Excursions in Geometry

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 when the plot was finally becoming interesting.In this superb treatment, Professor Ogilvy demonstrates the mathematical challenge and satisfaction to be had from geometry, the only requirements being two simple implements (straightedge and compass) and a little thought. Avoiding topics that require an array of new definitions and abstractions, Professor Ogilvy draws upon material that is either self-evident in the classical sense or very easy to prove. Among the subjects treated are: harmonic division and Apollonian circles, inversion geometry, the hexlet, conic sections, projective geometry, the golden section, and angle trisection. Also included are some unsolved problems of modern geometry, including Malfatti's problem and the Kakeya problem.Numerous diagrams, selected references, and carefully chosen problems enhance the text. In addition, the helpful section of notes at the back provides not only source references but also much other material highly useful as a running commentary on the text.