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The Babylonian Theorem: The Mathematical Journey to Pythagoras and Euclid Hardcover – January 26, 2010
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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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Top customer reviews
I have to say that it got off to a fairly good start, with a good description of Egyptian and Babylonian number systems and an explanation for how they might have evolved. Although some of the related equations are not difficult to derive, I think that a quick derivation would have been helpful. I also would not have been able to figure out what a greedy algorithm was from the explanation given if I did not already know it, but these are relatively minor points.
The problem comes when the author starts talking about what he calls the Babylonian Theorem mentioned in the title. He claims that the Babylonians knew how to prove the Pythagorean Theorem and he gives as justification a geometric diagram. Now the diagram does geometrically show that (a-b)^2 + 4ab = (a+b)^2, but I have hard time seeing how the Pythagorean Theorem follows, because the diagram contains no right triangles. There is a related diagram that can be used to prove the Pythagorean Theorem, but the author makes no reference to it, and I am not convinced that the Babylonians could have made use of it, because there is some algebraic manipulation required that they might not have been able to handle.
Okay, so at the very least the author showed how the Babylonians came up with a way of solving a particular type of quadratic equation. The author then claims to show how this was used to solve problems. He gives the following problem from a Babylonian text: A number subtracted from its inverse is equal to 7. I was guessing that in modern terms this would be: x - 1/x = 7, though neither this or any other interpretation is presented. My interpretation must be incorrect because it is stated that the equation has an integer solution and you can tell by inspection that this will not be true for my equation. There is then shown how the Babylonian student solved the problem and I have no idea how the manipulations relate to the original problem.
Later on, it is stated that Euclid proved the Babylonian Theorem using the Pythagorean Theorem. What is shown is a simple way of constructing a right triangle have a hypotenuse of (a+b) and a side of (a-b). Since there is a simple general method of constructing right triangles using straightedge and compass, I am not sure what this particular construction proves.
I would strongly suggest that the author do some serious editing of the book, providing explanations. It may yet prove to be useful, but in its present form it is one big mess.