Geometric Transformations II

202 Pages·1968·6.925 MB·English

by  Yaglom, Isaak Moiseevich

Anneli Lax New Mathematical Library, #21
Geometric Transformations II
Geometric Transformations II
I. M. Yaglom
translated by Allen Shields
I. M. Yaglom
G
e
Translated from the Russian by
o
This book is the sequel to Geometric Transformations I, volume 8 in
m Allen Shields
this series. Part I treats length-preserving transformations (isometries);
e
this volume treats shape-preserving transformation (similariries); Part t
r
III treats affine and protective transformations; and Part IV treats cir- i
c
cular transformations. These classes of transformations play a funda-
T
r
mental role in the group-theoretic approach to geometry. a
As in the previous volume, the treatment is direct and simple. The n
s
introduction of each new idea is supplemented by problems whose so- f
o
lutions employ the idea just presented, and whose detailed solutions r
m
are given in the second half of the book.
a
t
i
o
Isaac Moisevitch Yaglom was born on March 6, 1921 in the city of Kharkov. He n
graduated from Sverdlovsk University in 1942 and received his Candidate’s Degree s

(the equivalent of an American Ph.D.) from Moscow State University in 1945. He II

received the D.Sc. degree in 1965. An influential figure in mathematics education in

the Soviet Union, he was the author of many scientific and expository publications.

In addition to Geometric Transformations, English translations of his books include

Convex Figures (Holt, Rinehart and Winston, 1961, written jointly with V. G. Bolty-

anskii), Challenging Mathematical Problems with Elementary Solutions (Holden-

Day, 1964, written jointly with his twin brother Akiva M. Yaglom), Complex Num-

bers in Geometry (Academic Press, 1968), A Simple Non-Euclidean Geometry and

Its Physical Basis (Springer, 1979), Probability and Information (Reidel, 1983, writ-

ten jointly with Akiva), Mathematical Structures and Mathematical Modelling (Gor- I.

don and Breach, 1986), and Felix Klein and Sophus Lie (Birkhäuser, 1988). Professor M
.
Yaglom died April 17, 1988 in Moscow.
Y
a
g
l
Allen Shields (1927–1989), the translator of this volume, was professor of math- o
m
ematics at the University of Michigan for most of his career. He worked on a wide
range of mathematical topics including measure
theory, complex functions, functional analysis
and operator theory. ISBN 978-0-88385-621-5
9 780883 856215 MATHEMATICAL ASSOCIATION OF AMERICA
GEOMETRIC
TRANSFORMATIONS II

GEOMETRIC
TRANSFORMATIONS II
by
I. M. Yaglom
translated from the Russian by
Allen Shields
University of Michigan
Published and Distributed by
The Mathematical Association of America
Illustrated by George H . Buehler
©1968 by The Mathematical Association of America, (Inc.),
All rights reserved under International and
Pan-American Copyright Conventions.
Published in Washington, D.C. by
The Mathematical Association of America
Library of Congress Catalog Card Number: 67-20607
Print ISBN 978-0-88385-621-5
Electronic ISBN 978-0-88385-936-0
Manufactured in the United States of America
NEW MATHEMATICAL LIBRARY
published by
Random House and The L. W. Singer Company
for the Monograph Project of the
SCHOOL MATHEMATICS STUDY GROUP†
EDITORIAL PANEL
Ivan Niven, Chairman (1964–1968) Anneli Lax, Technical Editor
University of Oregon New York University
E. G. Begle Stanford University
M. Bell (1962–68) University of Chicago
L. Bers (1958–62) Columbia University
B. Bold (1963–66) Stuyvesant High School, N . Y .
W . G. Chinn (1961–67) San Francisco Public Schools
H. S. M. Coxeter (1958–61) University of Toronto
P. J. Davis (1961–64) Brown University
E. C. Douglas (1966–69) The Taft School, Conn.
E. Dyer (1963–66) City University of New York
B. Gordon (1966–69) University of California, Los Angeles
H. J . Greenberg (1964–67) University of Denver
P. R. Halmos (1958–63) University of Hawaii
J. H. Hlavaty (1958–63) DeWitt Clinton High School, NY
N. Jacobson (1958–61) Yale University
M. Kac (1961–65) Rockefeller University
M. Klamkin (1965–68) The Ford Motor Company
J. Landin (1966–69) University of Illinois, Chicago
R. S. Pieters (1958–62) Phillips Academy
H. 0. Pollak (1958–61) Bell Telephone Laboratories, Inc.
G. P6lya (1958–61) Stanford University
W. Prenowitz (1962–65) Brooklyn College
D. Richmond (1965–68) Williams College
A. Y. Rickey (1965–68) Dade County, Fla., Public Schools
H. E. Robbins (1958–61) Columbia University
W. W. Sawyer (1958–60) University of Toronto
N. E. Steenrod (1958–62) Stanford University
J. J. Stoker (1958–61) Princeton University
M. Zelinka (1962–65) New York University
L. Zippin (1958–61) Weston High School, Mass.
D. S. Scott (1963–66) City University of New York
Arlys Stritzel, Editorial Assistant
†The School Mathematics Study Group represents all parts of the mathematical
profession and all parts of the country. Its activities are aimed at the improvement
of teaching of mathematics in our schools. Further information can be obtained
from: School Mathematics Study Group, Cedar Hall, Stanford University, Stan-
ford, California 94305.

Note to the Reader
This book is one of a series written by professional mathematicians in
order to make some important mathematical ideas interesting and un-
derstandable to a large audience of high school students and laymen.
Most of the volumes in the New Mathematical Library cover topics not
usually included in the high school curriculum; they vary in difficulty,
and, even within a single book, some parts require a greater degree of
concentration than others. Thus, while the reader needs little technical
knowledge to understand most of these books, he will have to make an
intellectual effort.
If the reader has so far encountered mathematics only in classroom
work, he should keep in mind that a book on mathematics cannot be read
quickly. Nor must he expect to understand all parts of the book on first
reading. He should feel free to skip complicated parts and return to them
later; often an argument will be clarified by a subsequent remark. On the
other hand, sections containing thoroughly familiar material may be read
very quickly.
The best way to learn mathematics is to do mathematics, and each
book includes problems, some of which may require considerable
thought. The reader is urged to acquire the habit of reading with paper
and pencil in hand; in this way mathematics will become increasingly
meaningful to him.
For the authors and editors this is a new venture. They wish to ac-
knowledge the generous help given them by the many high school teach-
ers and students who assisted in the preparation of these monographs.
The Editors
vii
ANNELILAXNEWMATHEMATICALLIBRARY
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translatedbyAndyLiu
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44. GeometricTransformationsIVbyI.M.Yaglom,translatedbyA.Shenitzer
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