Excursions in Geometry [Paperback]

C. Stanley Ogilvy (Author)

Book Description

Publication Date: December 1, 1990

Topics including harmonic division and Apollonian circles, inversive geometry, the hexlet, conic sections, projective geometry, the Golden Section and angle trisection are addressed in a way that brings out the true intellectual excitement inherent in each. Also included: some unsolved problems of modern geometry. Notes. References. 132 line illustrations.

Product Details

• Paperback: 192 pages
• Publisher: Dover Publications (December 1, 1990)
• Language: English
• ISBN-10: 0486265307
• ISBN-13: 978-0486265308
• Product Dimensions: 8.6 x 5.4 x 0.4 inches
• Shipping Weight: 7.2 ounces (View shipping rates and policies)
• Average Customer Review: 4.5 out of 5 stars  See all reviews (10 customer reviews)
• Amazon Best Sellers Rank: #148,227 in Books (See Top 100 in Books)
  • #21 in Books > 4-for-3 Books > Science > History & Philosophy > General

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Customer Reviews

Most Helpful Customer Reviews

31 of 31 people found the following review helpful:

5.0 out of 5 stars A delightful book, June 3, 2000

By 

Michael Hardy (Minneapolis, MN, USA, for the Time Being) - See all my reviews
(REAL NAME)   

This review is from: Excursions in Geometry (Paperback)

I am very pleased to see there is a Dover edition of this excellent book, which might otherwise be out of print. I read this book when I was 14 years old. Most geometry books for people with very little prerequisite knowledge are boring. This one was fascinating to me when I read it, and still is now. The author's purpose is to show students with very little background how seductive the subject can be. He succeeds brilliantly.

The chapters on harmonic division and inversive geometry are a sort of preview of conformal mapping and (although Ogilvy doesn't say so, as far as I recall) of the geometry of the complex projective line. The chapter on the golden section is comprehensible to people who know no more math than what is known to almost everyone who can solve a quadratic equation. It shows clearly in only 13 pages how geometry, number theory, algebra, and analysis can be intimately connected with each other, along the way discussing pentagrams, spirals, knots, self-similarity, the five Platonic polyhedra, and the Fibonacci numbers (and quadratic equation, of course). The chapter on projective geometry is just as elementary even while it discusses topics that engage the attention of expert geometers (albeit at a more abstract level).

This is superb expository writing. Every 14-year-old who, as I did, has thoughts of becoming a mathematician, should read this book.

Is the previous reviewer right to say that "This book would only be reccomended to the top 2% of math students"? Perhaps. I would put it this way: No one who cannot understand, do, and enjoy mathematical reasoning will appreciate this book. So certainly this limits the market; as the previous reviewer said, it's not for the general public.

I am baffled by the previous reviewer's statement that this book tends to veer off course, or that the diagrams are not explained. Both statements are false and unjust.

8 of 8 people found the following review helpful:

5.0 out of 5 stars This is how geometry should be taught., May 17, 2002

By 

MS (British Columbia, Canada) - See all my reviews

This review is from: Excursions in Geometry (Paperback)

In this slim little volume, Ogilvy sets the standard for the genre. His subject matter is gloriously organized and impeccably motivated; he proves every result thoroughly but without getting bogged down in the sort of tedious formalism that all too often cripples mathematics texts; and the results themselves are the very picture of geometric elegance. (In particular, the chapter on Soddy's Hexlet is a gem.)

Ogilvy leads his readers on an excursion through geometric inversion, projective geometry, and the conic sections. Some of the subjects (most notably, conics, and that unexpected and magical projective invariant, the cross-ratio) appear again and again throughout the various chapters, and even the seasoned mathematician is almost guaranteed to find a new presentation of a familiar topic. Hence, I presume, one reviewer's assertion that the author has a tendency to veer off topic, which would be true if geometry were a disjoint collection of unrelated ideas. Ogilvy shows definitively that it's not; he's not changing the subject when he brings up the cross-ratio in a chapter on inversion - rather, he's unifying two (or more!) ostensibly disconnected subjects.

This book is suitable for anyone with even the slightest interest in geometry. Everything is developed from scratch, and so the lapsed mathematics student shouldn't be intimidated. The bright high school student will be captivated by the elegance and accessibility of the results; and the graduate student or professor of mathematics will find this book to be a lesson in mathematics pedagogy - or just a perfect leisurely read.

7 of 7 people found the following review helpful:

5.0 out of 5 stars Excursions in Geometry by Ogilvy, March 23, 2004

By 

Joseph S. Maresca "Dr. Joseph S. Maresca CPA,... (Bronxville, New York USA) - See all my reviews
(HALL OF FAME REVIEWER)    (TOP 1000 REVIEWER)    (REAL NAME)   

This review is from: Excursions in Geometry (Paperback)

The work describes many types of geometric challenges in
everyday life. For instance, the optimal angle theta is presented
in a movie theatre. The screen is depicted as the base and a
mid-point in the back of the theatre is the triangle peak.
Steiner's circles are shown so that equal circles can be
moved in an infinite combination of patterns. The work has
a variety of Euclidean topics to challenge the mathematically
inclined readers. This work is perfect for any class science
project. Some of the challenges presented could occupy a
graduate thesis.