The Pythagorean theorem may be the best-known equation in mathematics. Its origins reach back to the beginnings of civilization, and today every student continues to study it. What most nonmathematicians don't understand or appreciate is why this simply stated theorem has fascinated countless generations. In this entertaining and informative book, a veteran math educator makes the importance of the Pythagorean theorem delightfully clear.
He begins with a brief history of Pythagoras and the early use of his theorem by the ancient Egyptians, Babylonians, Indians, and Chinese, who used it intuitively long before Pythagoras's name was attached to it. He then shows the many ingenious ways in which the theorem has been proved visually using highly imaginative diagrams. Some of these go back to ancient mathematicians; others are comparatively recent proofs, including one by the twentieth president of the United States, James A. Garfield.
After demonstrating some curious applications of the theorem, the author then explores the Pythagorean triples, pointing out the many hidden surprises of the three numbers that can represent the sides of the right triangle (e.g, 3, 4, 5 and 5, 12, 13). And many will truly amaze the reader. He then turns to the "Pythagorean means" (the arithmetic, geometric, and harmonic means). By comparing their magnitudes in a variety of ways, he gives the reader a true appreciation for these mathematical concepts.
The final two chapters view the Pythagorean theorem from an artistic point of view - namely, how Pythagoras's work manifests itself in music and how the Pythagorean theorem can influence fractals.
The author's lucid presentation and gift for conveying the significance of this key equation to those with little math background will inform, entertain, and inspire the reader, once again demonstrating the power and beauty of mathematics!
About Alfred S. Posamentier
Alfred S. Posamentier is dean of the School of Education and professor of mathematics education at Mercy College in Dobbs Ferry, New York. Previously, he had the same positions at the City College of the City University of New York for forty years. He has published over fifty-five books in the area of mathematics and mathematics education, including, most recently, Numbers: Their Tales, Types, and Treasures (with Bernd Thaller) and Mathematical Curiosities: A Treasure Trove of Unexpected Entertainments (with Ingmar Lehmann).
"A delightful departure from the typical mathematics book…[it] is a must read for students, teachers, college professors, an anyone interested in mathematics."
- Mathematics Teacher
"[Posamentier's] work is nothing short of comprehensive and remains the most standard work to represent Pythagorian thought in a modern era…. A dynamic read for stimulating your brain."
- San Francisco Book Review
"Posamentier explains well. He doesn't condescend, and he assumes that we'll follow what he has to say because he explains it in such an order that it's very hard not to follow… It ought to be dull, but it's not: it's fascinating.... Posamentier is on the list of writers I'll watch for, because I know now that if he writes about a subject then I will end up understanding it."
"A fine addition to any math history library."
- The Bookwatch, The Midwest Book Review
"An enjoyable read and a good reference. Highly recommended."