pythagorean theorem the story of its power and beauty

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The Pythagorean Theorem

Author : Alfred S. Posamentier
ISBN : 9781616143213
Genre : Mathematics
File Size : 75. 8 MB
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Although we all remember the Pythagorean Theorem from our school days, not until you read this book will you find out about the marvelous treasures this most famous mathematical concept holds. In an easily understood manner, the author entertains us with the wonders surrounding this theorem. This is the sort of treatment that will help popularize mathematics!-Charlotte K. Frank, PhD, SVP, research and development, McGraw-Hill Education, The McGraw-Hill CompaniesUsing the familiar Pythagorean theorem as the main theme the authors show the power and beauty of mathematics as we would have perhaps wished to have seen it when we were first introduced to this ubiquitous theorem in our school days. This book is a must read for anyone with even a small interest in mathematics.-Daniel Jaye, principal, Bergen County Academies, Hackensack, NJThe first time I have enjoyed anything about mathematics.-Bob Simon, 60 Minutes CorrespondentNot only is this book a very valuable resource for mathematics teachers, but it is also a book that can convince the general public that there is genuine beauty in mathematics. Perhaps this book will help bring 'converts' to mathematics!-Dr. Anton Dobart, director general, Austrian Ministry for Education, Art and CultureIt is often overheard in academic environments that 'math is'fun!' This little book on the Pythagorean theorem is surely proof enough, especially since, like the theorem, the fun is on almost every page.-Leon M. Lederman, Nobel laureateThe 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, veteran math educator Alfred S. Posamentier 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, Posamentier 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.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!Alfred S. Posamentier, Ph.D. (New York, NY), is dean of the School of Education and professor of mathematics education at The City College of the City University of New York. He has published more than 40 books in the area of mathematics and mathematics education, including The Fabulous Fibonacci Numbers, Pi: A Biography of the World's Most Mysterious Number, and Math Charmers: Tantalizing Tidbits for the Mind.

The Pythagorean Theorem

Author : Alfred S. Posamentier
ISBN : STANFORD:36105215504585
Genre : Mathematics
File Size : 25. 35 MB
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entertaining and informative book, veteran math educator Alfred S. Posamentier makes the importance of the Pythagorean Theorem delightfully clear. Posamentier begins with a brief history of Pythagoras himself 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. Following this introduction to the topic, he shows the many ingenious ways in which the theorem has been proved visually by 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, Posamentier then explores the Pythagorean triples, pointing out the many hidden surprises of the three numbers that can represent the sides of a right triangle (e.g., 3, 4, 5 and 5, 12, 13). The relationships --

Pythagorean Triangles

Author : Waclaw Sierpinski
ISBN : 9780486174839
Genre : Mathematics
File Size : 38. 40 MB
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This classic text, written by a distinguished mathematician and teacher, focuses on a fundamental theory of geometry. Topics include all types of Pythagorean triangles.

Math Charmers

Author : Alfred S. Posamentier
ISBN : 9781615921720
Genre : Mathematics
File Size : 46. 46 MB
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Foreword by Nobel Laureate Herbert A. HauptmanDesigned as a combat to math phobias, this guide tells how to make math intriguing and fun. -The Bookwatch Midwest Book Review library newsletterI love this book. I made the mistake of starting to read it late one evening, only to find I could not put it down. It is as engrossing and as exciting as a good mystery. This is an extraordinary accomplishment for a book about mathematics. - Arthur Levine, President, Teachers College, Columbia UniversityDr. Posamentier has spent a lifetime making the subject of mathematics come to life for students and their teachers. This book is another fine tribute to the work that is possible when a brilliant mind is led by a wonderful heart. How lucky we are to add this new work to an outstanding life of achievement. - Merryl H. Tisch, Member, New York State Board of RegentsProfessional mathematicians often speak of the beauty of mathematics and the elegance of its solutions. Yet the esthetic appeal of math is rarely conveyed to students at the elementary, secondary, or even college level. Instead, most of us develop phobias in school about math's elusive logic and then pass these negative impressions on to our children. What a shame, says math professor Alfred S. Posamentier. We should all be having fun with math and helping our kids to do better in life by encouraging them to appreciate not only its usefulness but especially its charm. That's just what Posamentier sets out to do in this delightful exploration of math's many intriguing, interesting, and fun qualities.Beginning with the beauty of the number system, Posamentier doesn't just talk mathematics; he entices readers to do math and discover for themselves just how stimulating the process can be! Brief and entertaining introductions to each chapter invite readers to try their hands at arithmetic marvels, surprising solutions, algebraic entertainments, geometric wonders, and fun mathematical paradoxes, among other topics.Presented in a reader-friendly, conversational tone, the text is very accessible and the examples are geared to a beginner's level, so that even the most math-phobic individual will discover the hidden joy and inherent appeal of doing math.This is the ideal book for adults looking for a way to turn their kids on to an important subject or discover for themselves what they might have missed in their own math education.Alfred S. Posamentier, Ph.D. (New York, NY), is dean of the School of Education and professor of mathematics education at The City College of the City University of New York. He has published more than 40 books in the area of mathematics and mathematics education, including The Fabulous Fibonacci Numbers, Pi: A Biography of the World's Most Mysterious Number, and Math Charmers: Tantalizing Tidbits for the Mind.

The Pythagorean Theorem

Author : Eli Maor
ISBN : 9780691148236
Genre : Mathematics
File Size : 42. 99 MB
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The author presents a complex history of the Pythagorean Theorem, examining the earliest evidence of knowledge of the theorem to Einstein's theory of relativity.

The Metaphysics Of The Pythagorean Theorem

Author : Robert Hahn
ISBN : 9781438464916
Genre : Philosophy
File Size : 62. 77 MB
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Explores Thales’s speculative philosophy through a study of geometrical diagrams. 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 Secrets Of Triangles

Author : Alfred S. Posamentier
ISBN : 9781616145880
Genre : Mathematics
File Size : 50. 69 MB
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Requiring no more than a knowledge of high school mathematics and written in clear and accessible language, this book will give all readers a new insight into some of the most enjoyable and fascinating aspects of geometry. Everyone knows what a triangle is, yet very few people appreciate that the common three-sided figure holds many intriguing "secrets." For example, if a circle is inscribed in any random triangle and then three lines are drawn from the three points of tangency to the opposite vertices of the triangle, these lines will always meet at a common point-no matter what the shape of the triangle. This and many more interesting geometrical properties are revealed in this entertaining and illuminating book about geometry. Flying in the face of the common impression that mathematics is usually dry and intimidating, this book proves that this sometimes-daunting, abstract discipline can be both fun and intellectually stimulating. The authors, two veteran math educators, explore the multitude of surprising relationships connected with triangles and show some clever approaches to constructing triangles using a straightedge and a compass. Readers will learn how they can improve their problem-solving skills by performing these triangle constructions. The lines, points, and circles related to triangles harbor countless surprising relationships that are presented here in a very engaging fashion.

The Best Writing On Mathematics 2011

Author : Mircea Pitici
ISBN : 9781400839544
Genre : Mathematics
File Size : 55. 73 MB
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This anthology brings together the year's finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2011 makes available to a wide audience many articles not easily found anywhere else--and you don't need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday occurrences of math, and take readers behind the scenes of today's hottest mathematical debates. Here Ian Hacking discusses the salient features that distinguish mathematics from other disciplines of the mind; Doris Schattschneider identifies some of the mathematical inspirations of M. C. Escher's art; Jordan Ellenberg describes compressed sensing, a mathematical field that is reshaping the way people use large sets of data; Erica Klarreich reports on the use of algorithms in the job market for doctors; and much, much more. In addition to presenting the year's most memorable writings on mathematics, this must-have anthology includes a foreword by esteemed physicist and mathematician Freeman Dyson. This book belongs on the shelf of anyone interested in where math has taken us--and where it is headed.

Hidden Harmonies

Author : Ellen Kaplan
ISBN : 9781608192915
Genre : Mathematics
File Size : 25. 58 MB
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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.

Geometry Civilized

Author : J. L. Heilbron
ISBN : 0198506902
Genre : Mathematics
File Size : 23. 80 MB
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Geometry Civilized is a unique combination of history and mathematics. It contains a full introduction to plane geometry and trigonometry within a fascinating historical framework that sets off the technical material. This approach to geometrical ideas gives the book its unique, readable style. The author has included a wide range of unusual and engaging geometric problems, many of which are taken from practical applications, drawn from sources ranging from ancient to modern. The study of geometry has been an important element of education in Europe since the time of the Greeks. This book helps us to understand why such emphasis has been placed on obtaining a good understanding of geometry. But the history presented here is not confined to the Western tradition. Examples drawn from other cultures, particularly Chinese and Indian, underscore the peculiarities of the geometry we have inherited from the Greeks, and thereby make Euclid's approach more accessible. Book reviews from the hardback: 'He has written a marvellous tale of how, throughout much of recorded history, geometrical thinking and civilisation have been closely intertwined. ...Definitely a book to dip into and reflect on a superior form of brainfood for the beach this summer perhaps? Heilbron's enthusiasm is contagious.' Ian Stewart, New Scientist 'The book is wonderfully illustrated. There are diagrams on almost every page, apt illustrations from older books, and well chosen photographs,together with eight colour plates. The appearance of the book is quite seductive, for which Oxford University Press should be congratulated.' Jeremy Gray, Nature 'This is a handsome book, well researched and entertainingly written. It shows how powerfully a historically informed account can communicate. If you thought Euclidean geometry was something only your great-grandparents did - try it, you will be surprised.' BJune Barrow-Green, The TIMES Higher Education Supplement

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