Table Of Content

4 SIGNET SCIENCE LIBRARY adier irving THE AUnTHOeR OFwTHEiNEW MATHEMATICS a look at geometry DIAGRAMS BY RUTH ADLER A MANY-FACETED SCIENCE Modern geometry is subdivided into branches of analytic, differential, Euclidean, hyperbolic, elliptic, projective, and many other geometries. The student is apt to become lost in this maze of byroads; it is Irving Adler's purpose to enable students to see the science as a whole, to see the complete map of geometry today. The author begins by describing geometry in its earliest form. The simple measurement of objects was practiced by ancient Babylonians and Egyptians; the early Greek philosopher Thales was the first to formulate an abstract idea of physical space. From pre-Euclidean geometry, Adler goes on to describe the theories ofEuclid and Newton, to explain the workings of calculus and projective geometry, and finally, to show how geometry is used in a science of the atomic age, relativity physics. Here is a book that explains our changing conceptions — of physical and mathematical space an easily understood guide to the important new advances in. the field of geometry. )) Other SIGNET SCIENCE Books by Irving Adler (60 cents each except where otherwise indicated) How Life Began (#P2135) iNsroE THE Nucleus (#P2525) Magic House of Numbers #P2117 ( A NewLook atArithmetic #T2824—750 ( The New Mathematics (#P2099) Probability and Statistics for Everyman #T2850—750) ( Seeing the Earth from Space #P2050) ( The Stars (#P2093) The Sun and Its Family #P2037) ( Thinking Machines (#P2065) mVING ADLER A New Look At Geometry With Diagrams by Ruth Adler giGNET) A SIGNET SCIENCE LIBRARY BOOK Published by THE NEW AMERICAN LIBRARY, NEW YORK AND TORONTO Copyright © 1966 by Irving Adler All rights reserved. No part of this book may be reprinted, or reproduced or utilized in any form or by any electronic, mechanical or other means, now known or hereafter invented, including photocopying and recording, or in any information storage and retrieval system, without permission in writing from tChoempPuabnlyis,heIrn.c.,Fo6r2 iWnefsotrm4a5ttihonStardedetr,esNseTwheYoJrokh,n Day New York 10036. Published on the same day in Canada by Longmans Canada Limited. Library of Congress Catalog Card Number: 66-15089. The English translation of Gauss's letter to Taurinus is by Professor Harold E. Wolfe, and is reproduced from his book Non-Euclidean Geometry with the permission of Professor Wolfe and the publishers. Holt, Rinehart & Winston. This is an authorized reprint of a hardcover edition published by The John Day Company, Inc. First Printing, August, 1967 SIGNET TRADEMARK REG.—U.S. PAT. OFF. AND FOREIGN COtJNTRIES REGISTERED TRADEMARK MARCA REGISTRADA HECHO EN CHICAGO, U.S.A. SIGNET SCIENCE LIBRARY BOOKS are published i1n30t1heAUvneintueed oSftatthees AbmyerTihceasN,eNweAwmeYroircka,nNLeiwbraYroyr,kIn1c0.,019, in Canada by The New American Library of Canada Limited, 295 King Street East, Toronto 2, Ontario PRINTED IN THE UNITED STATES OF AMERICA Contents 1 One Book and Three Metaphors 9 2 Geometry Before Euclid 12 3 Euclid's Geometry 63 4 Geometry via Numbers 105 5 Geometry via Arrows 137 6 Geometry via Reflections 158 7 Geometry in Newtonian Physics 187 8 Non-Euclidean Geometry 195 9 The Calculus and Geometry 261 10 Projective Geometry 287 11 Geometry in Relativity Physics 356 12 Geometry Generalized 371 13 Geometry and Algebra 382 Bibliography 389 Answers to Exercises 391 Index 405 A New Look At Geometry (See page 288)