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 : 42. 45 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.

Of The Pythagorean Theorem

Author : Asa Whitley
ISBN : 9781304839749
Genre :
File Size : 74. 31 MB
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The Metaphysics Of The Pythagorean Theorem

Author : Robert Hahn
ISBN : 9781438464916
Genre : Philosophy
File Size : 67. 60 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 Best Writing On Mathematics 2011

Author : Mircea Pitici
ISBN : 9781400839544
Genre : Mathematics
File Size : 24. 94 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.

The Joy Of X

Author : Steven Strogatz
ISBN : 9783036992693
Genre : Mathematics
File Size : 49. 52 MB
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Mathematik durchdringt den ganzen Kosmos. Das weiß jeder, doch nur die wenigsten verstehen die Zusammenhänge wirklich. Steven Strogatz nimmt uns bei der Hand und spaziert mit uns durch diese Welt der Weisheit, Klarheit und Eleganz. Als Reiseleiter geht er neue, erfrischende Wege, deutet auf Besonderheiten, schildert Hintergründe und erklärt die unsichtbaren Mechanismen. Wir erfahren unter anderem von dem Wunder des Zählens, der genialen Einfachheit der Algebra, dem ewigen Erbe Newtons, dem Tango mit Quadraten, der Zweisamkeit von Primzahlen und der Macht des Unendlichen. Mit all seiner Begeisterung, seinem Scharfblick und seinem leichtem Ton hat Steven Strogatz ein herrliches Buch für alle geschrieben, die ihr Verständnis von Mathematik auf eine neue Art vertiefen möchten.

Das Mathebuch

Author : Clifford A. Pickover
ISBN : 9089982809
Genre :
File Size : 49. 55 MB
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K Ein Gesp R F R Zahlen

Author : Barbara Oakley
ISBN : 9783864157813
Genre : Mathematics
File Size : 67. 92 MB
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Mathematik versteht man oder eben nicht. Der eine ist dafür natürlich begabt, dem anderen bleibt dieses Fach für immer ein Rätsel. Stimmt nicht, sagt nun Barbara Oakley und zeigt mit ihrem Buch, dass wirklich jeder ein Gespür für Zahlen hat. Mathematik braucht nämlich nicht nur analytisches Denken, sondern auch den kreativen Geist. Denn noch mehr als um Formeln geht es um die Freiheit, einen der vielen möglichen Lösungsansätze zu finden. Der Weg ist das Ziel. Und wie man zum richtigen Ergebnis kommt, ist eine Kunst, die man entwickeln, entdecken und in sich wecken kann. Die Autorin vermittelt eine Vielfalt an Techniken und Werkzeugen, die das Verständnis von Mathematik und Naturwissenschaft grundlegend verbessern. (K)ein Gespür für Zahlen nimmt Ihnen — vor allem wenn Sie sich in Schule, Uni oder Beruf mathematisch oder naturwissenschaftlich beweisen müssen — nicht nur die Grundangst, sondern stärkt Ihren Mut, Ihren mathematischen Fähigkeiten zu vertrauen. So macht Mathe Spaß!

Why Beauty Is Truth

Author : Ian Stewart
ISBN : 9780465008759
Genre : Science
File Size : 50. 88 MB
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At the heart of relativity theory, quantum mechanics, string theory, and much of modern cosmology lies one concept: symmetry. In Why Beauty Is Truth, world-famous mathematician Ian Stewart narrates the history of the emergence of this remarkable area of study. Stewart introduces us to such characters as the Renaissance Italian genius, rogue, scholar, and gambler Girolamo Cardano, who stole the modern method of solving cubic equations and published it in the first important book on algebra, and the young revolutionary Evariste Galois, who refashioned the whole of mathematics and founded the field of group theory only to die in a pointless duel over a woman before his work was published. Stewart also explores the strange numerology of real mathematics, in which particular numbers have unique and unpredictable properties related to symmetry. He shows how Wilhelm Killing discovered “Lie groups” with 14, 52, 78, 133, and 248 dimensions-groups whose very existence is a profound puzzle. Finally, Stewart describes the world beyond superstrings: the “octonionic” symmetries that may explain the very existence of the universe.

Denker Des Abendlandes

Author : Bertrand Russell
ISBN : 3868201270
Genre :
File Size : 53. 80 MB
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Ist Gott Ein Mathematiker

Author : Mario Livio
ISBN : 9783406616600
Genre : Mathematics
File Size : 24. 19 MB
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Von der Antike bis in unsere Tage haben sich Wissenschaftler und Philosophen darüber gewundert, dass eine so abstrakte Disziplin wie die Mathematik die Natur derart perfekt erklären kann. Sogar mehr als das: Mathematiker haben oft Voraussagen gemacht, etwa über die Existenz bestimmter Teilchen, die sich später als richtig erwiesen haben. Was ist es, das der Mathematik solch unglaubliche Macht verleiht? Oder, wie Einstein sich einst fragte: „Wie ist es möglich, dass die Mathematik, die doch ein von aller Erfahrung unabhängiges Produkt des menschlichen Denkens ist, auf die Gegenstände der Welt so vortrefflich passt?“ Werden mathematische Erkenntnisse also nicht erfunden, sondern entdeckt? Diese Fragestellung bildet den roten Faden, an dem der Astrophysiker Mario Livio mit großer Lebendigkeit durch die Geistesgeschichte des mathematischen und naturwissenschaftlichen Denkens führt. Zugleich wirft sein Buch einen frischen und unterhaltsamen Blick auf die Lebensgeschichte und die Erkenntnisse großer Denker wie Pythagoras, Platon, Newton und Einstein. „Eine lebendige und faszinierende Lektüre für ein breites Publikum“ – Nature

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