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The Babylonian Theorem: The Mathematical Journey to Pythagoras and Euclidby Peter S. Rudman
Synopses & Reviews
In this sequel to his award-winning How Mathematics Happened, physicist Peter S. Rudman explores the history of mathematics among the Babylonians and Egyptians, showing how their scribes in the era from 2000 to 1600 BCE used visualizations of how plane geometric figures could be partitioned into squares, rectangles, and right triangles to invent geometric algebra, even solving problems that we now do by quadratic algebra. Using illustrations adapted from both Babylonian cuneiform tablets and Egyptian hieroglyphic texts, Rudman traces the evolution of mathematics from the metric geometric algebra of Babylon and Egypt—which used numeric quantities on diagrams as a means to work out problems—to the nonmetric geometric algebra of Euclid (ca. 300 BCE). Thus, Rudman traces the evolution of calculations of square roots from Egypt and Babylon to India, and then to Pythagoras, Archimedes, and Ptolemy. Surprisingly, the best calculation was by a Babylonian scribe who calculated the square root of two to seven decimal-digit precision. Rudman provocatively asks, and then interestingly conjectures, why such a precise calculation was made in a mud-brick culture. From his analysis of Babylonian geometric algebra, Rudman formulates a "Babylonian Theorem", which he shows was used to derive the Pythagorean Theorem, about a millennium before its purported discovery by Pythagoras.
He also concludes that what enabled the Greek mathematicians to surpass their predecessors was the insertion of alphabetic notation onto geometric figures. Such symbolic notation was natural for users of an alphabetic language, but was impossible for the Babylonians and Egyptians, whose writing systems (cuneiform and hieroglyphics, respectively) were not alphabetic. Rudman intersperses his discussions of early math conundrums and solutions with "Fun Questions" for those who enjoy recreational math and wish to test their understanding. The Babylonian Theorem is a masterful, fascinating, and entertaining book, which will interest both math enthusiasts and students of history.
Book News Annotation:
In this book on ancient Near Eastern and Egyptian mathematics, Rudman (physics, Technion Institute, Haifa, emeritus)explores the ways in which ancient mathematicians worked out mathematical solutions to practical problems, like building pyramids and ziggurats, or tracing the square root of two apparently just for fun. He begins by explaining the numbering systems of Egyptians, Babylonians and Greeks, including explaining the use of agricultural measurements and parts of the body as standards. Along the way, we learn that the Babylonians worked in base 60 and the Egyptians wrote fractions using the hieroglyph for the eye of Horus. Much of the book, though, consists of formulae that demonstrate the mathematical skill of these societies and how much Greeks like Pythagoras and Euclid were building on earlier work. The text is sprinkled with "fun questions" that can be used to enliven the teaching of geometry and algebra even at a high school level. Annotation ©2010 Book News, Inc., Portland, OR (booknews.com)
Rudman explores the facisnating history of mathematics among the Babylonians and Egyptians. He formulates a Babylonian Theorem, which he shows was used to derive the Pythagorean Theorem about a millennium before its purported discovery by Pythagoras.
About the Author
Peter S. Rudman (Tel Aviv, Israel), a retired professor of physics at the Technion-Israel Institute of Technology, is the author of How Mathematics Happened: The First 50,000 Years, which was selected in 2008 as an Outstanding Academic Text by the American Library Association.
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Science and Mathematics » History of Science » General
Science and Mathematics » Mathematics » Geometry » Algebraic Geometry
Science and Mathematics » Mathematics » History