The Facts On File Geometry Handbook

353 Pages·2009·3.16 MB·English

THE FACTS ON FILE
Geometry
HANDBOOK
Revised Edition
CATHERINE A. GORINI, Ph.D.
Maharishi University of Management, Fairfield, Iowa
To Roy Lane for introducing me to the fascination and joys of geometry.
To my parents for their love, support, and encouragement.
To Maharishi Mahesh Yogi for the gift of pure knowledge.
The Facts On File Geometry Handbook, Revised Edition
Copyright © 2009, 2003 by Catherine A. Gorini, Ph.D.
Illustrations © 2009, 2003 by Infobase Publishing
All rights reserved. No part of this book may be reproduced or utilized in any form
or by any means, electronic or mechanical, including photocopying, recording, or by
any information storage or retrieval systems, without permission in writing from the
publisher. For information contact:
Facts On File, Inc.
An imprint of Infobase Publishing
132 West 31st Street
New York NY 10001
Library of Congress Cataloging-in-Publication Data
Gorini, Catherine A.
The Facts on File geometry handbook / Catherine A. Gorini.—Rev. ed.
p. cm.
Includes bibliographical references and index.
ISBN 978-0-8160-7389-4
1. Geometry. I. Title. II. Title: Geometry handbook.
QA445.2.G67 2000
516—dc22 2009005775
Facts On File books are available at special discounts when purchased in bulk quantities
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Text design adapted by James Scotto-Lavino
Illustrations by Melissa Ericksen
Photo research by Katherine Bourbeau
Printed in the United States of America
VB FOF 10 9 8 7 6 5 4 3 2 1
This book is printed on acid-free paper and contains 30 percent postconsumer
recycled content.
contents
Acknowledgments v
Introduction vii
SECTION ONE Glossary 1
SECTION TwO Biographies 209
SECTION THREE chronology 257
SECTION FOUR charts & tables 283
APPENDIx recommended reading 316
INDEx 330

AcknowledGments
I would like to express my deepest appreciation for all those who have
helped me in many different ways with the completion of this second
edition and who have given comments and feedback on the first edition.
In particular, I want to mention Lijuan Cai, Paul Calter, Anne Dow,
Penny Fitz-Randolph, Marianne Freundlich, Eric Hart, Jay Kappraff,
Janet Kernis, Walter Meyer, Doris Schattschneider, Lawrence Sheaff,
Joe Tarver, Eric Weisstein, and Peter Yff for their valuable conversations,
suggestions, encouragement, and assistance.
I am deeply indebted to Katherine Bourbeau for her care and
persistence in finding just the right pictures of important individuals and
concepts.
To Elizabeth Frost-Knappman, I wish to express my admiration and
gratitude for her great knowledge, penetrating wisdom, and valuable
advice.
This book would be completely impossible without the
conscientious care and support of Frank K. Darmstadt, executive editor,
and I wish to express to him my most sincere gratitude and appreciation.
v

IntroductIon
Like other areas of mathematics, geometry is a continually growing
and evolving field. Even in the six years since the first edition of
the Facts On File Geometry Handbook, developments in geometry
have been considerable. This revised edition highlights these new
developments while also correcting and expanding on the material in
the first edition.
Much new material has been added in this edition, including:
· more than 300 new glossary terms
· 12 new biographies
· 34 new events in the chronology
· more than 150 new resources in the recommended readings,
including more than 50 books published since the year 2000, 20
books giving the historical background of geometry, and new and
updated Web resources
· additional tables and theorems
Certainly the most exciting recent development in geometry is the
proof of the Poincaré conjecture by the Russian mathematician Grigory
Perelman, based on work by the American mathematician Richard
Hamilton. This conjecture about the properties of three-dimensional
topological spaces was one of the most challenging unsolved problems
in all of mathematics during the 20th century. Significant steps in the
proof of this conjecture were recorded in the first edition, and many
additional entries in the revised edition are related to various aspects
of this discovery, including cigar, Ricci curvature, Ricci flow, and
Witten’s black hole.
Computers, technology, and the sciences drive many new
discoveries in mathematics. For geometry, the areas of quantum
computers, computer graphics, nanotechnology, crystallography, and
theoretical physics have been particularly relevant in the past few
years. New items related to these areas include fullerene map, linear
code, nanohedron, racemic mixture, stereoisomers, and voxel in the
glossary as well as numerous chronological events and biographies.
vii
Introduction
There is a blossoming of interest by artists and mathematicians
nowadays in the connections and applications of mathematics to art.
Many areas of geometry, including symmetry, tiling, perspective,
properties of surfaces, and fractals, have special roles in the visual arts.
Some new glossary terms related to the arts are Alhambra, anamorphic
image, geodesic dome, girih tiles, kirigami, kolam, multifractal, parquet
transformation, and sacred cut.
The study of various aspects of Euclidean geometry has
continued for more than 2,000 years, with renewed interest today
especially in the properties of triangles and their associated centers
and circles. Mathematicians are finding that computer tools such as
the Geometer’s Sketchpad dynamic geometry program make these
constructions more accessible and easier to study. Among new terms
in this edition related to new discoveries in Euclidean geometry
are anticomplementary triangle, antipedal triangle, circumnormal
triangle, de Longchamps point, extouch triangle, isoscelizer,
Kimberling center, Lucas circles, Malfatti circles, Soddy center, and
Yff circles.
It should be noted that in geometry many objects or concepts have
several different names and sometimes a name, such as segment or pole,
is used to refer to many different concepts. When a glossary entry refers
the reader to another term, it is usually the case that this entry is just
another name for that term. In some cases, the term can only be defined
using some other concept and the reader is referred to the place where
the definition of the term is given. Fortunately, for those names that
have many different meanings, it is usually clear from the context which
definition is appropriate.
A feature of the revised edition is the inclusion of five additional
sets of axioms, three for Euclidean geometry and two for projective
geometry. The axioms of Euclid, given in the first edition, had been the
basis for 2,000 years of geometry, but eventually geometers found minor
inconsistencies in them. The axioms given by David Hilbert in 1899
were the first to remove these inconsistencies, followed by those of G.
D. Birkhoff in 1932. The School Mathematics Study Group gave another
set of axioms for use in school mathematics in 1958. All of these axioms
are in section 4, “Charts and Tables.”
All of these additions should convince the student that geometry is
a rich and lively field, still firmly based in its ancient roots and proud to
Introduction
viii
Introduction
be of service to science, technology, and the arts. I hope that this revised
edition of the Facts On File Geometry Handbook will be as warmly
received as the first edition and will prove to be a valuable resource to all
those who study and use geometry.
Introduction
ix