Symmetry , livre ebook

Wooden Books - David Wade

Découvre YouScribe en t'inscrivant gratuitement

Je m'inscris

Obtenez un accès à la bibliothèque pour le consulter en ligne
En savoir plus

66 pages

English

Vous pourrez modifier la taille du texte de cet ouvrage

Obtenez un accès à la bibliothèque pour le consulter en ligne
En savoir plus

A propos
Informations
Extrait

Description

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 exactly what it is, symmetry can be found in almost every corner of science, nature and human culture. WOODEN BOOKS are small but packed with information. "Fascinating" FINANCIAL TIMES. "Beautiful" LONDON REVIEW OF BOOKS. "Rich and Artful" THE LANCET. "Genuinely mind-expanding" FORTEAN TIMES. "Excellent" NEW SCIENTIST. "Stunning" NEW YORK TIMES. Small books, big ideas.

Sujets

History of art

Informations

Publié par	Wooden Books
Date de parution	01 avril 2018
Nombre de lectures	0
EAN13	9781912706044
Langue	English
Poids de l'ouvrage	15 Mo

Informations légales : prix de location à la page 0,0238€. Cette information est donnée uniquement à titre indicatif conformément à la législation en vigueur.

Extrait

First published 2006
eBook edition © Wooden Books Ltd 2018
Published by Wooden Books Ltd. Glastonbury, Somerset.
British Library Cataloguing in Publication Data Wade, D. Symmetry - The Ordering Principle
A CIP catalogue record for this book is available from the British Library.
eBook ISBN: 978-1-912706-04-4 Physical ISBN: 978-1-904263-51-7
All rights reserved. For permission to reproduce any part of this symmetrical little book please contact the publishers.
Designed and typeset in Glastonbury, UK.
Converted and optimised for digital display by CPI Anthony Rowe, Chippenham, UK.
SYMMETRY
THE ORDERING PRINCIPLE
written and illustrated by
David Wade
For Emile Boulanger
All pictures by the author, except for Japanese “pine-bark” pattern on page 39 , reproduced from Japanese Patterns, by Jeanne Allen, with kind permission of Chronicle Books; and the Portrait of Emmy Noether on page 45 by Jesse Wade.
For further reading, try “Symmetry and the Beautiful Universe,” by Leon Lederman and Christopher Hill, Mario Livio’s “The Equation that couldn’t be Solved,” or “Symmetry, a Unifying Concept” by Istvan and Magdolna Hargittai.
“Let proportions be found not only in numbers and measures, but also in sounds, weights, times and positions, and whatever force there is” - Leonardo da Vinci.
Above - Da Vinci’s conjecture that the total cross-sectional area of a tree remains the same at all branching levels; a balance illustrates the hidden symmetry of force equal to mass x distance. Overleaf a sample of nature’s infinite symmetrical variety; Ernst Haekel’s drawings of various species of diatoms.
CONTENTS
Introduction
1
Arrays
2
Rotations and Reflections
4
Geometric Self-Similarity
6
Radial
8
Sections and Skeletons
10
Spherical
12
Symmetries in 3-D
14
Stacking and Packing
16
The Crystalline World
18
Basic Stuff
20
Dorsiventrality
22
Enantiomorphy
24
Curvature and Flow
26
Spirals and Helices
28
Fabulous Fibonacci
30
Branching Systems
32
Fascinating Fractals
34
Penrose Tiling and Quasicrystals
36
Asymmetry
38
Self-organising Symmetries
40
Symmetries in Chaos
42
Symmetry in Physics
44
Symmetry in Art
46
A Passion for Pattern
48
Symmetria
50
Formalism
52
Experiential Symmetries
54
Appendix
56
Glossary
58

INTRODUCTION
Symmetry has a very wide appeal; it is of as much interest to mathematicians as it is to artists, and is as relevant to physics as it is to architecture. In fact, many other disciplines lay their own claims on the subject, each having their own ideas of what symmetry is, or should be. Clearly, whatever approach is taken, we are dealing here with a universal principle, however, in our day-to-day experience conspicuous symmetries are comparatively rare and most are far from obvious. So what is symmetry? Are there general terms for it? Can it, indeed, be clearly defined at all?
On investigation, it soon becomes clear that the whole field is hedged about with paradox. To begin with, any notion of symmetry is completely entangled with that of asymmetry; we can scarcely conceive of the former without invoking thoughts of the latter (as with the related concepts of order and disorder)—and there are other dualities. Symmetry precepts are always involved with categorisation, with classification and observed regularities; in short, with limits. But in itself symmetry is unlimited; there is nowhere that its principles do not penetrate. In addition, symmetry principles are characterised by a quietude, a stillness that is somehow beyond the bustling world; yet, in one way or another, they are almost always involved with transformation, or disturbance, or movement.
The more deeply one investigates this subject the more apparent it becomes that this is at the same time one of the most mundane and extensive areas of study—but that, in the final analysis, it remains one of the most mysterious.
1
Arrays
the regular disposition of elements
When it comes to understanding just what the common factors are among the many and various aspects of symmetry, the notions of congruence and periodicity take us a long way. Most symmetries present these aspects in one form or another , and the absence of one or the other usually leads to a reduction, or even the lack of symmetry.
For instance: two like objects, in no particular relation with each other, are merely similar (since although they may be congruent they are not arranged in any order) ( 1, opposite ). The addition of a third object allows a degree of regularity to come into play, creating the basis of a recognisable pattern ( 2 ).
So, in its simplest form, symmetry is expressed as a regularly repeating figure along a line ( below ), a series that may easily be extended into an array ( 3 ). Obviously, simple arrangements of this kind could in theory be indefinitely extended, but symmetry will be maintained just so long as both the repeating element and the spacing remain consistent.
We can recognise array symmetries in many natural formations, from the familiar rows of kernels in sweet corn ( 4 ), to the patterns of scales in fish and reptiles ( 5 ). And of course such regular arrangements feature in a great deal of human art and artefacts—as in the decorated shaman’s cloak opposite ( 6 ). Naturally, there are often functional as well as aesthetic criteria operating in the formation of arrays, which is evident in the sort of patterns created by brickwork and roof-tiles ( 7,8 ).
2

Univers
Ebooks
Livres audio
Presse
Podcasts
BD
Documents

Symmetry , livre ebook

History of art

YouScribe

Le catalogue

Le service

Les conditions