Geometry Civilized: History, Culture, and Technique [Paperback]

J. L. Heilbron (Author)

Book Description

ISBN-10: 0198506902 | ISBN-13: 978-0198506904 | Publication Date: March 16, 2000

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.

Editorial Reviews

Review

"Wonderfully illustrated...Heilbron covers Euclidean geometry, including behavior of circles, and plane trigonometry. All is explained from scratch, but not in the style of a textbook. Nor is it exactly a history of these topics, although it is erudite. The effect is to impart dignity to the subject and wisdom to its readers.... Heilbron's [book] is a deeply humanist work, which is a strange thing to say about a book with detailed geometry on every page. It may be that the devil is in the details, but so too is the step-by-step, line by painful line, progress of human achievement. The full immersion in the subject that Heilbron provides allows one to recognize oneself in the work of others, and to share in that inclusive web of our history, culture and technique." --Nature

"A marvellous tale of how, throughout much of recorded history, geometrical thinking and civilization have been closely intertwined... Geometry Civilized is a beautifully illustrated book. And you'll find that it can be read in at least two ways. For pleasure, in which case you can skip the exercises if you wish, or for mathematical enlightenment, in which case you definitely can't. Either way, you will be richly entertained with topics such as the problems solved geometrically in the construction of decorative cathedral windows around 1300 and the role played by geometry in Christopher Columbus's creative misconception about the distance from Spain to Japan." --Ian Stewart in The New Scientist

About the Author

John L Heilbron, MA, PhD, April House, Shilton, Burford, OX18 4AB Telephone/fax: [phone]

Product Details

• Paperback: 328 pages
• Publisher: Oxford University Press, USA (March 16, 2000)
• Language: English
• ISBN-10: 0198506902
• ISBN-13: 978-0198506904
• Product Dimensions: 9.6 x 7.4 x 0.7 inches
• Shipping Weight: 1.7 pounds
• Average Customer Review: 4.2 out of 5 stars  See all reviews (5 customer reviews)
• Amazon Best Sellers Rank: #1,773,836 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

27 of 28 people found the following review helpful:

5.0 out of 5 stars A truly unique book, July 3, 2000

By 

Robert Osserman (Berkeley, CA United States) - See all my reviews
(REAL NAME)   

This review is from: Geometry Civilized: History, Culture, and Technique (Paperback)

All books are unique, as George Orwell might have said, but some are more unique than others. And Heilbron's "Geometry Civilized" may be the most unique of all. 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, in the words of W.S. Gilbert, "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.

4 of 4 people found the following review helpful:

4.0 out of 5 stars Geometry and history intertwined, July 10, 2003

By 

Charles Ashbacher (Marion, Iowa United States) - See all my reviews
(TOP 500 REVIEWER)    (VINE VOICE)    (HALL OF FAME REVIEWER)   

This review is from: Geometry Civilized: History, Culture, and Technique (Paperback)

The rise of geometry was simultaneous with the rise of civilization. When people are aggregated into permanent population centers, it becomes necessary to precisely measure areas so that the proper taxes can be collected and also measure in the third dimension so that magnificent buildings can be constructed. While both require knowledge of geometry, they are experiential in nature.
The true rise of Western civilization as we know it took place in Greece, and the most permanent feature of that culture was the development of abstract mathematics. From this point one, mathematics was an endeavor that involved objects whose true nature was only in the mind. Any geometric diagram could only at best be a crude approximation of the true situation. It is hard to underestimate how much of a change this was from earlier forms of reasoning. I for one, firmly believe that all of the other ideas of democratic government, ethics, logic and philosophy that arose at the same time and place were a consequence of the new, more abstract and theoretical thinking that was taking place in geometry.
This book is a combination of history and geometry, showing how intertwined the two are. It is also one of the more extensive collections of solved geometry problems that exists today. Heilbron poses many problems, solving nearly all of them immediately after they are posed. As you step through the solutions, it is with a sense of wonderment as the steps are so direct, sequential and easy to understand, which is the hallmark of good geometric proofs.
Packed with figures, this book is suitable as a text for courses in geometry that the students will love, and I will point it out to anyone who claims that geometry is dull. With supplements, it could also be used as a text for courses in the history of mathematics.

2 of 2 people found the following review helpful:

4.0 out of 5 stars Geometry and history intertwined, July 10, 2003

By 

Charles Ashbacher (Marion, Iowa United States) - See all my reviews
(TOP 500 REVIEWER)    (VINE VOICE)    (HALL OF FAME REVIEWER)   

This review is from: Geometry Civilized: History, Culture, and Technique (Paperback)

The rise of geometry was simultaneous with the rise of civilization. When people are aggregated into permanent population centers, it becomes necessary to precisely measure areas so that the proper taxes can be collected and also measure in the third dimension so that magnificent buildings can be constructed. While both require knowledge of geometry, they are experiential in nature.
The true rise of Western civilization as we know it took place in Greece, and the most permanent feature of that culture was the development of abstract mathematics. From this point one, mathematics was an endeavor that involved objects whose true nature was only in the mind. Any geometric diagram could only at best be a crude approximation of the true situation. It is hard to underestimate how much of a change this was from earlier forms of reasoning. I for one, firmly believe that all of the other ideas of democratic government, ethics, logic and philosophy that arose at the same time and place were a consequence of the new, more abstract and theoretical thinking that was taking place in geometry.
This book is a combination of history and geometry, showing how intertwined the two are. It is also one of the more extensive collections of solved geometry problems that exists today. Heilbron poses many problems, solving nearly all of them immediately after they are posed. As you step through the solutions, it is with a sense of wonderment as the steps are so direct, sequential and easy to understand, which is the hallmark of good geometric proofs.
Packed with figures, this book is suitable as a text for courses in geometry that the students will love, and I will point it out to anyone who claims that geometry is dull. With supplements, it could also be used as a text for courses in the history of mathematics.