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Circles: A Mathematical View (Spectrum) Paperback – March 31, 1997

by Dan Pedoe (Author)

2 customer reviews

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This revised edition of a mathematical classic originally published in 1957 will bring to a new generation of students the enjoyment of investigating that simplest of mathematical figures, the circle. The author has supplemented this new edition with a special chapter designed to introduce readers to the vocabulary of circle concepts with which the readers of two generations ago were familiar. Readers of Circles need only be armed with paper, pencil, compass, and straight edge to find great pleasure in following the constructions and theorems. Those who think that geometry using Euclidean tools died out with the ancient Greeks will be pleasantly surprised to learn many interesting results which were only discovered in modern times. Novices and experts alike will find much to enlighten them in chapters dealing with the representation of a circle by a point in three-space, a model for non-Euclidean geometry, and the isoperimetric property of the circle.

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Product Details

Series: Spectrum
Paperback: 138 pages
Publisher: The Mathematical Association of America; 2 edition (March 31, 1997)
Language: English
ISBN-10: 0883855186
ISBN-13: 978-0883855188
Product Dimensions: 6 x 0.4 x 9 inches
Shipping Weight: 8 ounces
Average Customer Review: 4.5 out of 5 stars See all reviews (2 customer reviews)
Amazon Best Sellers Rank: #2,512,658 in Books (See Top 100 in Books)
- #710 in Books > Science & Math > Mathematics > Geometry & Topology > Topology
- #14984 in Books > Science & Math > Mathematics > Applied

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6 of 6 people found the following review helpful

Geometry Hobbyist

By Ken Burns on June 15, 2010

Format: Paperback

This is the only book I've seen concentrating solely on the geometry of the circle. So it discusses topics not usually covered in general, lower-level (high school or elementary college) texts: inversion, centers of similitude, coaxal systems, others. (There's no point in telling you what's in this book, since you can "Look Inside" and see for yourself.) This is intermediate in its level of difficulty, and certainly requires a familiarity of more than basic geometry and algebra. There is nothing of the elementary properties and theorems of the circle involving: arcs, radii, diameter, chords, secants, tangents, inscribed geometric figures, etc. This knowledge of all this is all presumed. It seems to be oriented to a person very comfortable with the material being presented using mathematical symbols and terms. This is why I gave it 4 stars, rather than 5.

Four chapters:
Chapter 1 discusses some more esoteric properties of circles (see the "Look Inside!").
Chapter 2 "adopt(s) a completely different point of view from that pursued in the first chapter." (page 26) I couldn't figure out how to summarize it for you.
Chapter 3 discusses the circle's part in "the Poincare model of hyperbolic non-Euclidean geometry." (page 44)
Chapter 4 talks about the circle's property of enclosing the greatest area with a given perimeter.

This text, problems, and solutions of this "new" edition are verbatim the same as the previous 1979 (corrected) edition. Even the typeset and layout are identical. Pedoe (1910-1998) has added three items to this "new" edition.
1) A 27-page "Chapter 0, designed to introduce readers the special vocabulary of circle concepts" (from back cover of new book).Read more ›

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10 of 13 people found the following review helpful

As is their nature, circles make a comeback

By Charles Ashbacher HALL OF FAMETOP 500 REVIEWERVINE VOICE on February 22, 2000

Format: Paperback

Although it is the simplest of all nonlinear geometric forms, the circle is far from trivial. It is indeed a pleasure that The Mathematical Association of America chose to reprint an update of this classic first printed in 1957. Geometry teaching has been in retreat for many years in the US and that has been a sad (and very bad) thing. It is also puzzling as so many people say that the reason why they cannot do mathematics (i.e. algebra) is that they need to see something in order to understand it. Furthermore, the first mathematical education that most children receive contains the differentiation of shapes and their different properties.
Circles and lines as used in geometry are abstractions that are easily grasped, much simpler to many than the abstract generalizations of algebra. One can only hope that this book signals a rebirth in interest in geometry education. Without question, it can be used as a text for that education and would help parent a rebirth. To remedy this modern affliction and make the material available to the current readership, a chapter zero was included. This new chapter is used to introduce the background concepts and terminology that could be assumed when is was first published.
No one can truly appreciate the intellectual achievements of the ancients as summarized by Euclid without doing some of the problems. There is also a stark beauty to a form of mathematics where the tools are a compass, straightedge and a mind. Particularly in the age of calculators and computers. All of the basic, ancient results concerning circles are covered as well as some very recent ones. The theorems are well presented and compete without being overdone. In keeping with the ancient traditions, pencil, paper, compass and straightedge are the only tools used.Read more ›

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