Maths With Pictures John D Barrow

12 th Century Latin copy of Euclid Book IV gives Theorems without proofs and provides incomplete diagrams Copied from Adelard’s (complete) original, Adelard of Bath ( ). Checkmarks link pictures to theorems

Manuscript of Euclid’s Elements Adelard of Bath, 4 th Dec 1480

The First ‘Pop-up’ Book, Euclid’s The Elements of Geometrie, (1570)

A 10 th century graph illustrating planetary and solar positions versus time

Nicole Oresme, The Latitude of Forms and Treatise on the Configurations of Qualities and Motions’ ‘Latitude’ = speed is vertical and ‘Longitude’ = time is horizontal

Oresme’s Latitudes Sicut hic…

Christiaan Huygens, First graph of a continuous function Median life remaining for a person of given age, 1669

Johann Lambert, 1779

James Watt’s Indicator of steam engine pressure vs. volume, 1796 (he kept it secret until 1822)

William Playfair 1786

William Playfair (1821)

Adolph Quetelet, ‘la loi de possibilité (1846) The social physics of the ‘average man’. The ‘bell -shaped curve’ Espirit Jouffret, 1872

Augustus de Morgan An Essay on Probabilities and on their Application to Life Contingencies (1838) Charles Dickens, Hard Times, illustrations by Harry French (1875)

The Cover of Gerardus Mercator’s Atlas, or Cosmographical Meditations upon the Creation of the Universe (1585)

The Earth At Night

A Map of the Information Highway Network

Francis Galton The First Weather Chart April 1 st 1875, in The Times

The 1908 London Underground Map

Harry Beck’s first exercise book sketch of his Underground Diagram ‘I tried to imagine I was using a convex lens or mirror to present the central area on a larger scale’

Harry Beck, The London Underground ‘Diagram’, August 1933

The Four-Colour Conjecture Named The Geographical Problem By Arthur Kempe (1878) Do Four Colours Suffice? (Francis Guthrie 1850s) Yes! (Appel and Haken 1976)

Helge von Koch’s ‘Snowflake’, 1904

Karl Menger’s Sponge (original 1926)

Mandelbrot’s set: the set of points that stay at finite distances form the black region with its infinitely intricate boundary

Any part of the boundary contains copies of the whole set

Cosmic Imagery John D Barrow

Charles Hinton The Fourth Dimension, (1904) Salvador Dali, Corpus Hypercubus, (1954)

Oscar Reutersvärd, 1934 ImpossibleFigures

Maurits Escher, Waterfall

Maurits Escher, woodcut Moebius Strip II (Red Ants), 1963

August Möbius, notebook 1858 Möbius and His Bands

US Patent Möbius Belts, Tape-drives and Conveyor belts

The Möbius Universal Recycling Symbol Gary Anderson, Student at USC, design competition winner, 1970 Not a trademark!

The Mushroom Cloud

Energy of bomb  air density × (radius) 5  (time) 2 G.I. Taylor (radius) 5  Energy × (time) 2  air density 94 m increase in 0.09 sec Air density = 1.2Kg/m 3  E = 25 kilotons of TNT Life Magazine pictures of 1945 Trinity Test still Top Secret in 1950

Simulated Higgs boson decay after two protons Simulated Higgs boson decay after two protons collide