Geometry Civilized: History, Culture, and Technique by J. L. Heilbron (PDF)

Description

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 solidgeometry and conic sections.

User’s Reviews

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 subjectand 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 fullimmersion 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 theexercises 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 inChristopher 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: (01993) 840830

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I was forewarned: this is basically a geometry book. Too bad. There is so many opportunities to elaborate on how geometry influenced culture, architecture, art, and even science that could have been delved into and intermingled with the material. The title is somewhat misleading and all of the material in the introduction could have been in more depth, lots of material added, and strategically placed throughout the book.

⭐Heilbron is simply a wonderful, sardonic, articulate writer even on complex topics. A first rate introduction to geometry in a more civilized manner than how it is delivered in the vast majority of classrooms..

⭐Exquisite book!

⭐I’ll be brief since others have written a bit more. The book is beautifully illustrated and argued. Perhaps 25% of the book is about applications of geometry and 75%, especially the problems, is solving “famous” or intriguing geometry problems. It does have a significant of Chinese geometry, but the focus is Euclidian and its descendants, though it does have lot of intriguing methods used by medieval masons/architects. If you are interested in an analogous book, consider Squaring the Circle, but its focus is less on classic geometry and more on finding applications of geometry in art, so you get far more on the golden ratio, etc. I thought Geometry Civilized could add a lot of intriguing applications to a sophisticated geometry class.

⭐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.

⭐Heilbron’s greatest accomplishment in this work is the very thorough cutting and pasting that brings us many pretty pictures, especially from the worlds of art and architecture and old textbooks. Other than that there is little of value. The bulk of the book is the same old terse Euclidean geometry that you can find in just about any geometry book. You might as well read Euclid because Heilbron adds basically nothing in terms of insight and readability when it comes to the geometry itself. In fact, he repeatedly manages to create technical obstacles even in clear terrain; see for example what must surely be the most incomprehensible introduction ever of radian angle measure on page 278.Still, the book also discusses many diverse applications which perhaps makes it worthwhile? Unfortunately, no. First of all there are some horrendously formulated statements, such as the claim that pi “cannot be expressed as a number, even an irrational one” (p. 241) and the implicit claim that three points need not lie in a plane: “Assuming, what is more or less true, that Rhodes and Alexandria lie on the same noon circle or meridian (that is, that Rhodes, Alexandria, and the centre of the earth lie in the same plane), …” (p. 66). One wonders how such things survived into the “corrected” paperback edition.More seriously, Heilbron frequently breaks the rule that in science and mathematics everything should be explained and nothing should be pulled out of a hat. He is forced to do so because he doesn’t have very many interesting applications of Euclidean geometry to offer and so has to discuss applications that are thoroughly incompatible with the mathematics covered. This is completely unnecessary since Euclidean geometry has many wonderful applications, but Heilbron simply ignores them: remarkably, conic sections, for example, are never mentioned even though there is a section on burning mirrors (!?), where we are told in a parenthesis that “a slightly different surface, whose intersection with the plane of the paper makes a parabola, gives a more intense focus” than a spherical mirror (p. 282, this is the only occurrence of the word parabola in the book). Instead, for example, we learn that “a Dutch geometer named Willebrord Snel” simply “proposed” the law of refraction (p. 107), apparently on a whim, and there is no indication of why nature would choose to obey this curious law. Later this law is fundamental when we study the rainbow, yet another topic that our methods are completely incapable of handling. Lacking calculus, we resort to the use of a table of values and read off that “evidently” the properties of refraction in raindrops are such-and-such (p. 197). If this is a valid method then why did we bother toiling with proofs of the Pythagorean theorem, for example? We could have just thrown up a bunch of numerical calculations and said that “evidently” the theorem is true. Geometry is not “civilized” by betraying the very soul of rational inquiry.

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