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 |
Pythagorean Triples | 123 |
The Pythagorean Means | 169 |
Tuning the Soul Pythagoras | 185 |
The Pythagorean Theorem | 211 |
Final Thoughts | 235 |
About the Mathematics Work | 237 |
Some Selected Proofs | 253 |
List of Primitive Pythagorean | 273 |
303 | |
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Common terms and phrases
ABCD algebraic altitude apply the Pythagorean area of square area of triangle arithmetic mean BCPR complex number consecutive numbers consider consonance construction Demonstration diagonal diezeugmenon equations established Euclidean formula famous theorem Fibonacci numbers fourth fractal geometric mean Greek hammer harmonic mean hypote hypotenuse inradius integer intervals Jos de Mey legs magic square mathematician mathematics meson n2 Primitive natural numbers notice octave odd numbers original triangle pattern perfect square perimeter pitch Posamentier Primitive 38 Primitive 46 Primitive 50 Primitive m n a=m Primitive or multiple primitive Pythagorean triple produce proof proportion prove the Pythagorean Pythago Pythagoras Pythagoras’s Pythagorean means Pythagorean Theorem Pythagorean tree Pythagorean triangle quadrilateral ratio rean Theorem rean triples rectangle relationship right triangle ABC semiperimeter sequence shown in figure side lengths simply square ACNM Stage strings superparticular ratio tetrachord tetraktys trapezoid triangular number whole tone