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The Art Of The Infinite

Author: Robert Kaplan
Publisher: Bloomsbury Publishing USA
ISBN: 160819888X
Size: 52.80 MB
Format: PDF
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A witty, conversational, and accessible tour of math's profoundest mysteries. Mathematical symbols, for mathematicians, store worlds of meaning, leap continents and centuries. But we need not master symbols to grasp the magnificent abstractions they represent, and to which all art aspires. Through language, anyone can come to delight in the works of mathematical art, which are among our kind's greatest glories. Taking the concept of infinity, in its countless guises, as a starting point and a helpful touchstone, the founders of Harvard's pioneering Math Circle program Robert and Ellen Kaplan guide us through the “Republic of Numbers,” where we meet both its upstanding citizens and its more shadowy dwellers, explore realms where only the imagination can go, and grapple with math's most profound uncertainties, including the question of truth itself-do we discover mathematical principles, or invent them?

The Art Of The Infinite

Author: Robert Kaplan
Publisher: Oxford University Press, USA
ISBN: 9780195147438
Size: 45.97 MB
Format: PDF
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Traces the development of mathematical thinking and describes the characteristics of the "republic of numbers" in terms of humankind's fascination with, and growing knowledge of, infinity.

Stars On The Earth

Author: Richard Leviton
Publisher: iUniverse
ISBN: 0595851452
Size: 21.93 MB
Format: PDF, ePub, Docs
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Discover the wonderful secret the Earth holds for us-that the stars of the galaxy live on our planet. Holograms of high-magnitude stars over holy mountains. Physical travel to other planets through stargates on the Earth's surface. Near instantaneous transportation across the planet through quick-way portals. Outrageous science fiction or sober geomantic fact? Earth Mysteries researcher Richard Leviton takes you on a wild tour of three geomantic features of our planet and reveals that what science fiction has dreamed the Earth in fact offers us. Stars on the Earth combines scholarship, clairvoyance, and field experience with the latest discoveries of geology and astrophysics and the timeless insights of the world's myths to open the planetary door to the stars. It's all part of the Earth's unsuspected but staggeringly rich endowment as a designer planet. Our planet was precisely designed and implemented for us, and it's equipped with a visionary geography that mirrors features of the galaxy and Heavens. Why are so many of the Earth's mountains said to be holy, producing visions and encounters with the "gods?" They all have canopies of light called domes, each transmitting the presence of a galactic star. What is the geomantic origin of the Bermuda Triangle? Two dysfunctional stargates. If working properly, they and the Earth's other two million stargates could transport us rapidly to other planets. Is there a way to travel quickly across the planet without using cars, airplanes, boats, or trains? Yes, and it's called a traversable wormhole, and the Earth has thousands of them awaiting our discovery and use. Come join the tour of a planet you've never seen before: our own star-infused Earth.

Euclid In The Rainforest

Author: Joseph Mazur
Publisher: Dutton Juvenile
Size: 32.11 MB
Format: PDF
View: 1991
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"How does one summarize a book about rainforest adventures, probability, the Cafè Luxembourg, Euclid, and prime numbers? This is an absolutely delightful book, full of insight, suffused with gentle humor-a picaresque novel of mathematics. What do we mean by proof and persuasion in the most symbolic of fields, Mazur asks, and responds with stories that effortlessly guide us to the heartland of reason. This is a fabulous book, in all senses, from beginning to end." Peter Galison, Mallinckrodt Professor of the History of Science and of Physics, Harvard University, author of Einstein''s Clocks, Poincairè''s Maps "Euclid in the Rainforest is beautifully written and packed with insights into how mathemeticians convince themselves they are right. Mazur is a talented teacher who knows his subject inside out, and his delightful stories take his readers to the heart of mathematics-logic and proof. This original and charming book is accessible to anyone, and deserves major success." Ian Stewart, Professor of Mathematics, University of Warwick, author of Math Hysteria, and Flatterland "My chief regret after more than forty years of trying to teach concepts in mathematics and statistics to biology students is that I did not have Mazur''s book available. It should be assigned reading for all undergraduates in science." R. C. Lewontin, Alexander Agassiz Professor, Harvard University "Mazur is an excellent storyteller. Euclid in the Rainforest is a warm and creative masterpiece that reveals the spirit of mathematics." Tadatoshi Akiba, Mayor of the City of Hiroshima "Mazur has a wonderfully engaging writing style, and a marvelous feel for the interface between the physical world as we experience it every day and the mathematical one. This book is a pleasure to read." Joseph Harris, Chair, Department of Mathematics, Harvard University "Mazur''s Euclid in the Rainforest is written with warmth and a lifetime''s attachment to the things of this world and the forms of the world it manifests. Here are the pleasures of sitting with the author, as a young man, learning his craft in a Greenwich Village cafe from an old professor; and later on, teaching the craft in turn to an eight-year-old. Inspiring stuff. By overhearing such conversations as these, the reader too is led to savor the beauties of mathematics." Robert and Ellen Kaplan, co-founders of The Math Circle, and co-authors of The Art of the Infinite: The Pleasures of Mathematics "Delightful, full of insight, suffused with gentle_humor-a picaresque novel of mathematics." Peter Galison How do we know that something is true? How do we know that things really are what they seem? Many people think math and science are the ultimate authorities on reality. Math defines abstract, universal truths; scientific truths are established by experiments in the real world-but underlying both kinds of knowledge is logic. In Euclid in the Rainforest, Joseph Mazur examines the three types of logic that are the basis of our knowledge about the world we live in: the classical logic of the Ancient Greeks, the weird logic of infinity, and the everyday logic of plausible reasoning that guides all science today. Through tales of great moments in the history of math and science, stories of students making discoveries in the classroom, and his own quirky adventures in the Greek Islands, New York, and the jungles of South America, Mazur illuminates how we uncover truth in the tangled web of our experiences-and convince ourselves that we are right. Euclid took the incipient logic of his time to new heights with his magnificent geometry, the whole edifice of which is built on just five assumptions. That logic rigorously defined proof, cleverly avoiding problems with infinity that were introduced when the Pythagoreans discovered that the diagonal of a square could not be measured and Zeno of Elea used infinity to argue that motion is logically impossible. It would be almost two millenia, though, before a good understanding of the logic infinity emerged and made all kinds of technology possible. Plausible reasoning-which is based on the math of probability- lets us assess the general conclusions we derive from specific cases in scientific studies. It gives us the confidence to believe that a conclusion reached today will be true tomorrow, ultimately driving scientific, and human, progress. In lucid, ebullient language, Mazur, a professor of mathematics for over thirty years, makes the fundamentals of the three fundamental types of logic widely accessible for the first time. Deeper questions at the heart of the process of discovery are laid bare: What does it mean to believe a proof? Where does the finite end and the infinite begin? How can we be sure that the statements we make about the material world are accurate? Exposing the surprising roles of intuition, belief and persuasion in logic and math, Mazur tells a real-life detective story that has been going on for millenia: the pursuit of ultimate truth about our world, our universe, and ourselves. © Copyright Pearson Education. All rights reserved.

Out Of The Labyrinth

Author: Robert Kaplan
Publisher: Bloomsbury Publishing USA
ISBN: 1608198898
Size: 51.63 MB
Format: PDF, Mobi
View: 311
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“In this sparkling narrative, mathematics is indeed set free.” -Michael Shermer, author of The Believing Brain In classrooms around the world, Robert and Ellen Kaplan's pioneering Math Circle program, begun at Harvard, has introduced students ages six to sixty to the pleasures of mathematics, exploring topics that range from Roman numerals to quantum mechanics. In Out of the Labyrinth, the Kaplans reveal the secrets of their highly successful approach, which embraces the exhilarating joy of math's “accessible mysteries.” Stocked with puzzles, colorful anecdotes, and insights from the authors' own teaching experience, Out of the Labyrinth is both an engaging and practical guide for parents and educators, and a treasure chest of mathematical discoveries. For any reader who has felt the excitement of mathematical discovery-or tried to convey it to someone else-this volume will be a delightful and valued companion.

Mathematical Sorcery

Author: Calvin Clawson
Publisher: Hachette UK
ISBN: 0786731206
Size: 53.43 MB
Format: PDF, Docs
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The secret of constellations, the enigma of the golden mean, and the brilliance of a proof-these are just some of the wonders Clawson explores with unbridled delight in this recreational math book. Throughout the book he divulges the wisdom of the ancient Greeks, Sumerians, Babylonians, and Egyptians, whose stunning revelations still have deep meaning today.Transporting us beyond mere appreciation, Clawson urges us to tackle functions, tangents, and the concept of infinity. He helps us intuitively comprehend these and other building blocks of mathematics through explaining their discovery and uses. By accompanying him on his journey, we taste the fruit of knowledge that has eluded us until now.

Mathematics And Art

Author: Lynn Gamwell
Publisher: Princeton University Press
ISBN: 0691165289
Size: 18.28 MB
Format: PDF, Mobi
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This is a cultural history of mathematics and art, from antiquity to the present. Mathematicians and artists have long been on a quest to understand the physical world they see before them and the abstract objects they know by thought alone. Taking readers on a tour of the practice of mathematics and the philosophical ideas that drive the discipline, Lynn Gamwell points out the important ways mathematical concepts have been expressed by artists. Sumptuous illustrations of artworks and cogent math diagrams are featured in Gamwell’s comprehensive exploration. Gamwell begins by describing mathematics from antiquity to the Enlightenment, including Greek, Islamic, and Asian mathematics. Then focusing on modern culture, Gamwell traces mathematicians’ search for the foundations of their science, such as David Hilbert’s conception of mathematics as an arrangement of meaning-free signs, as well as artists’ search for the essence of their craft, such as Aleksandr Rodchenko’s monochrome paintings. She shows that self-reflection is inherent to the practice of both modern mathematics and art, and that this introspection points to a deep resonance between the two fields: Kurt Gödel posed questions about the nature of mathematics in the language of mathematics and Jasper Johns asked “What is art?” in the vocabulary of art. Throughout, Gamwell describes the personalities and cultural environments of a multitude of mathematicians and artists, from Gottlob Frege and Benoît Mandelbrot to Max Bill and Xu Bing. Mathematics and Art demonstrates how mathematical ideas are embodied in the visual arts and will enlighten all who are interested in the complex intellectual pursuits, personalities, and cultural settings that connect these vast disciplines.