The Babylonian Theorem by Peter S. Rudman

2010-01-26T00:30:00-05:00

The Babylonian Theorem The Mathematical Journey to Pythagoras and Euclid
Written by Peter S. Rudman

Hardcover, 248 pages | Prometheus Books | Mathematics - History; Mathematics - Geometry - Algebraic | $26.00 | 978-1-59102-773-7 (1-59102-773-X)

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.

The Fabulous Fibonacci Numbers by Alfred S. Posamentier

2007-05-30T00:30:00-05:00

The Fabulous Fibonacci Numbers
Written by Alfred S. Posamentier

Hardcover, 364 pages | Prometheus Books | Mathematics - Algebra; Mathematics - Number Theory; Mathematics - Geometry - Algebraic | $28.99 | 978-1-59102-475-0 (1-59102-475-7)

Accessible and appealing to even the most math-phobic individual, this fun and enlightening book allows the reader to appreciate the elegance of mathematics and its amazing applications in both natural and cultural settings. The most ubiquitous, and perhaps the most intriguing, number pattern in mathematics is the Fibonacci sequence. In this simple pattern beginning with two ones, each succeeding number is the sum of the two numbers immediately preceding it (1, 1, 2, 3, 5, 8, 13, 21, ad infinitum). Far from being just a curiosity, this sequence recurs in structures found throughout nature-from the arrangement of whorls on a pinecone to the branches of certain plant stems. All of which is astounding evidence for the deep mathematical basis of the natural world. With admirable clarity, two veteran math educators take us on a fascinating tour of the many ramifications of the Fibonacci numbers. They begin with a brief history of a distinguished Italian discoverer, who, among other accomplishments, was responsible for popularizing the use of Arabic numerals in the West. Turning to botany, the authors demonstrate, through illustrative diagrams, the unbelievable connections between Fibonacci numbers and natural forms (pineapples, sunflowers, and daisies are just a few examples). In art, architecture, the stock market, and other areas of society and culture, they point out numerous examples of the Fibonacci sequence as well as its derivative, the "golden ratio." And of course in mathematics, as the authors amply demonstrate, there are almost boundless applications in probability, number theory, geometry, algebra, and Pascal's triangle, to name a few.

Random House New Releases - Mathematics - Geometry - Algebraic

The Babylonian Theorem by Peter S. Rudman

The Babylonian Theorem The Mathematical Journey to Pythagoras and EuclidWritten by Peter S. Rudman

The Fabulous Fibonacci Numbers by Alfred S. Posamentier

The Fabulous Fibonacci Numbers Written by Alfred S. Posamentier

The Babylonian Theorem The Mathematical Journey to Pythagoras and Euclid
Written by Peter S. Rudman

The Fabulous Fibonacci Numbers
Written by Alfred S. Posamentier