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