The Pythagorean Theorem: The Story of Its Power and BeautyThe 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! |
Contents
Acknowledgments | 9 |
Proving the Pythagorean Theorem | 37 |
Applications of the Pythagorean | 77 |
Copyright | |
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The Pythagorean Theorem: The Story of Its Power and Beauty Alfred S. Posamentier Limited preview - 2010 |
Common terms and phrases
AABC AB² ABCD AC² algebraic altitude apply the Pythagorean area of square area of triangle arithmetic mean BC² BCPR CE² consecutive numbers consider consonance construction Demonstration diezeugmenon equal equations famous theorem Fibonacci numbers fourth fractal geometric mean Greek hammer harmonic mean Heron's formula hypaton hypotenuse inradius integer intervals legs magic square mathematician mathematics meson natural numbers notice octave odd numbers original triangle parallelogram pattern perfect square perimeter Pierre de Fermat pitch Primitive 48 Primitive or multiple Primitive Primitive primitive Pythagorean triple produce proof prove the Pythagorean Ptolemy's Theorem Pythago Pythagoras Pythagoras's Pythagorean means Pythagorean Theorem Pythagorean tree quadrilateral ratio rean Theorem rean triples rectangle relationship right triangle ABC segment semiperimeter sequence shown in figure side lengths Stage strings tetrachord tetraktys trapezoid triangular numbers