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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!

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• Acknowledgments(p. 9)
• Introduction(p. 11)
• Chapter 1 Pythagoras and His Famous Theorem(p. 17)
• Chapter 2 Proving the Pythagorean Theorem without (Many) Words(p. 37)
• Chapter 3 Applications of the Pythagorean Theorem(p. 77)
• Chapter 4 Pythagorean Triples and Their Properties(p. 123)
• Chapter 5 The Pythagorean Means(p. 169)
• Chapter 6 Tuning the Soul: Pythagoras and Music(p. 185)
• Chapter 7 The Pythagorean Theorem in Fractal Art(p. 211)
• Final Thoughts(p. 235)
• Afterword: About the Mathematics Work That Led to the 1985 Nobel Prize in Chemistry: Thanks Ultimately to Pythagoras(p. 237)
• Pictorial Depictions of Pythagoras and His Famous Theorem(p. 241)
• Appendix A Some Selected Proofs(p. 253)
• Appendix B Some More Proofs and Solutions(p. 265)
• Appendix C List of Primitive Pythagorean Triples(p. 273)
• Appendix D List of Pythagorean Triples-Primitive and Nonprimitive(p. 279)
• Further References(p. 303)
• Index(p. 305)

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CHOICE Review

Posamentier (CUNY), author of numerous mathematics works (e.g., Mathematical Amazements and Surprises, CH, Jan'10, 47-2627; The (Fabulous) Fibonacci Numbers, CH, Jan'08, 45-2660; both works coauthored with I. Lehman), takes readers on a journey concerning the Pythagorean theorem. He introduces its namesake, credits others (Egyptians, Mesopotamians, Indians, Chinese) for their contributions, and offers 21 different proofs of the theorem. The author also shares numerous applications, reveals links to number theory (Pythagorean triples, Pythagorean means), and relates it to the arts (musical scales, fractal art). The author's prose is particularly clear and readable. This characteristic will make the title stand out among others on the same topic. It complements, rather than competes with, E. Maor's The Pythagorean Theorem (CH, Dec'07, 45-2087) by appealing to a more general audience. Some sections--for instance, the historical aspects including reproductions of commemorative stamps from around the world, the more visual proofs, the theorem's presence in musical tone systems, and construction of Pythagorean trees in fractal art--are simple enough for laypersons. Other sections, such as more advanced proofs and topics in number theory, will appeal to academics. The text is well laid out with crisp illustrations. An enjoyable read and a good reference. Summing Up: Highly recommended. All levels/libraries. W. R. Lee Minnesota State University, Mankato

Notas de autor provistas por Syndetics

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  The Fabulous Fibonacci Numbers (with Ingmar Lehmann).