## 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.

## Contributors

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 © Mathigon.org.

### 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

### Introduction

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

### Fractals

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

### Sequences

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

### Infinity

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

### Combinatorics

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

### Probability

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

Earth: NASA/JPL

Coin Toss Image: © Andrew Davidhazy

Random Number Generator: Random.org

### 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.