory links:
L-Glucose
Change ringing video and article
Symmetries of particles
The Classification of Finite Simple Groups
Voronoi diagrams
Voronoi diagram generator
Voronoi diagrams in the world
Fortune's parabolic front algorithm
Spherical Voronoi diagrams
Non-Euclidean geometry links:
Euclid's Elements
Shortest paths on the Earth
Shortest paths on a sphere
Hyperbolic triangle tiling
Hyperbolic plane crochet pattern and exhibit
Poincare disk model
Poincare disk in MC Escher's work
Gauss's great triangle
Henry Segerman's Non-Euclidean VR
Polyhedron links:
Plato's theory of Platonic solids
Kepler's theory of Platonic solids
Unusual dice from the Dice Lab
Proofs of Euler's formula
Stereographic projection
Matt Parker's soccer ball petition
4D links:
Unfolding a 4D cube
Slicing a 4D cube
Hypernom game
4D toys app
Miegakure game
The book Flatland
4D Rubik's cube
The regular polychora
All unfoldings of a 4D cube
Cellular automata links:
A 1D cellular automaton tool
Play Conway's Game of Life
Golly, a sophisticated Game of Life application
SmoothLife videos one, two, three
Fractal links:
The Chaos Game
The IFS Construction kit fractal generator
Fractal images: Koch snowflake, Sierpinski triangle
MegaMenger
Geogebra apps by Ben Sparks: Barnsley's fern, Julia set boundaries,
Mandelbrot painter, Mandelbrot orbits
Mandelbrot set orbit calculator
Examples of Julia sets
Interactive Mandelbrot and Julia sets
Zooming into a Mandelbrot set
Mandelbrot set song
Knot theory links:
A table of knots
A large database of knots and their invariants
Topology links:
Coffee cups and donuts
Coffee cups and donuts 2
Two-holed torus trick
Turning a torus inside out
Topology puzzles
Cutting paper strips
Unzipping a Klein bottle
Torus and Klein bottle games
Klein bottle video
Projective plane video
Buy a Klein bottle here
Mobius bands in knitting
Linked bagels
Stephen Colbert on the Poincare Conjecture
Picture hanging puzzle version 1
Picture hanging puzzle version 2
Cake-cutting links:
Rent calculator
Redistricting links:
GerryMander puzzle game
District game
Hexapolis game
Moon Duchin on redistricting
The MGGG Redistricting Lab
Districtr tool
Dave's Redistricting
Differential equations links:
Slope field generator
Real example of predator-prey interaction
Predator-prey simulation and another
3Blue1Brown on fluid flow
Clay Millenium Problems
