Maths With Pictures John D Barrow. 12 th Century Latin copy of Euclid Book IV gives Theorems without...

Maths With PicturesMaths With Pictures

John D BarrowJohn D Barrow

1212thth Century Latin copy of Euclid Book IV gives Century Latin copy of Euclid Book IV givesTheorems without proofs Theorems without proofs and provides incomplete diagramsand provides incomplete diagrams

Copied from Adelard’s (complete) original, Copied from Adelard’s (complete) original, Adelard of Bath (1082-1152).Adelard of Bath (1082-1152).Checkmarks link pictures to theoremsCheckmarks link pictures to theorems

Manuscript of Euclid’s ElementsManuscript of Euclid’s ElementsAdelard of Bath, 4Adelard of Bath, 4thth Dec 1480 Dec 1480

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

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

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

Oresme’s LatitudesOresme’s Latitudes

Sicut hic…Sicut hic…

Christiaan Huygens, First graph of a continuous functionMedian 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 Playfair1786

William Playfair (1821)

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

Augustus de MorganAugustus de MorganAn Essay on Probabilities An Essay on Probabilities and on their Application to and on their Application to Life ContingenciesLife Contingencies (18 (1838)38)

Charles Dickens, Charles Dickens, Hard TimesHard Times, illustrations by Harry French (1875), 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 GaltonThe First Weather ChartApril 1st 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 ConjectureThe Four-Colour Conjecture

NamedThe Geographical ProblemBy Arthur Kempe (1878)

Do Four Colours Suffice?Do Four Colours Suffice?(Francis Guthrie 1850s)(Francis Guthrie 1850s)

Yes!Yes!(Appel and Haken 1976)(Appel and Haken 1976)

Helge von Koch’sHelge von Koch’s‘‘Snowflake’, 1904Snowflake’, 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 ImageryJohn D Barrow

Charles HintonThe Fourth Dimension, (1904)

Salvador Dali, Corpus Hypercubus, (1954)

Oscar Reutersvärd , 1934Oscar Reutersvärd , 1934

ImpossibleImpossibleFiguresFigures

Maurits Escher, Waterfall

Maurits Escher, woodcutMoebius Strip II (Red Ants), 1963

August Möbius, notebook 1858

Möbius and His Bands

US Patent 3991631US Patent 3991631

MMööbius Belts, Tape-drives and Conveyor beltsbius Belts, Tape-drives and Conveyor belts

The MThe Mööbiusbius UniversalUniversal Recycling SymbolRecycling Symbol

Gary Anderson, Student at USC, design competition winner, 1970

Not a trademark!

The Mushroom Cloud

Energy of bomb Energy of bomb air density × (radius) air density × (radius)55(time)(time)22

G.I. Taylor

(radius)(radius)5 5 Energy Energy × (time)× (time)22 air density air density

94 m increase in 0.09 sec94 m increase in 0.09 secAir density = 1.2Kg/mAir density = 1.2Kg/m33

E = 25 kilotons of TNTE = 25 kilotons of TNT

LifeLife Magazine pictures of 1945 Trinity Test still Top Secret in 1950 Magazine pictures of 1945 Trinity Test still Top Secret in 1950

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