Pythagoras His Theorem
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The Pythagorean Theorem
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Author : Eli Maor
language : en
Publisher: Princeton University Press
Release Date : 2019-11-19
The Pythagorean Theorem written by Eli Maor and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-19 with Mathematics categories.
An exploration of one of the most celebrated and well-known theorems in mathematics By any measure, the Pythagorean theorem is the most famous statement in all of mathematics. In this book, Eli Maor reveals the full story of this ubiquitous geometric theorem. Although attributed to Pythagoras, the theorem was known to the Babylonians more than a thousand years earlier. Pythagoras may have been the first to prove it, but his proof—if indeed he had one—is lost to us. The theorem itself, however, is central to almost every branch of science, pure or applied. Maor brings to life many of the characters that played a role in its history, providing a fascinating backdrop to perhaps our oldest enduring mathematical legacy.
The Metaphysics Of The Pythagorean Theorem
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Author : Robert Hahn
language : en
Publisher: State University of New York Press
Release Date : 2017-05-01
The Metaphysics Of The Pythagorean Theorem written by Robert Hahn and has been published by State University of New York Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-01 with Philosophy categories.
Bringing together geometry and philosophy, this book undertakes a strikingly original study of the origins and significance of the Pythagorean theorem. Thales, whom Aristotle called the first philosopher and who was an older contemporary of Pythagoras, posited the principle of a unity from which all things come, and back into which they return upon dissolution. He held that all appearances are only alterations of this basic unity and there can be no change in the cosmos. Such an account requires some fundamental geometric figure out of which appearances are structured. Robert Hahn argues that Thales came to the conclusion that it was the right triangle: by recombination and repackaging, all alterations can be explained from that figure. This idea is central to what the discovery of the Pythagorean theorem could have meant to Thales and Pythagoras in the sixth century BCE. With more than two hundred illustrations and figures, Hahn provides a series of geometric proofs for this lost narrative, tracing it from Thales to Pythagoras and the Pythagoreans who followed, and then finally to Plato's Timaeus. Uncovering the philosophical motivation behind the discovery of the theorem, Hahn's book will enrich the study of ancient philosophy and mathematics alike.
The Pythagorean Theorem
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Author : Alfred S. Posamentier
language : en
Publisher:
Release Date : 2010
The Pythagorean Theorem written by Alfred S. Posamentier and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
among the numbers of a Pythagorean triple will truly amaze the reader. Posamentier next turns to "Pythagorean means" (the arithmetic, geometric, and harmonic means). Outlining Pythagoras's contributions to the methods used for measuring and comparing quantities in a variety of ways gives the reader a true appreciation for these valuable mathematical concepts. Finally, the last two chapters take a some what different approach to the topic and view the Pythagorean Theorem from an artistic point of view. The author shows how Pythagoras's work manifests itself in music and how the Pythagorean Theorem has influenced fractals, including the founding of a new class of fractals called "Pythagorean trees." Posamentier'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. --Book Jacket.
Pythagorean Triangles
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Author : Waclaw Sierpinski
language : en
Publisher: Courier Corporation
Release Date : 2013-04-10
Pythagorean Triangles written by Waclaw Sierpinski and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-10 with Mathematics categories.
This classic text, written by a distinguished mathematician and teacher, focuses on a fundamental theory of geometry. Topics include all types of Pythagorean triangles.
The Pythagorean Theorem
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Author : Merle A. Barlow
language : en
Publisher: WestBow Press
Release Date : 2016-02-05
The Pythagorean Theorem written by Merle A. Barlow and has been published by WestBow Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-02-05 with Mathematics categories.
Pythagoras, a famous Greek scholar, sathematician, and philosopher, formulated a proof for a theorem that is named for him—the Pythagorean theorem. This theorem states that in any right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. The Pythagorean theorem for right-angled triangles likely was known long before the time of Pythagoras. It was probably used by the ancient Egyptians to construct the pyramids. The theorem is quite believable without rigorous proof to anyone willing to expend a modest effort in some experimentation. One method is to draw a number of right-angled triangles in as wide a variety as practicable and measure all of the sides. It will be determined that, for each triangle drawn, the square of the length of the side opposite the right angle is about equal to the sum of the lengths of the squares of the other two sides. Another method requires the availability of a balance. For this more interesting experiment, construct a right-angled triangle and a square on each side using a piece of sheet metal or cardboard. Then cut out the three squares and weigh them on the balance. The square on the hypotenuse should balance the other two. Contained within this book are some rigorous proofs and some interesting perspectives regarding right angles and right-angled triangles. Doubtless, this theorem is one of the most useful concepts in mathematics.
Hidden Harmonies
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Author : Ellen Kaplan
language : en
Publisher: Bloomsbury Publishing USA
Release Date : 2011-01-11
Hidden Harmonies written by Ellen Kaplan and has been published by Bloomsbury Publishing USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-01-11 with Mathematics categories.
A squared plus b squared equals c squared. It sounds simple, doesn't it? Yet this familiar expression is a gateway into the riotous garden of mathematics, and sends us on a journey of exploration in the company of two inspired guides, acclaimed authors Robert and Ellen Kaplan. With wit, verve, and clarity, they trace the life of the Pythagorean theorem, from ancient Babylon to the present, visiting along the way Leonardo da Vinci, Albert Einstein, President James Garfield, and the Freemasons-not to mention the elusive Pythagoras himself, who almost certainly did not make the statement that bears his name. How can a theorem have more than one proof? Why does this one have more than two hundred-or is it four thousand? The Pythagorean theorem has even more applications than proofs: Ancient Egyptians used it for surveying property lines, and today astronomers call on it to measure the distance between stars. Its generalizations are stunning-the theorem works even with shapes on the sides that aren't squares, and not just in two dimensions, but any number you like, up to infinity. And perhaps its most intriguing feature of all, this tidy expression opened the door to the world of irrational numbers, an untidy discovery that deeply troubled Pythagoras's disciples. Like the authors' bestselling The Nothing That Is and Chances Are . . .-hailed as "erudite and witty," "magnificent," and "exhilarating"-Hidden Harmonies makes the excitement of mathematics palpable.
Pythagoras And His Theorem
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Author : Paul Strathern
language : en
Publisher: Random House
Release Date : 2012-10-31
Pythagoras And His Theorem written by Paul Strathern and has been published by Random House this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-31 with Science categories.
At a moment of great discovery, one Big Idea can change the world... Pythagoras was arguably the first 'genius' of Western culture, establishing a blend of high intellect and high lunacy, both of which have become recurrent features of this scholarly heritage.Most memorably, he created the Pythagorean Theorem, and established the concept of proofs in mathematics. Less well known was the religion he founded which forbade his disciples from eating beans or stepping over fallen poles! Pythagoras & His Theorem tells the remarkable story of the life of this poorly understood genius and the transformation his work brought about in mathematics. Pythagoras' Big Idea is presented in an accessible and enthralling way, providing an explanation of the meaning of his work, its historical and scientific context, and significance for the world in which we live. The Big Idea series is a fascinating look at the greatest advances in our scientific history, and at the men and women who made these fundamental breakthroughs.
A Pythagorean Introduction To Number Theory
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Author : Ramin Takloo-Bighash
language : en
Publisher: Springer
Release Date : 2018-11-26
A Pythagorean Introduction To Number Theory written by Ramin Takloo-Bighash and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-26 with Mathematics categories.
Right triangles are at the heart of this textbook’s vibrant new approach to elementary number theory. Inspired by the familiar Pythagorean theorem, the author invites the reader to ask natural arithmetic questions about right triangles, then proceeds to develop the theory needed to respond. Throughout, students are encouraged to engage with the material by posing questions, working through exercises, using technology, and learning about the broader context in which ideas developed. Progressing from the fundamentals of number theory through to Gauss sums and quadratic reciprocity, the first part of this text presents an innovative first course in elementary number theory. The advanced topics that follow, such as counting lattice points and the four squares theorem, offer a variety of options for extension, or a higher-level course; the breadth and modularity of the later material is ideal for creating a senior capstone course. Numerous exercises are included throughout, many of which are designed for SageMath. By involving students in the active process of inquiry and investigation, this textbook imbues the foundations of number theory with insights into the lively mathematical process that continues to advance the field today. Experience writing proofs is the only formal prerequisite for the book, while a background in basic real analysis will enrich the reader’s appreciation of the final chapters.
The Pythagorean Proposition
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Author : Elisha Scott Loomis
language : en
Publisher:
Release Date : 1968
The Pythagorean Proposition written by Elisha Scott Loomis and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with Mathematics categories.
Pythagoras
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Author : Alicia Klepeis
language : en
Publisher: Mitchell Lane
Release Date : 2019-09-04
Pythagoras written by Alicia Klepeis and has been published by Mitchell Lane this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-04 with Juvenile Nonfiction categories.
Mathematician. Philosopher. World traveler. Pythagoras was an intellgient and curious scholar and teacher. While he’s best known for the Pythagorrean theorem, he shared ideas about numbers, animals and many other areas of knwoledge with his students. Since none of his writingers were left behind, it’s not always easy for historians to know what’s true about Pythagoras and what may be legendary. What does seem apparent is that he was a vegetarian but not a trendy dresser. Some people saw him as godlike. Others felt he made false claims about things. No matter what, Pythagoras’s curiosity and willinngness to grapplw with complex issues have helped further the knowledge of mathemativs and philosophy for thousands of years.