Geometry and Algebra in Ancient Civilizations [Hardcover]

Bartel L. van der Waerden (Author)

Product Details

• Hardcover: 223 pages
• Publisher: Springer; 1 edition (April 9, 2002)
• Language: English
• ISBN-10: 3540121595
• ISBN-13: 978-3540121596
• Average Customer Review: 4.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #6,364,469 in Books (See Top 100 in Books)

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3 of 3 people found the following review helpful:

4.0 out of 5 stars Bold, June 19, 2010

By 

Viktor Blasjo - See all my reviews
(REAL NAME)   

This review is from: Geometry and Algebra in Ancient Civilizations (Hardcover)

Van der Waerden is a delightful historian because he is not afraid of proposing bold hypotheses. His most provocative claim in this book is that all major mathematical cultures have a common origin in the Neolithic period. This common core of mathematics was focused on Pythagoras' theorem and Pythagorean triples.

Although van der Waerden's thesis is surely too simplistic to be literally true, it is nevertheless good fun to view history through his lens, for from it flow neat answers to intractable why-questions, such as:

Why did ancient man care about Pythagoras' theorem? Because it can be used to calculate the duration of a lunar eclipse as a function of the moon's deviation from the ecliptic (p. 32).

Why did ancient man care about proofs of mathematical theorems? If one starts with a problem such as the eclipse problem then one is virtually forced to discover Pythagoras' theorem by proving it, as neither the theorem nor any empirical rule of thumb that could take its place is likely to suggest itself by other means.

Why did ancient man want to generate Pythagorean triples? In order to construct textbook problems on Pythagoras' theorem that have numerically neat solutions (p. 33).

Why did ancient man become interested in ruler-and-compass constructions? For the sake of the constructions of altars (pp. 10-14). "Those who deprive the agni (altar) of its true proportions will suffer the worse for sacrificing" (p. 13), we read in an ancient Indian text which treats a number of construction problems about areas. The Greeks, for their part, of course had the problem of the duplication of the cube, which is also said to have originated as an altar-construction problem (p. 13).

This indicates the point at which the development from the common Neolithic origin split into two branches, driven by textbook texts (Babylonian, Egyptian, Chinese) and ritual geometry (Hindu, Greek) respectively (pp. 66-69).

Of course more mainstream historians will reject van der Waerden's reconstructions, on good grounds, as Knorr does in his excellent review in the British Journal for the History of Science. But I for one will still read books like van der Waerden's, because the same scrupulousness that drives such reviews also drives these respectable historians to shy away from tackling interesting why-questions head on in the refreshing manner of van der Waerden.