image: 314 pages • ISBN 978-1-59102-477-4 • Hardcover $26 • Publication July 24, 2007 view more
Credit: Prometheus Books
The fascinating discussion of ancient mathematics unfolds in the book, How Mathematics Happened: The First 50,000 Years (Prometheus Books, $26). Author Peter S. Rudman does not just chronicle the archeological record of what mathematics was done; he digs deeper into the more important question of why it was done in a particular way. Why did the Egyptians use a bizarre method of expressing fractions" Why did the Babylonians use an awkward number system based on multiples of 60"
Rudman answers such intriguing questions, arguing that some mathematical thinking is universal and timeless. The similarity of the Babylonian and Mayan number systems, two cultures widely separated in time and space, illustrates the argument. He then traces the evolution of number systems from finger counting in hunter-gatherer cultures to pebble counting in herder-farmer cultures of the Nile and Tigris-Euphrates valleys, which defined the number systems that continued to be used even after the invention of writing.
With separate chapters devoted to the remarkable Egyptian and Babylonian mathematics of the era from about 3500 to 2000 BCE, when all of the basic arithmetic operations and even quadratic algebra became doable, Rudman concludes his interpretation of the archeological record.
Since some of the mathematics formerly credited to the Greeks is now known to be a prior Babylonian invention, Rudman adds a chapter that discusses the math used by Pythagoras, Eratosthenes, and Hippasus, which has Babylonian roots, illustrating the watershed difference in abstraction and rigor that the Greeks introduced. He also suggests that we might improve present-day teaching by taking note of how the Greeks taught math.
Complete with sidebars offering recreational math brainteasers, this engrossing discussion of the evolution of mathematics will appeal to both scholars and lay readers with an interest in mathematics and its history.
To appreciate the elegance of mathematics and its amazing applications in both natural and cultural settings, another new book entitled The Fabulous Fibonacci Numbers (Prometheus Books, $28) by Alfred Posamentier and Ingmar Lehmann, is accessible and appealing to even the most math-phobic individual. The authors take the reader on a fascinating tour of the many ramifications of the Fibonacci sequence--the most ubiquitous, and perhaps the most intriguing, number pattern in mathematics.
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.
The authors begin with a brief history of their 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.
Dr. Charlotte Frank, Senior Vice President of Research and Development at McGraw-Hill Education says, “This book provides evidence of the beauty of mathematics through this amazing phenomenon that seems to permeate just about everything – both in– and out-side of the world of mathematics.”