Product Description
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 visualisations 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 non-metric 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. This is a masterful, fascinating, and entertaining book, which will interest both math enthusiasts and students of history. ... Read more

Customer Reviews (3)

College-level math and science collections especially will find this an intriguing math analysis
The Babylonian Theorem: The Mathematical Journey to Pythagoras and Euclid offers a fine sequel to HOW MATHEMATICS HAPPENED and comes from a physicist who explores the early history of math and how it was used to solve amazing problems. Illustrations from early Egyptian texts shows how math evolved and presents a 'Babylonian Theorem' which he shows was used to drive the Pythagorean Theorem. College-level math and science collections especially will find this an intriguing math analysis.

It all adds up through history
Get this book only if you love math, algebra, and geometry. //The Babylonian Theorem// is a mind-boggling examination of ancient Babylonian and Egyptian mathematical prowess. Until reading this book, this reviewer mistakenly thought advanced math was mostly a modern invention. Rudman shows us how Old Babylonian and Egyptian scribes avoided nonterminating fractions, though today the electronic calculator makes them less maddening. Rudman includes a generous portion of square root calculations courtesy of Archimedes, the most famous mathematician in ancient history. The chapter on pyramid volume will intrigue anyone interested in how the ancient Egyptians might have attempted to determine the needed material to build pyramids. Rudman delves into Pythagoras' founding of a religious cult with the motto "All is number," or as Rudman interprets it, "All is rational numbers." We learn that Pythagoras and his followers studied patterns that are formed by numbers, which led to number theory. Rudman concludes with a chapter on Euclid, the ancient Greek mathematician who wrote history's most popular textbook. Throughout the book, Rudman posts "Fun Questions" which are mathematical problems for the reader to solve. This is a mathematics book that includes a little history of ancient people and cultures. It's a good read for number lovers.

Reviewed by Grady Jones

I don't get it
This is a very good idea for a book and perhaps some day someone will do it right.Combining history and mathematics is a wonderful way of teaching students and I really wish that this book had been done right.

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.
... Read more

Customer Reviews (1)

IF YOU KNOW ANYTHING ABOUT PYTHAGORAS TO BEGIN WITH,
THIS IS A TERRIFIC BOOK. SHORT AND VERY INSIGHTFUL, IT DEALS WITH THE SPLIT PERSONALITY (OR WAS IT) OF MR P'S MATH BRILLIANCE AND FIRM BELIEF IN METAMPSYCHOSIS (REBIRTH ACCORDING TO JUDGMENT OF ONE'S PRESENT ACTIVITIES). READ IT. IT WILL INSPIRE YOUR INTEREST IN HIS THEOREM AGAIN.



... Read more

Product Description
This Book Is In German. ... Read more

Product Description
Package (in clear plastic stretch wrap) of five identical soft cover CONNECTED MATHEMATICS Looking For Pythagoras student books. The ISBN for each of these books is 0-13-053078-6. There are 79 pages in each book. ... Read more

Product Description
Package (in clear plastic stretch wrap) of five identical soft cover LOOKING FOR PYTHAGORAS The Pythagorean Theorem student editions, copyright 1998, by DALE SEYMOUR PUBLICATIONS. There are 76 pages in each of these books. Each book has the ISBN# 1-57232-180-6. ... Read more

Product Description
This Book Is In German. ... Read more

Product Description
This Book Is In German. ... Read more

Product Description

Why is ancient Greece important? Because, quite simply, if we want to understand the modern Western world, we need to look back to the Greeks. Consider the way we think about ethics, about the nature of beauty and truth, about our place in the universe, about our mortality. All this we have learned from the ancient Greeks. They molded the basic disciplines and genres in which we still organize thought, from poetry to drama, from medicine to philosophy, from history to ethnography.

Customer Reviews (1)

Higgins has witten a great little book
Charlotte Higgins has written an eminently readable book on Ancient Greece that has whet my appetite for more on this subject.

I studied Ancient Greek history and mythology at school and, 30 years on, have forgotten just about everything I learned. I am now sufficiently inspired to put together a reading list (and Ms Higgins has some fine suggestions) to remedy this lacuna.

Highly recommended to all those wanting to revisit the foundations of our civilisation after a long absence. ... Read more

Product Description
This digital document is an article from Macmillan Reference USA Science Library: Mathematics, brought to you by Gale®, a part of Cengage Learning, a world leader in e-research and educational publishing for libraries, schools and businesses.The length of the article is 1139 words.The article is delivered in HTML format and is available in your Amazon.com Digital Locker immediately after purchase.You can view it with any web browser.Explores the functions of math in daily life, as well as its role as a tool for measurement, data analysis, and technological development. This illustrated set also explains basic concepts of math and geometry, and provides information on historical milestones, notable mathematicians, and today's career choices. ... Read more

Product Description
This digital document is an article from UXL Encyclopedia of Science, brought to you by Gale®, a part of Cengage Learning, a world leader in e-research and educational publishing for libraries, schools and businesses.The length of the article is 145 words.The article is delivered in HTML format and is available in your Amazon.com Digital Locker immediately after purchase.You can view it with any web browser.This collection of entries covers major areas of science including: biology, genetics, microbiology, astronomy, chemistry, physics, engineering, technology, geology, weather, archaeology, psychology, mathematics, and medicine, and provides readers with a wide range of up-to-date, relevant, and accurate information. ... Read more