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Philipp Legner
Created by Philipp Legner

Philipp studied Mathematics at the University of Cambridge, St John’s College, and Mathematics Education at the UCL Institute of Education in London.

He is currently a Software Engineer at Google, having worked at Bloomberg, TouchPress, BBC Horizon, Wolfram Research and Goldman Sachs in the past.

In addition to creating Mathigon, Philipp has volunteered with projects like Code Club, ReachOut! and the Millennium Mathematics Project in Cambridge.


Lovkush Agarwal: Functions and Series

Wolfgang Laun: Logic and Paradoxes

Anwit Roy: Dimensions and Distortions

Many thanks to Wolfgang Laun and many others who helped proofread the content and test the interactives.

Javascript Plugins

This website uses jQuery 2 and jQuery UI
Geometric Diagrams: JSXGraph, LGPL Licence, developed at the University of Bayreuth
Touch Sliders: iDangero’s Swiper, GPL and MIT Licence
jQuery UI Touch Support: David Furfero’s TouchPunch, MIT Licence
Inline Variables: inspired by Bret Victor’s Tangle
Touch 360° Rotators: Alexander Gräfenstein’s SpriteSpin, MIT Licence

Article Image, Video and Audio Credits

Below is a list of all images, videos, animations or audio from external sources used in the World of Mathematics. They all are either in the public domain, have an open or royalty-free licence, or were included with permission of the owners. All other media content in the World of Mathematics is ©

Chapter Backgrounds

Title Page: based on an image Sergio Schnitzler, YIO Multimedia
Numbers and Patterns: based on an image © Depositphotos / Bezergheanu Mircea
Combinatorics and Logic: based on an image © Depositphotos / hunthomas
Motion and Matter: Nasa/JPL

Article Icons

Introduction: Created by Digital Visions Queenstown
Credits: © Depositphotos / agsandrew
Circles, Orbits, Conic Sections: Nasa/JPL
Symmetry and Groups: based on an image by Michael Gäbler, published under a CC-BY-3.0 licence
Modelling Space: Public Domain
Dimensions and Distortions: Aurélien Alvarez, Étienne Ghys and Jos Leys via IMAGINARY
Sequences: © Depositphotos / EpicStockMedia
Functions and Series: © Depositphotos / agsandrew
Prime Numbers: based on an image © Depositphotos / defotoberg
More Number Theory: © Depositphotos / dip2000
Real, Irrational, Imaginary: created by Paul Schubert
Infinity: © Depositphotos / agsandrew
Combinatorics: © Depositphotos / nikkytok
Graph Theory: © Depositphotos / Antartis
Knots, Mazes, Labyrinths: Public Domain
Optimisation: based on images © Paul Nylander
Logic and Paradoxes: © Depositphotos / anterovium
Axioms and Proof: Public Domain
Understanding Probability: © Depositphotos / logoff
The Normal Distribution: Public Domain
Random Walks: © Depositphotos / Yermek
Statistics: © Depositphotos / zentilia
Game Theory: © Depositphotos / white78
Coding and Cryptography: Final Cut Pro Stock Graphics
Forces, Motion, Calculus: Nasa/JPL
Waves and Music: based on an image © Depositphotos / jineekeo
Fluid Dynamics: © Depositphotos / masterclem
Chaos: created by Paul Schubert
Theory of Relativity: Based on images by Nasa/JPL and © Depositphotos / frenta
Quantum Mechanics: © Depositphotos / prill


Rudolphine Tables: Public Domain
Backpack: © Depositphotos / Rafael Angel Irusta Machin

Conic Sections

The Ptolemaic Cosmos: Public Domain
Flower:Pascalou Petit, published under a CC BY-SA 3.0 licence on Wikimedia
Earth (Apollo 11): Nasa/JPL
Water Ripples: by MorgueFile user hotblack
Orange: Ekko, published under a >CC BY-SA 3.0 licence on Wikimedia
Hurricane: National Oceanic and Atmospheric Administration
Ellipse Videos: Animations programmed in Elica Logo, and with permission of the Elica team
Epicycles, Geocentric Model, Heliocentric Model: Public Domain
Copernicus, Brahe, Kepler, Galilei, Newton: Public Domain

Polygons and Polyhedra

Honey Comb: © Fir0002, published under a CC-BY-NC 3.0 licence on Wikimedia
Pavement Pattern: Roger McLassus, published under a CC BY-SA 3.0 licence on Wikimedia
Greenhouse Roof: photo taken at the Eden Project in Cornwall
Penrose Tiling Image: Urs Schmid, freely available under a CC BY-SA 3.0 licence on Wikimedia
3D Tessellations: TED-43, freely available under a CC BY 3.0 licence
Radiolarian Diagram: Ernst Haeckel’s “Kunstformen der Natur” (1899), Public Domain, Wikipedia Page
HIV Virus: © Depositphotos / Eraxion
Crystal Lattice: © Depositphotos / Scanrail
Cystal: Public Domain (USDA), from Wikipedia
Space Frames: Public Domain, from Wikipedia
Stacked Oranges: © Depositphotos / Doroshin
Platonic Dice: Diacritica, freely available under a CC BY-SA 3.0 licence on Wikimedia
Football: Stock.xchng user Proman77

Symmetry and Space

Butterfly, Leonardo Drawing, Playing Card, Tilings: Public Domain
Galois Portrait: Public Domain
Crystal Lattice: © Depositphotos / Scanrail
Particle Accelerator: © CERN
Spacetime Diagram: Nasa/JPA
Monster Grafitti: Public Domain, from Wikipedia

Dimensions and Distortions

Polar Bear: Alan Wilson, freely available under a CC BY-SA 3.0 licence on Wikimedia
Cooling Tower: Alan Murray-Rust, published under a CC BY-SA 2.0 licence on Wikimedia
Corals: Toby Hudson, published under a CC BY-SA 3.0 licence on Wikimedia
Vase: Public Domain, acquired by Henry Waltersin 1911 (Wikipedia page)
Circle Limit III: © M. C. Escher Foundation, see Wikipedia for fair use rationale
Teacup and Torus: Public Domain, created by Wikipedia user LucasVB
Henri Poincare: Public Domain


Nature Images, Fractal Rendering: Public Domain, primarily from Wikipedia
Snowflakes Image: © Depositphotos / Brad Calkins
Menger Sponge: Niabot, published on Wikimedia under a CC BY-SA 3.0 licence
Mandel Bulb: Prokofiev, published on Wikimedia under a CC BY-SA 3.0 licence


Action Sequences 1 and 2: © Depositphotos / EpicStockMedia
Action Sequences 3 and 7: © Jason Halayko
Action Sequences 4: © Marcio Abe
Action Sequences 5 and 6: © Ray Demski
Action Sequences 8: © Jake Ashcraft
Fibonacci Portrait: based on a Public Domain photo
Nautilus Spiral: Wikipedia user Chris 73, published under aCC BY-SA 3.0 licence on Wikimedia

Prime Numbers

Erathostenes, Fermat, Goldbach, Fields Medal: Public Domain
Internet Code Animation: © Depositphotos / Vicente Barcelo Varona

Real, Irrational, Imaginary

Babylonian numerals: Public Domain
Waves Photo: © Depositphotos / masterclem


Hilbert and Cantor Photos: Public Domain
Frog Legs Rat: Wikipedia user Adam Cuerden and Jujutacular, published under a CC BY-SA 3.0 licence on Wikimedia
Miss Marple Video Extract: © 1964 and 1989 Turner Entertainment Co. See below for Fair use policies.
The Hilbert Logo: loosely based on the Hilton Hotels & Resorts logo


Leonard Euler: Public domain
Chair Silhuettes: © Depositphotos / leremy
Maths Class: © Depositphotos / masterclem
Lock Photo: © Depositphotos / scanrail
Party Photo: © Depositphotos / Yuri_Arcurs
Fruit Photo: © Depositphotos / Валентин Волков
T-shirt Vectors: © Depositphotos / Кучумова Наталья
Lotto Balls: © Depositphotos / zentilia

Graph Theory

Königsberg Map: Based on a public domain photo
Congestion Photo: © Depositphotos / Paha_L
Plane Take Off:© Depositphotos / marchcattle
Computer Chip: Public domain
Internet Graphic:© Depositphotos / Iuliia Kvasha
Social Networking Illustration: © Depositphotos / cienpies

Logic and Paradoxes

All Images: Public Domain

Axioms and Proof

School of Athens: Public Domain
Flowers in Sets: Final Cut Pro Stock Images
Dominoes: © Depositphotos / Aleksandr Ugorenkov
Towers of Hanoi Game: Based on code by Stoyan Rachev

Gödel Photo: Public Domain


Basilisk: Public Domain, from Wikipedia
Red Die: Brunurb, published under a CC BY-SA 3.0 licence on Wikipedia
Coin: Ssolbergj, published under a CC BY-SA 3.0 licence on Wikipedia
Coin Toss Image: © Andrew Davidhazy

Random Number Generator:

Game Theory

Box of Chocolates: © Depositphotos / Kitch Bain
Indivicual chocolates in animations: © Depositphotos / Mikhaylova
Chess Board: © Depositphotos / white78
Prison Boy: © Depositphotos / Yuri_Arcurs
John Nash Photo: Sandstein, published under a CC BY-SA 3.0 licence on Wikimedia
Opera: © Depositphotos / Roman Rodionov
Stadium: Stock.xchng user rafbalance

Fair Use

Some videos on this website include stills and short clips from motion pictures, which belong to the respective movie studios. Based on the AUSOC Code of Best Practices, this qualifies as ‘Fair Use’ under US law, since we are “quoting in order to recombine elements to make a new work that depends for its meaning on [often unlikely] relationships between the elements”.

Of course all extracts are used solely for non-profit educational purposes, extracts are very short, and the use has no effect upon the value of the original. Different laws may apply in other countries.