Geometry Civilized: History, Culture, and Technique
by J. L. Heilbron
Oxford University Press | March 2000 | ISBN-10: 0198506902 | DJVU | 328 pages | 33.5 mb 
http://www.amazon.com/Geometry-Civilized-History-Culture-Technique/dp/0198506902

This lavishly illustrated book provides an unusually accessible approach to geometry by placing it in historical context. With concise discussions and carefully chosen illustrations the author brings the material to life by showing what problems motivated early geometers throughout the world. Geometry Civilized covers classical plane geometry, emphasizing the methods of Euclid but also drawing on advances made in China and India. It includes a wide range of problems, solutions, and illustrations, as well as a chapter on trigonometry, and prepares its readers for the study of solid geometry and conic sections.
It is, on the one hand, a coffee table book, in size and presentation, with beautiful illustations. On the other hand, it is a serious geometry text with full proofs of many theorems in Euclidean geometry, and plenty of interesting exercises for the reader. But perhaps most of all, it is a fascinating ramble through a wide range of topics, written by a leading historian of science with a strong esthetic sense and equally strong views on math and science education. He is "Teeming with a lot o' news", including "Many cheerful facts about the square of the hypotenuse" -- the title of his chapter on the Pythagorean Theorem. Another chapter, "From Polygons to Pi," includes the exact geometry of a Gothic arch and much of the accompanying ornamentation, as well as other topics ranging from Stonehenge to the Pentagon building, and from the idea behind burning mirrors attributed to Archimedes and actually constructed by Lavoisier and others, to the octagonal room designed by Thomas Jefferson. Anybody who enjoyed geometry in high school should love this book, and many people who feared or hated high school geometry may discover what they missed by not having a John Heilbron to show them the wonderful richness and flavor of what, presented badly, can appear a dry and useless subject.