The M Bius Strip Topology
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The M Bius Strip Topology
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Author : Klaus Möbius
language : en
Publisher: CRC Press
Release Date : 2022-11-30
The M Bius Strip Topology written by Klaus Möbius and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-30 with Science categories.
In the 19th century, pure mathematics research reached a climax in Germany, and Carl Friedrich Gauss (1777–1855) was an epochal example. August Ferdinand Möbius (1790–1868) was his doctoral student whose work was profoundly influenced by him. In the 18th century, it had been mostly the French school of applied mathematics that enabled the rapid developments of science and technology in Europe. How could this shift happen? It can be argued that the major reasons were the devastating consequences of the Napoleonic Wars in Central Europe, leading to the total defeat of Prussia in 1806. Immediately following, far-reaching reforms of the entire state system were carried out in Prussia and other German states, also affecting the educational system. It now guaranteed freedom of university teaching and research. This attracted many creative people with new ideas enabling the “golden age” of pure mathematics and fundamental theory in physical sciences. Möbius’ legacy reaches far into today’s sciences, arts, and architecture. The famous one-sided Möbius strip is a paradigmatic example of the ongoing fascination with mathematical topology. This is the first book to present numerous detailed case studies on Möbius topology in science and the humanities. It is written for those who believe in the power of ideas in our culture, experts and laymen alike.
Experiments In Topology
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Author : Stephen Barr
language : en
Publisher: Courier Corporation
Release Date : 2012-12-04
Experiments In Topology written by Stephen Barr and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-04 with Mathematics categories.
Classic, lively explanation of one of the byways of mathematics. Klein bottles, Moebius strips, projective planes, map coloring, problem of the Koenigsberg bridges, much more, described with clarity and wit.
Topology
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Author : Richard Earl
language : en
Publisher: Oxford University Press, USA
Release Date : 2020-01-11
Topology written by Richard Earl and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-11 with MATHEMATICS categories.
How is a subway map different from other maps? What makes a knot knotted? What makes the M�bius strip one-sided? These are questions of topology, the mathematical study of properties preserved by twisting or stretching objects. In the 20th century topology became as broad and fundamental as algebra and geometry, with important implications for science, especially physics. In this Very Short Introduction Richard Earl gives a sense of the more visual elements of topology (looking at surfaces) as well as covering the formal definition of continuity. Considering some of the eye-opening examples that led mathematicians to recognize a need for studying topology, he pays homage to the historical people, problems, and surprises that have propelled the growth of this field. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.
The M Bius Strip
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Author : Clifford A. Pickover
language : en
Publisher: Basic Books
Release Date : 2007-01-09
The M Bius Strip written by Clifford A. Pickover and has been published by Basic Books this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-01-09 with Science categories.
The road that leads from the Möbius strip — a common-sense-defying continuous loop with only one side and one edge, made famous by the illustrations of M.C. Escher — goes to some of the strangest spots imaginable. It takes us to where the purely intellectual enters our world: where our senses, overloaded with grocery bills, the price of gas, and what to eat for lunch, are expected to absorb really bizarre ideas. And no better guide to this weird universe exists than the brilliant thinker Clifford A. Pickover, the 21st century's answer to Buckminster Fuller. From molecules and metal sculptures to postage stamps, architectural structures, and models of the universe, The Möbius Strip gives readers a glimpse of new ways of thinking and other worlds as Pickover reaches across cultures and peers beyond our ordinary reality. Lavishly illustrated, this is an infinite fountain of wondrous forms that can be used to help explain how mathematics has permeated every field of scientific endeavor, such as the colors of a sunset or the architecture of our brains; how it helps us build supersonic aircraft and roller coasters, simulate the flow of Earth's natural resources, explore subatomic quantum realities, and depict faraway galaxies.
Algebraic Topology An Intuitive Approach
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Author : Hajime Satō
language : en
Publisher: American Mathematical Soc.
Release Date : 1999
Algebraic Topology An Intuitive Approach written by Hajime Satō and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.
The single most difficult thing one faces when one begins to learn a new branch of mathematics is to get a feel for the mathematical sense of the subject. The purpose of this book is to help the aspiring reader acquire this essential common sense about algebraic topology in a short period of time. To this end, Sato leads the reader through simple but meaningful examples in concrete terms. Moreover, results are not discussed in their greatest possible generality, but in terms of the simplest and most essential cases. In response to suggestions from readers of the original edition of this book, Sato has added an appendix of useful definitions and results on sets, general topology, groups and such. He has also provided references. Topics covered include fundamental notions such as homeomorphisms, homotopy equivalence, fundamental groups and higher homotopy groups, homology and cohomology, fiber bundles, spectral sequences and characteristic classes. Objects and examples considered in the text include the torus, the Möbius strip, the Klein bottle, closed surfaces, cell complexes and vector bundles.
The M Bius Strip
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Author : Clifford A. Pickover
language : en
Publisher: Basic Books
Release Date : 2006
The M Bius Strip written by Clifford A. Pickover and has been published by Basic Books this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Science categories.
An analysis of the one-sided and one-edged shape made famous by the illustrations of M.C. Escher, written by an award-winning IBM researcher, traces the Mbius strip's history from the mid-1800s to its present role in mathematics, science, engineering, and other disciplines.
Geometry And Topology
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Author : Miles Reid
language : en
Publisher: Cambridge University Press
Release Date : 2005-11-10
Geometry And Topology written by Miles Reid and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-11-10 with Mathematics categories.
Geometry aims to describe the world around us. It is central to many branches of mathematics and physics, and offers a whole range of views on the universe. This is an introduction to the ideas of geometry and includes generous helpings of simple explanations and examples. The book is based on many years teaching experience so is thoroughly class-tested, and as prerequisites are minimal, it is suited to newcomers to the subject. There are plenty of illustrations; chapters end with a collection of exercises, and solutions are available for teachers.
Basic Topology
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Author : M.A. Armstrong
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-09
Basic Topology written by M.A. Armstrong and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-09 with Mathematics categories.
In this broad introduction to topology, the author searches for topological invariants of spaces, together with techniques for their calculating. Students with knowledge of real analysis, elementary group theory, and linear algebra will quickly become familiar with a wide variety of techniques and applications involving point-set, geometric, and algebraic topology. Over 139 illustrations and more than 350 problems of various difficulties help students gain a thorough understanding of the subject.
Topology For Physicists
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Author : Albert S. Schwarz
language : en
Publisher: Springer Science & Business Media
Release Date : 1996-07-16
Topology For Physicists written by Albert S. Schwarz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-07-16 with Mathematics categories.
In recent years topology has firmly established itself as an important part of the physicist's mathematical arsenal. Topology has profound relevance to quantum field theory-for example, topological nontrivial solutions of the classical equa tions of motion (solitons and instantons) allow the physicist to leave the frame work of perturbation theory. The significance of topology has increased even further with the development of string theory, which uses very sharp topologi cal methods-both in the study of strings, and in the pursuit of the transition to four-dimensional field theories by means of spontaneous compactification. Im portant applications of topology also occur in other areas of physics: the study of defects in condensed media, of singularities in the excitation spectrum of crystals, of the quantum Hall effect, and so on. Nowadays, a working knowledge of the basic concepts of topology is essential to quantum field theorists; there is no doubt that tomorrow this will also be true for specialists in many other areas of theoretical physics. The amount of topological information used in the physics literature is very large. Most common is homotopy theory. But other subjects also play an important role: homology theory, fibration theory (and characteristic classes in particular), and also branches of mathematics that are not directly a part of topology, but which use topological methods in an essential way: for example, the theory of indices of elliptic operators and the theory of complex manifolds.
A Ludic Journey Into Geometric Topology
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Author : Ton Marar
language : en
Publisher: Springer Nature
Release Date : 2022-09-01
A Ludic Journey Into Geometric Topology written by Ton Marar and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-01 with Mathematics categories.
This book draws on elements from everyday life, architecture, and the arts to provide the reader with elementary notions of geometric topology. Pac Man, subway maps, and architectural blueprints are the starting point for exploring how knowledge about geometry and, more specifically, topology has been consolidated over time, offering a learning journey that is both dense and enjoyable. The text begins with a discussion of mathematical models, moving on to Platonic and Keplerian theories that explain the Cosmos. Geometry from Felix Klein's point of view is then presented, paving the way to an introduction to topology. The final chapters present the concepts of closed, orientable, and non-orientable surfaces, as well as hypersurface models. Adopting a style that is both rigorous and accessible, this book will appeal to a broad audience, from curious students and researchers in various areas of knowledge to everyone who feels instigated by the power of mathematics in representing our world - and beyond.