Search Results for "pythagorean-theorem-the-story-of-its-power-and-beauty"

The Pythagorean Theorem

The Pythagorean Theorem

The Story of Its Power and Beauty

  • Author: Alfred S. Posamentier
  • Publisher: Prometheus Books
  • ISBN: 1616143215
  • Category: Mathematics
  • Page: N.A
  • View: 822
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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.

Of The Pythagorean Theorem

Of The Pythagorean Theorem

  • Author: Asa Whitley
  • Publisher: Lulu.com
  • ISBN: 1304839745
  • Category:
  • Page: N.A
  • View: 9993
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Pythagorean Triangles

Pythagorean Triangles

  • Author: Waclaw Sierpinski
  • Publisher: Courier Corporation
  • ISBN: 0486174832
  • Category: Mathematics
  • Page: 128
  • View: 3482
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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.

The Glorious Golden Ratio

The Glorious Golden Ratio

  • Author: Alfred S. Posamentier,Ingmar Lehmann
  • Publisher: Prometheus Books
  • ISBN: 1616144246
  • Category: Mathematics
  • Page: 363
  • View: 4709
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What exactly is the Golden Ratio? How was it discovered? Where is it found? These questions and more are thoroughly explained in this engaging tour of one of mathematics' most interesting phenomena. The authors trace the appearance of the Golden Ratio throughout history, demonstrate a variety of ingenious techniques used to construct it, and illustrate the many surprising geometric figures in which the Golden Ratio is embedded. Requiring no more than an elementary knowledge of geometry and algebra, the authors give readers a new appreciation of the indispensable qualities and inherent beauty of mathematics. From the Hardcover edition.

Math Charmers

Math Charmers

Tantalizing Tidbits for the Mind

  • Author: Alfred S. Posamentier
  • Publisher: Prometheus Books
  • ISBN: 1615921729
  • Category: Mathematics
  • Page: 301
  • View: 7926
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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

The Pythagorean Theorem

A 4,000-Year History

  • Author: Eli Maor
  • Publisher: Princeton University Press
  • ISBN: 0691148236
  • Category: Mathematics
  • Page: 280
  • View: 5373
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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.

Pythagoras

Pythagoras

His Life, Teaching, and Influence

  • Author: Christoph Riedweg,Steven Rendall
  • Publisher: Cornell University Press
  • ISBN: 9780801474521
  • Category: Biography & Autobiography
  • Page: 184
  • View: 6197
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One of the most important mathematical theorems is named after Pythagoras of Samos, but this semi-mythical Greek sage has more to offer than formulas. He is said to have discovered the numerical nature of the basic consonances and transposed the musical proportions to the cosmos, postulating a "harmony of the spheres." He may have coined the words "cosmos" and "philosophy." He is also believed to have taught the doctrine of transmigration of souls and therefore to have advised a vegetarian diet. Ancient legends have Pythagoras conversing with dogs, bears, and bulls. A distinctly Pythagorean way of life, including detailed ritual regulations, was observed by his disciples, who were organized as a secret society. Later, Pythagorean and Platonic teachings became fused. In this Platonized form, Pythagoreanism has remained influential through medieval Christianity and the Renaissance down to the present. Christoph Riedweg's book is an engaging introduction to the fundamental contributions of Pythagoras to the establishment of European culture. To penetrate the intricate maze of lore and ascertain what history can tell us about the philosopher, Riedweg not only examines the written record but also considers Pythagoras within the cultural, intellectual, and spiritual context of his times. The result is a vivid overview of the life and teachings of a crucial Greek thinker and his most important followers.

The Metaphysics of the Pythagorean Theorem

The Metaphysics of the Pythagorean Theorem

Thales, Pythagoras, Engineering, Diagrams, and the Construction of the Cosmos out of Right Triangles

  • Author: Robert Hahn
  • Publisher: SUNY Press
  • ISBN: 1438464916
  • Category: Philosophy
  • Page: 300
  • View: 8999
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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 Metaphysics of the Pythagorean Theorem

The Metaphysics of the Pythagorean Theorem

Thales, Pythagoras, Engineering, Diagrams, and the Construction of the Cosmos out of Right Triangles

  • Author: Robert Hahn
  • Publisher: SUNY Press
  • ISBN: 1438464916
  • Category: Philosophy
  • Page: 300
  • View: 5003
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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

The Secrets of Triangles

A Mathematical Journey

  • Author: Alfred S. Posamentier,Ingmar Lehmann
  • Publisher: Prometheus Books
  • ISBN: 1616145889
  • Category: Mathematics
  • Page: 387
  • View: 1246
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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.

Beautiful Geometry

Beautiful Geometry

  • Author: Eli Maor,Eugen Jost
  • Publisher: Princeton University Press
  • ISBN: 1400848334
  • Category: Mathematics
  • Page: 208
  • View: 2400
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If you've ever thought that mathematics and art don't mix, this stunning visual history of geometry will change your mind. As much a work of art as a book about mathematics, Beautiful Geometry presents more than sixty exquisite color plates illustrating a wide range of geometric patterns and theorems, accompanied by brief accounts of the fascinating history and people behind each. With artwork by Swiss artist Eugen Jost and text by math historian Eli Maor, this unique celebration of geometry covers numerous subjects, from straightedge-and-compass constructions to intriguing configurations involving infinity. The result is a delightful and informative illustrated tour through the 2,500-year-old history of one of the most important branches of mathematics.

Geometry Civilized

Geometry Civilized

History, Culture, and Technique

  • Author: J. L. Heilbron
  • Publisher: Oxford University Press
  • ISBN: 9780198506904
  • Category: Mathematics
  • Page: 309
  • View: 4076
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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

Pythagoras' Trousers

Pythagoras' Trousers

God, Physics, and the Gender Wars

  • Author: Margaret Wertheim
  • Publisher: W. W. Norton & Company
  • ISBN: 9780393317244
  • Category: Science
  • Page: 297
  • View: 6370
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An "immensely accessible tour (which tells) how the physics lab became another Vatican with a no-girls-allowed sign on its door" (Susan Faludi) this spirited look at the relationship between physics and religion argues that gender inequity in physics is a result of the religious origins of the enterprise.

The Best Writing on Mathematics 2011

The Best Writing on Mathematics 2011

  • Author: Mircea Pitici
  • Publisher: Princeton University Press
  • ISBN: 0691153159
  • Category: Mathematics
  • Page: 383
  • View: 4771
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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.

Euler's Gem

Euler's Gem

The Polyhedron Formula and the Birth of Topology

  • Author: David S. Richeson
  • Publisher: Princeton University Press
  • ISBN: 0691154570
  • Category: Mathematics
  • Page: 317
  • View: 4645
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Leonhard Euler's polyhedron formula describes the structure of many objects--from soccer balls and gemstones to Buckminster Fuller's buildings and giant all-carbon molecules. Yet Euler's formula is so simple it can be explained to a child. Euler's Gem tells the illuminating story of this indispensable mathematical idea. From ancient Greek geometry to today's cutting-edge research, Euler's Gem celebrates the discovery of Euler's beloved polyhedron formula and its far-reaching impact on topology, the study of shapes. In 1750, Euler observed that any polyhedron composed of V vertices, E edges, and F faces satisfies the equation V-E+F=2. David Richeson tells how the Greeks missed the formula entirely; how Descartes almost discovered it but fell short; how nineteenth-century mathematicians widened the formula's scope in ways that Euler never envisioned by adapting it for use with doughnut shapes, smooth surfaces, and higher dimensional shapes; and how twentieth-century mathematicians discovered that every shape has its own Euler's formula. Using wonderful examples and numerous illustrations, Richeson presents the formula's many elegant and unexpected applications, such as showing why there is always some windless spot on earth, how to measure the acreage of a tree farm by counting trees, and how many crayons are needed to color any map. Filled with a who's who of brilliant mathematicians who questioned, refined, and contributed to a remarkable theorem's development, Euler's Gem will fascinate every mathematics enthusiast.

In Pursuit of the Unknown

In Pursuit of the Unknown

17 Equations That Changed the World

  • Author: Ian Stewart
  • Publisher: Basic Books
  • ISBN: 0465029744
  • Category: Mathematics
  • Page: 360
  • View: 4377
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In In Pursuit of the Unknown, celebrated mathematician Ian Stewart uses a handful of mathematical equations to explore the vitally important connections between math and human progress. We often overlook the historical link between mathematics and technological advances, says Stewart—but this connection is integral to any complete understanding of human history. Equations are modeled on the patterns we find in the world around us, says Stewart, and it is through equations that we are able to make sense of, and in turn influence, our world. Stewart locates the origins of each equation he presents—from Pythagoras's Theorem to Newton's Law of Gravity to Einstein's Theory of Relativity—within a particular historical moment, elucidating the development of mathematical and philosophical thought necessary for each equation's discovery. None of these equations emerged in a vacuum, Stewart shows; each drew, in some way, on past equations and the thinking of the day. In turn, all of these equations paved the way for major developments in mathematics, science, philosophy, and technology. Without logarithms (invented in the early 17th century by John Napier and improved by Henry Briggs), scientists would not have been able to calculate the movement of the planets, and mathematicians would not have been able to develop fractal geometry. The Wave Equation is one of the most important equations in physics, and is crucial for engineers studying the vibrations in vehicles and the response of buildings to earthquakes. And the equation at the heart of Information Theory, devised by Claude Shannon, is the basis of digital communication today. An approachable and informative guide to the equations upon which nearly every aspect of scientific and mathematical understanding depends, In Pursuit of the Unknown is also a reminder that equations have profoundly influenced our thinking and continue to make possible many of the advances that we take for granted.

Hidden Harmonies

Hidden Harmonies

The Lives and Times of the Pythagorean Theorem

  • Author: Ellen Kaplan
  • Publisher: Bloomsbury Publishing USA
  • ISBN: 1596915226
  • Category: Mathematics
  • Page: 290
  • View: 4205
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The Harvard mathematician authors of The Art of the Infinite present a history of the famous relation "A squared plus B squared equals C squared" that assesses its contributors from da Vinci to the Freemasons while analyzing its numerous proofs and applications.

The Joy of X

The Joy of X

A Guided Tour of Math, from One to Infinity

  • Author: Steven Henry Strogatz
  • Publisher: Houghton Mifflin Harcourt
  • ISBN: 0547517653
  • Category: MATHEMATICS
  • Page: 316
  • View: 6422
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A comprehensive tour of leading mathematical ideas by an award-winning professor and columnist for the New York Times Opinionator series demonstrates how math intersects with philosophy, science and other aspects of everyday life. By the author of The Calculus of Friendship. 50,000 first printing.

The Circle

The Circle

A Mathematical Exploration beyond the Line

  • Author: Alfred S. Posamentier,Robert Geretschläger
  • Publisher: Prometheus Books
  • ISBN: 1633881687
  • Category: Mathematics
  • Page: 300
  • View: 1224
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The circle has fascinated mathematicians since ancient times. This entertaining book describes in layperson’s terms the many intriguing properties of this fundamental shape. If math has intimidated you, this may be the ideal book to help you appreciate the discipline through one of its most important elements. The authors begin with a brief review of the basic properties of the circle and related figures. They then show the many ways in which the circle manifests itself in the field of geometry—leading to some amazing relationships and truly important geometric theorems. In addition, they explore remarkable circle constructions and demonstrate how all constructions in geometry that usually require an unmarked straightedge and a compass can also be done with the compass alone. Among other things, the reader will learn that circles can generate some unusual curves – many even quite artistic. Finally, the role of circles in art and architecture and a discussion of the circle’s place on the sphere bring "full circle" this presentation of a key element of geometry.