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

Of The Pythagorean Theorem

Of The Pythagorean Theorem

  • Author: Asa Whitley
  • Publisher: Lulu.com
  • ISBN: 1304839745
  • Category:
  • Page: N.A
  • View: 6312
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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: 3168
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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.

Pythagorean Triangles

Pythagorean Triangles

  • Author: Waclaw Sierpinski
  • Publisher: Courier Corporation
  • ISBN: 0486174832
  • Category: Mathematics
  • Page: 128
  • View: 7283
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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 Pythagorean Theorem

The Pythagorean Theorem

A 4,000-Year History

  • Author: Eli Maor
  • Publisher: Princeton University Press
  • ISBN: 0691148236
  • Category: Mathematics
  • Page: 280
  • View: 4201
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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 Glorious Golden Ratio

The Glorious Golden Ratio

  • Author: Alfred S. Posamentier,Ingmar Lehmann
  • Publisher: N.A
  • ISBN: 9781616144234
  • Category: Mathematics
  • Page: 363
  • View: 429
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The Golden Ratio is a key pattern that has perhaps endless applications and manifestations. Requiring no more than an elementary knowledge of geometry and algebra this book will give readers a new appreciation of the inherent beauty of mathematics.

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: 6920
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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.

Math Charmers

Math Charmers

Tantalizing Tidbits for the Mind

  • Author: Alfred S. Posamentier
  • Publisher: Prometheus Books
  • ISBN: 1615921729
  • Category: Mathematics
  • Page: 301
  • View: 2102
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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.

A Certain Ambiguity

A Certain Ambiguity

A Mathematical Novel

  • Author: Gaurav Suri,Hartosh Singh Bal
  • Publisher: Princeton University Press
  • ISBN: 9781400834778
  • Category: Fiction
  • Page: 296
  • View: 8282
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While taking a class on infinity at Stanford in the late 1980s, Ravi Kapoor discovers that he is confronting the same mathematical and philosophical dilemmas that his mathematician grandfather had faced many decades earlier--and that had landed him in jail. Charged under an obscure blasphemy law in a small New Jersey town in 1919, Vijay Sahni is challenged by a skeptical judge to defend his belief that the certainty of mathematics can be extended to all human knowledge--including religion. Together, the two men discover the power--and the fallibility--of what has long been considered the pinnacle of human certainty, Euclidean geometry. As grandfather and grandson struggle with the question of whether there can ever be absolute certainty in mathematics or life, they are forced to reconsider their fundamental beliefs and choices. Their stories hinge on their explorations of parallel developments in the study of geometry and infinity--and the mathematics throughout is as rigorous and fascinating as the narrative and characters are compelling and complex. Moving and enlightening, A Certain Ambiguity is a story about what it means to face the extent--and the limits--of human knowledge.

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: 2137
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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: 318
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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.

The Divine Proportion

The Divine Proportion

  • Author: H. E. Huntley
  • Publisher: Courier Corporation
  • ISBN: 0486131874
  • Category: Mathematics
  • Page: 208
  • View: 1056
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Discussion ranges from theories of biological growth to intervals and tones in music, Pythagorean numerology, conic sections, Pascal's triangle, the Fibonnacci series, and much more. Excellent bridge between science and art. Features 58 figures.

The Golden Ratio

The Golden Ratio

The Divine Beauty of Mathematics

  • Author: Gary B. Meisner
  • Publisher: Race Point Publishing
  • ISBN: 163106486X
  • Category: Mathematics
  • Page: 224
  • View: 5856
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The Golden Ratio examines the presence of this divine number in art and architecture throughout history, as well as its ubiquity among plants, animals, and even the cosmos. This gorgeous book—with layflat dimensions that closely approximate the golden ratio—features clear, enlightening, and entertaining commentary alongside stunning full-color illustrations by Venezuelan artist and architect Rafael Araujo. From the pyramids of Giza, to quasicrystals, to the proportions of the human face, the golden ratio has an infinite capacity to generate shapes with exquisite properties. This book invites you to take a new look at this timeless topic, with a compilation of research and information worthy of a text book, accompanied by over 200 beautiful color illustrations that transform this into the ultimate coffee table book. Author Gary Meisner shares the results of his twenty-year investigation and collaboration with thousands of people across the globe in dozens of professions and walks of life. The evidence will close the gaps of understanding related to many claims of the golden ratio’s appearances and applications, and present new findings to take our knowledge further yet. Whoever you are, and whatever you may know about this topic, you’ll find something new, interesting, and informative in this book, and may find yourself challenged to see, apply, and share this unique number of mathematics and science in new ways.

Pythagoras' Revenge

Pythagoras' Revenge

A Mathematical Mystery

  • Author: Arturo Sangalli
  • Publisher: Princeton University Press
  • ISBN: 9780691049557
  • Category: Fiction
  • Page: 183
  • View: 4476
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The celebrated mathematician and philosopher Pythagoras left no writings. But what if he had and the manuscript had never been found? Where would it be located? Two mathematicians, one American, one British, set out, unbeknownst to each other, to find the missing manuscript.

Beautiful Geometry

Beautiful Geometry

  • Author: Eli Maor,Eugen Jost
  • Publisher: N.A
  • ISBN: 9780691175881
  • Category: Art
  • Page: 208
  • View: 894
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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 acclaimed 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 and beautiful branches of mathematics"--

The Proof is in the Pudding

The Proof is in the Pudding

The Changing Nature of Mathematical Proof

  • Author: Steven G. Krantz
  • Publisher: Springer Science & Business Media
  • ISBN: 9780387487441
  • Category: Mathematics
  • Page: 264
  • View: 3618
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This text explores the many transformations that the mathematical proof has undergone from its inception to its versatile, present-day use, considering the advent of high-speed computing machines. Though there are many truths to be discovered in this book, by the end it is clear that there is no formalized approach or standard method of discovery to date. Most of the proofs are discussed in detail with figures and equations accompanying them, allowing both the professional mathematician and those less familiar with mathematics to derive the same joy from reading this book.

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: 3797
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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.

Pythagorean Crimes

Pythagorean Crimes

  • Author: Teukros Michaēlidēs
  • Publisher: Parmenides Pub
  • ISBN: 9781930972261
  • Category: Fiction
  • Page: 272
  • View: 5631
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After his friend Stefanos Kantartzis is found murdered in 1929 Athens, Michael Igerinos investigates whether the solution of a mathematical problem drove someone to commit the dirty deed. Reprint.

The Secrets of Triangles

The Secrets of Triangles

A Mathematical Journey

  • Author: Alfred S. Posamentier,Ingmar Lehmann
  • Publisher: N.A
  • ISBN: 9781616145873
  • Category: Mathematics
  • Page: 387
  • View: 1171
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Reveals interesting geometrical properties designed to present the discipline as fun, and improve the reader's problem-solving skills.

The Geometry of Art and Life

The Geometry of Art and Life

  • Author: Matila Costiescu Ghyka
  • Publisher: Courier Corporation
  • ISBN: 9780486235424
  • Category: Mathematics
  • Page: 174
  • View: 4597
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This classic study probes the geometric interrelationships between art and life in discussions ranging from dissertations by Plato, Pythagoras, and Archimedes to examples of modern architecture and art. Other topics include the Golden Section, geometrical shapes on the plane, geometrical shapes in space, crystal lattices, and other fascinating subjects. 80 plates and 64 figures.