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Book Synopsis The Pythagorean Theorem by : Eli Maor
Download or read book The Pythagorean Theorem written by Eli Maor and published by Princeton University Press. This book was released on 2019-11-19 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: Frontmatter --Contents --List of Color Plates --Preface --Prologue: Cambridge, England, 1993 --1. Mesopotamia, 1800 BCE --Sidebar 1: Did the Egyptians Know It? --2. Pythagoras --3. Euclid's Elements --Sidebar 2: The Pythagorean Theorem in Art, Poetry, and Prose --4. Archimedes --5. Translators and Commentators, 500-1500 CE --6. François Viète Makes History --7. From the Infinite to the Infinitesimal --Sidebar 3: A Remarkable Formula by Euler --8. 371 Proofs, and Then Some --Sidebar 4: The Folding Bag --Sidebar 5: Einstein Meets Pythagoras --Sidebar 6: A Most Unusual Proof --9. A Theme and Variations --Sidebar 7: A Pythagorean Curiosity --Sidebar 8: A Case of Overuse --10. Strange Coordinates --11. Notation, Notation, Notation --12. From Flat Space to Curved Spacetime --Sidebar 9: A Case of Misuse --13. Prelude to Relativity --14. From Bern to Berlin, 1905-1915 --Sidebar 10: Four Pythagorean Brainteasers --15. But Is It Universal? --16. Afterthoughts --Epilogue: Samos, 2005 --Appendixes --Chronology --Bibliography --Illustrations Credits --Index.
Book Synopsis Math with Bad Drawings by : Ben Orlin
Download or read book Math with Bad Drawings written by Ben Orlin and published by Black Dog & Leventhal. This book was released on 2018-09-18 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt: A hilarious reeducation in mathematics-full of joy, jokes, and stick figures-that sheds light on the countless practical and wonderful ways that math structures and shapes our world. In Math With Bad Drawings, Ben Orlin reveals to us what math actually is; its myriad uses, its strange symbols, and the wild leaps of logic and faith that define the usually impenetrable work of the mathematician. Truth and knowledge come in multiple forms: colorful drawings, encouraging jokes, and the stories and insights of an empathetic teacher who believes that math should belong to everyone. Orlin shows us how to think like a mathematician by teaching us a brand-new game of tic-tac-toe, how to understand an economic crises by rolling a pair of dice, and the mathematical headache that ensues when attempting to build a spherical Death Star. Every discussion in the book is illustrated with Orlin's trademark "bad drawings," which convey his message and insights with perfect pitch and clarity. With 24 chapters covering topics from the electoral college to human genetics to the reasons not to trust statistics, Math with Bad Drawings is a life-changing book for the math-estranged and math-enamored alike.
Book Synopsis The Metaphysics of the Pythagorean Theorem by : Robert Hahn
Download or read book The Metaphysics of the Pythagorean Theorem written by Robert Hahn and published by State University of New York Press. This book was released on 2017-05-01 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Hidden Harmonies written by Ellen Kaplan and published by Bloomsbury Publishing USA. This book was released on 2011-01-04 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis The Pythagorean Theorem by : Merle A. Barlow
Download or read book The Pythagorean Theorem written by Merle A. Barlow and published by WestBow Press. This book was released on 2016-02-05 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Euclid's Elements written by Euclid and published by . This book was released on 2002 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The book includes introductions, terminology and biographical notes, bibliography, and an index and glossary" --from book jacket.
Book Synopsis The Pythagorean Theorem by : Alfred S. Posamentier
Download or read book The Pythagorean Theorem written by Alfred S. Posamentier and published by Prometheus Books. This book was released on 2010-06-22 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 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, a veteran math educator 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, the author 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. The author''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 Synopsis The Pythagorean Proposition by : Elisha Scott Loomis
Download or read book The Pythagorean Proposition written by Elisha Scott Loomis and published by . This book was released on 1927 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Pythagoras written by Christoph Riedweg and published by Cornell University Press. This book was released on 2012-03-27 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Pythagoras & His Theorem by : Paul Strathern
Download or read book Pythagoras & His Theorem written by Paul Strathern and published by Vintage. This book was released on 1997 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Pythagoras' Revenge by : Arturo Sangalli
Download or read book Pythagoras' Revenge written by Arturo Sangalli and published by Princeton University Press. This book was released on 2009-04-20 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: The celebrated mathematician and philosopher Pythagoras left no writings. But what if he had and the manuscript was never found? Where would it be located? And what information would it reveal? These questions are the inspiration for the mathematical mystery novel Pythagoras' Revenge. Suspenseful and instructive, Pythagoras' Revenge weaves fact, fiction, mathematics, computer science, and ancient history into a surprising and sophisticated thriller. The intrigue begins when Jule Davidson, a young American mathematician who trolls the internet for difficult math riddles and stumbles upon a neo-Pythagorean sect searching for the promised reincarnation of Pythagoras. Across the ocean, Elmer Galway, a professor of classical history at Oxford, discovers an Arabic manuscript hinting at the existence of an ancient scroll--possibly left by Pythagoras himself. Unknown to one another, Jule and Elmer each have information that the other requires and, as they race to solve the philosophical and mathematical puzzles set before them, their paths ultimately collide. Set in 1998 with flashbacks to classical Greece, Pythagoras' Revenge investigates the confrontation between opposing views of mathematics and reality, and explores ideas from both early and cutting-edge mathematics. From academic Oxford to suburban Chicago and historic Rome, Pythagoras' Revenge is a sophisticated thriller that will grip readers from beginning to surprising end.
Book Synopsis Connecting Mathematics and Mathematics Education by : Erich Christian Wittmann
Download or read book Connecting Mathematics and Mathematics Education written by Erich Christian Wittmann and published by Springer Nature. This book was released on 2020-12-09 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access book features a selection of articles written by Erich Ch. Wittmann between 1984 to 2019, which shows how the “design science conception” has been continuously developed over a number of decades. The articles not only describe this conception in general terms, but also demonstrate various substantial learning environments that serve as typical examples. In terms of teacher education, the book provides clear information on how to combine (well-understood) mathematics and methods courses to benefit of teachers. The role of mathematics in mathematics education is often explicitly and implicitly reduced to the delivery of subject matter that then has to be selected and made palpable for students using methods imported from psychology, sociology, educational research and related disciplines. While these fields have made significant contributions to mathematics education in recent decades, it cannot be ignored that mathematics itself, if well understood, provides essential knowledge for teaching mathematics beyond the pure delivery of subject matter. For this purpose, mathematics has to be conceived of as an organism that is deeply rooted in elementary operations of the human mind, which can be seamlessly developed to higher and higher levels so that the full richness of problems of various degrees of difficulty, and different means of representation, problem-solving strategies, and forms of proof can be used in ways that are appropriate for the respective level. This view of mathematics is essential for designing learning environments and curricula, for conducting empirical studies on truly mathematical processes and also for implementing the findings of mathematics education in teacher education, where it is crucial to take systemic constraints into account.
Book Synopsis Common Core Math For Parents For Dummies with Videos Online by : Christopher Danielson
Download or read book Common Core Math For Parents For Dummies with Videos Online written by Christopher Danielson and published by John Wiley & Sons. This book was released on 2015-04-06 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: Help your child succeed with a better understanding of Common Core Math Common Core Math For Parents For Dummies is packed with tools and information to help you promote your child's success in math. The grade-by-grade walk-through brings you up to speed on what your child is learning, and the sample problems and video lessons help you become more involved as you study together. You'll learn how to effectively collaborate with teachers and keep tabs on your child's progress, so minor missteps can be corrected quickly, before your child falls behind. The Common Core was designed to improve college- and career-readiness, and to prepare U.S. students to be more competitive on an international stage when it's time to enter the workforce. This guide shows you how the standards were created, and how they've evolved over time to help ensure your child's future success. The Common Core Math Standards prepare students to do real math in the real world. Many new teaching methods are very different from the way most parents learned math, leading to frustration and confusion as parents find themselves unable to help with homework or explain difficult concepts. This book cuts the confusion and shows you everything you need to know to help your child succeed in math. Understand the key concepts being taught in your child's grade Utilize the homework tools that help you help your child Communicate more effectively with your child's teacher Guide your child through sample problems to foster understanding The Common Core was designed to ensure that every student, regardless of location or background, receives the education they need. Math skills are critical to real-world success, and the new standards reflect that reality in scope and rigorousness. Common Core Math For Parents For Dummies helps you help your child succeed.
Book Synopsis The Art of Problem Solving, Volume 1 by : Sandor Lehoczky
Download or read book The Art of Problem Solving, Volume 1 written by Sandor Lehoczky and published by Mitchell Beazley. This book was released on 2006 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: " ... offer[s] a challenging exploration of problem solving mathematics and preparation for programs such as MATHCOUNTS and the American Mathematics Competition."--Back cover
Book Synopsis From Pythagoras to Einstein by : Kurt Otto Friedrichs
Download or read book From Pythagoras to Einstein written by Kurt Otto Friedrichs and published by . This book was released on 1965 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Prealgebra 2e written by Lynn Marecek and published by . This book was released on 2020-03-11 with total page 1148 pages. Available in PDF, EPUB and Kindle. Book excerpt: The images in this book are in color. For a less-expensive grayscale paperback version, see ISBN 9781680923254. Prealgebra 2e is designed to meet scope and sequence requirements for a one-semester prealgebra course. The text introduces the fundamental concepts of algebra while addressing the needs of students with diverse backgrounds and learning styles. Each topic builds upon previously developed material to demonstrate the cohesiveness and structure of mathematics. Students who are taking basic mathematics and prealgebra classes in college present a unique set of challenges. Many students in these classes have been unsuccessful in their prior math classes. They may think they know some math, but their core knowledge is full of holes. Furthermore, these students need to learn much more than the course content. They need to learn study skills, time management, and how to deal with math anxiety. Some students lack basic reading and arithmetic skills. The organization of Prealgebra makes it easy to adapt the book to suit a variety of course syllabi.
Book Synopsis The Pythagorean Theorem by : Eli Maor
Download or read book The Pythagorean Theorem written by Eli Maor and published by Princeton University Press. This book was released on 2019-11-19 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.