Excursions in Geometry

by C. Stanley Ogilvy

Book Overview

"A charming, entertaining, and instructive book .... The writing is exceptionally lucid, as in the author's earlier books, ... and the problems carefully selected for maximum interest and elegance." -- Martin Gardner.
This book is intended for people who liked geometry when they first encountered it (and perhaps even some who did not) but sensed a lack of intellectual stimulus and wondered what was missing, or felt that the play was ending just...

• Format: Paperback
• Language: English
• ISBN: 0486265307
• ISBN13: 9780486265308
• Release Date: December 1990
• Publisher: Dover Publications
• Length: 192 Pages
• Weight: 0.95 lbs.
• Dimensions: 0.4" x 5.4" x 8.6"

Customer Reviews

A review from an amateur Geometer

This was an excellent little book which I thoroughly enjoyed and which taught me a lot of Geometry not commonly available in schools or Universities or on the WEB. For example the coverage of "Soddy's Hexlet" was one of the most concise and rewarding pieces of Mathematics I've ever read. It deserves its five stars. The material was easy to follow and yet left plenty of gaps for the reader to fill in to consolidate their knowledge. Some traditional books on a subject like this simply assume too much knowledge and experience on the part of the reader and therefore quickly lose their appeal and remain largely unread outside of the Univerities. If more books like this were widely available I think they would spawn some very adept Geometers. Books like this hold one's interest, teaching the subject in a step by step unassuming fashion and indeed lead into more advanced work. Congratulations to the author.

Excursions in Geometry by Ogilvy

The work describes many types of geometric challenges ineveryday life. For instance, the optimal angle theta is presentedin a movie theatre. The screen is depicted as the base and amid-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 hasa variety of Euclidean topics to challenge the mathematicallyinclined readers. This work is perfect for any class scienceproject. Some of the challenges presented could occupy agraduate thesis.

This is how geometry should be taught.

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.

A Charming and Brief Excursion.

Dover is to be commended for reprinting both of Ogilvy's books"Excursions in Number Theory" and "Excursions in Geometry". Theyimpressed me as a young high school student and I borrowedthem from the library many times. I hope they arouse interestin mathematics for a new generation of young readers. Teacherswill find much material of interest for classes.I also recommend another Dover reprint "Geometric Exercisesin Paper Folding" by T Sundara Row.Also look at "Geometry Revisited" by H S M Coxeter and S L Greitzer.

A delightful book

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.