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Harmony (Philosophy) --- Mathematics, Greek --- Pythagorean theorem

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By any measure, the Pythagorean theorem is the most famous statement in all of mathematics, one remembered from high school geometry class by even the most math-phobic students. Well over four hundred proofs are known to exist, including ones by a twelve-year-old Einstein, a young blind girl, Leonardo da Vinci, and a future president of the United States. Here--perhaps for the first time in English--is the full story of this famous theorem. Although attributed to Pythagoras, the theorem was known to the Babylonians more than a thousand years before him. He may have been the first to prove it, but his proof--if indeed he had one--is lost to us. Euclid immortalized it as Proposition 47 in his 'Elements', and it is from there that it has passed down to generations of students. The theorem is central to almost every branch of science, pure or applied. It has even been proposed as a means to communicate with extraterrestrial beings, if and when we discover them. And, expanded to four-dimensional space-time, it plays a pivotal role in Einstein's theory of relativity. In this book, Eli Maor brings to life many of the characters that played a role in the development of the Pythagorean theorem, providing a fascinating backdrop to perhaps our oldest enduring mathematical legacy.

Pythagorean theorem --- History. --- Pythagoras' theorem --- Pythagorean proposition --- Theorem, Pythagorean --- Geometry, Plane --- History --- Pythagore, théorème de --- Histoire

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Was Plato a Pythagorean? Plato's students and earliest critics thought so, but later scholars have been more skeptical. This book reconsiders this question by arguing that a specific type of Pythagorean philosophy, called 'mathematical' Pythagoreanism played a profound role in Plato's philosophy.

Philosophy, Ancient --- Mathematics, Ancient. --- Pythagorean theorem. --- Pythagoras and Pythagorean school. --- Philosophie ancienne --- Mathématiques anciennes --- Pythagore, Théorème de --- Pythagorisme --- Plato. --- Pythagoriciens --- Platon, --- Et les mathématiques --- Mathématiques anciennes --- Pythagore, Théorème de --- Mathematics, Ancient --- Pythagoras and Pythagorean school --- Pythagorean theorem --- Ancient mathematics --- Pythagoras' theorem --- Pythagorean proposition --- Theorem, Pythagorean --- Geometry, Plane --- Aflāṭūn --- Aplaton --- Bolatu --- Platonas --- Platone --- Po-la-tʻu --- Pʻŭllatʻo --- Pʻŭllatʻon --- Pʻuratʻon --- Πλάτων --- אפלטון --- פלאטא --- פלאטאן --- פלאטו --- أفلاطون --- 柏拉圖 --- 플라톤 --- Plato --- Platon --- Platoon --- Théorème de Pythagore --- Théorème de Pythagore. --- Pythagoriciens. --- Платон --- プラトン --- Et les mathématiques. --- Théorème de Pythagore. --- Et les mathématiques.

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The purpose of the conference “On Pythagoreanism”, held in Brasilia in 2011, was to bring together leading scholars from all over the world to define the status quaestionis for the ever-increasing interest and research on Pythagoreanism in the 21st century. The papers included in this volume exemplify the variety of topics and approaches now being used to understand the polyhedral image of one of the most fascinating and long-lasting intellectual phenomena in Western history. Cornelli’s paper opens the volume by charting the course of Pythagorean studies over the past two centuries. The remaining contributions range chronologically from Pythagoras and the early Pythagoreans of the archaic period (6th-5th centuries BCE) through the classical, hellenistic and late antique periods, to the eighteenth century. Thematically they treat the connections of Pythagoreanism with Orphism and religion, with mathematics, metaphysics and epistemology and with politics and the Pythagorean way of life.

Philosophy, Ancient --- Pythagoras and Pythagorean school --- Pythagorean theorem --- Pythagoras' theorem --- Pythagorean proposition --- Theorem, Pythagorean --- Geometry, Plane --- Plato --- Pythagoras --- Platon --- Aflāṭūn --- Aplaton --- Bolatu --- Platonas --- Platone --- Po-la-tʻu --- Pʻŭllatʻo --- Pʻŭllatʻon --- Pʻuratʻon --- Πλάτων --- אפלטון --- פלאטא --- פלאטאן --- פלאטו --- أفلاطون --- 柏拉圖 --- 플라톤 --- Платон --- プラトン --- Pitágora --- Pitagora di Samo --- Pitágoras --- Pitágoras de Samos --- Pythagore --- Πυθαγόρας --- فيثاغورس --- Presocratics. --- Pythagoras. --- Pythagoreanism.

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By virtue of their special algebraic structures, Pythagorean-hodograph (PH) curves offer unique advantages for computer-aided design and manufacturing, robotics, motion control, path planning, computer graphics, animation, and related fields. This book offers a comprehensive and self-contained treatment of the mathematical theory of PH curves, including algorithms for their construction and examples of their practical applications. Special features include an emphasis on the interplay of ideas from algebra and geometry and their historical origins, detailed algorithm descriptions, and many figures and worked examples. The book may appeal, in whole or in part, to mathematicians, computer scientists, and engineers.

Mathematics. --- Computer graphics. --- Computer-aided engineering. --- Algebra. --- Computer mathematics. --- Geometry. --- Computational intelligence. --- Computer-Aided Engineering (CAD, CAE) and Design. --- Computational Mathematics and Numerical Analysis. --- Computer Imaging, Vision, Pattern Recognition and Graphics. --- Computational Intelligence. --- Intelligence, Computational --- Artificial intelligence --- Soft computing --- Mathematics --- Euclid's Elements --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Mathematical analysis --- CAE --- Engineering --- Automatic drafting --- Graphic data processing --- Graphics, Computer --- Computer art --- Graphic arts --- Engineering graphics --- Image processing --- Math --- Science --- Data processing --- Digital techniques --- Pythagorean-hodograph curves. --- Hodograph equations. --- Pythagorean theorem. --- Geometry, Analytic. --- Curves --- Computer-aided design. --- Calculus --- Conic sections --- Geometry, Analytic --- Geometry, Differential --- Geometry, Enumerative --- Shapes --- Analytical geometry --- Geometry, Algebraic --- Algebra --- Pythagoras' theorem --- Pythagorean proposition --- Theorem, Pythagorean --- Geometry, Plane --- Equations, Hodograph --- Differential equations, Partial --- Fluid mechanics --- PH curves --- Graphic methods --- Computer aided design. --- Computer science --- Computer vision. --- Engineering. --- Construction --- Industrial arts --- Technology --- Machine vision --- Vision, Computer --- Pattern recognition systems --- CAD (Computer-aided design) --- Computer-assisted design --- Computer-aided engineering --- Design --- Optical data processing. --- Optical computing --- Visual data processing --- Bionics --- Integrated optics --- Photonics --- Computers --- Optical equipment