Symmetry

Why on earth do cars have the same symmetry as dragonflies Is there really a beautiful swirling pattern lurking in every dripping tap What do insect eggs have in common with planets, and why In this exquisite book, the smallest and most concise ever produced, designer David Wade introduces the main principles of symmetry, and shows how, despite opinions over what exactly it is, symmetry can be found in almost every corner of science, nature, and human culture.

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• 3 First published 2006 AD This edition Wooden Books Ltd 2006 AD Published by Wooden Books Ltd. 8A M
• 4 For Emile Boulanger CONTENTS Introduction 1 Arrays 2 Rotations and Reflections 4 Geome
• 1 INTRODuCTION Symmetry has a very wide appeal it is of as much interest to mathematicians as it is
• 2 3 ArrAys the regular disposition of elements When it comes to understanding just what the common f
• 4 5 rotAtions And reflection point symmetries There are two further basic expressions of symmetry, n
• 6 7 Geometric selfsimilArity gnomons and other selfsimilar figures Symmetry is an invariable charact
• 8 9 rAdiAl centred symmetries Radial symmetries are probably the most familiar of all regular arrang
• 10 11 sections And skeletons internal symmetries of plants and animals The great majority of plants
• 12 13 sphericAl the perfect 3dimensional symmetry Just as the circle is the perfect figure in 2dimen
• 14 15 symmetries in 3d spatial isometries Just as the sphere is the threedimensional equivalent of
• 16 17 stAckinG And pAckinG fruit, froth, foams and other spacefillers Finding the easiest and most e
• 18 19 the crystAlline World the stronghold of symmetrical order Of all natural objects, wellformed c
• 20 21 BAsic stuff symmetries at the heart of matter Toward the end of the 19th century the pioneerin
• 22 23 dorsiventrAlity the symmetry of moving creatures Animals, by definition, are multicellular, fo
• 24 25 enAntiomorphy left and righthandedness Amongst other things, our dorsiventral bodyform gives u
• 26 27 curvAture And floW waves and vortices, parabola and ellipses As we have considered symmetry th
• 28 29 spirAls And helices natures favourite structures Of all the regular curves, spirals and helice
• 30 31 fABulous fiBonAcci golden angles and a golden number Around the end of the 12th century a youn
• 32 33 BrAnchinG systems patterns of distribution Branched networks can be thought of as having a rea
• 34 35 fAscinAtinG frActAls selfconsistency to the nth degree There are many natural phenomena, perha
• 36 37 penrose tilinGs QuAsicrystAls surprising fivefold symmetries In the mid1980s the world of cry
• 38 39 Asymmetry the paradox of inconstancy Where does symmetry end and asymmetry begin Take a close
• 40 41 selforGAnisinG symmetries regularities in nonlinear systems There are many natural patterns th
• 42 43 symmetries in chAos regularities in highly complex systems Invariance equates with symmetry, s
• 44 45 symmetry in physics invariance and the laws of nature Since the amount of energy in a closed s
• 46 47 symmetry in Art constraint and creative potentiality In view of its universality, we have to v
• 48 49 A pAssion for pAttern the perennial appeal of repeating designs Pattern arises almost of itsel
• 50 51 symmetriA sublime proportions The Renaissance saw a revival of interest in classical notions o
• 52 53 formAlism symmetry symbolising stability Symmetry is frequently involved in places and occasio
• 54 55 experientiAl symmetries percepts and precepts It is clear that symmetry is an allencompassing
• 56 57 Appendix Groups 56 POINTGROUPS 2d symmetry about a centre, with rotation around a centre left
• 58 Algorithm A mathematical rule for computation involving a succession of procedural steps Array