Babylonian Theorem Hardcover – 15 Jul 2010
- Choose from over 13,000 locations across the UK
- Prime members get unlimited deliveries at no additional cost
- Find your preferred location and add it to your address book
- Dispatch to this address when you check out
Enter your mobile number below and we'll send you a link to download the free Kindle App. Then you can start reading Kindle books on your smartphone, tablet, or computer - no Kindle device required.
Getting the download link through email is temporarily not available. Please check back later.
To get the free app, enter your mobile phone number.
Most Helpful Customer Reviews on Amazon.com (beta)
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.
Look for similar items by category
- Books > History > Ancient History & Civilisation > Middle East
- Books > Science & Nature > History & Philosophy > History of Mathematics
- Books > Science & Nature > Mathematics > Geometry & Topology
- Books > Science & Nature > Mathematics > History of Mathematics
- Books > Science & Nature > Popular Science > Maths
- Books > Scientific, Technical & Medical > Mathematics