Space Through The Ages The Evolutionof Geometrical Ideas From Pythagoras To Hilbert And Einstein
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Space Through The Ages
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Author : Cornelius Lanczos
language : en
Publisher:
Release Date : 1970
Space Through The Ages written by Cornelius Lanczos and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with Mathematics categories.
Space Through The Ages
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Author : Cornelius Lanczos
language : en
Publisher:
Release Date : 1970
Space Through The Ages written by Cornelius Lanczos and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with categories.
Space Through The Ages The Evolutionof Geometrical Ideas From Pythagoras To Hilbert And Einstein
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Author : C. Lanczos
language : en
Publisher:
Release Date :
Space Through The Ages The Evolutionof Geometrical Ideas From Pythagoras To Hilbert And Einstein written by C. Lanczos and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Giordano Bruno And The Geometry Of Language
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Author : Arielle Saiber
language : en
Publisher: Routledge
Release Date : 2017-03-02
Giordano Bruno And The Geometry Of Language written by Arielle Saiber and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-02 with Literary Criticism categories.
Giordano Bruno and the Geometry of Language brings to the fore a sixteenth-century philosopher's role in early modern Europe as a bridge between science and literature, or more specifically, between the spatial paradigm of geometry and that of language. Arielle Saiber examines how, to invite what Bruno believed to be an infinite universe-its qualities and vicissitudes-into the world of language, Bruno forged a system of 'figurative' vocabularies: number, form, space, and word. This verbal and symbolic system in which geometric figures are seen to underlie rhetorical figures, is what Saiber calls 'geometric rhetoric.' Through analysis of Bruno's writings, Saiber shows how Bruno's writing necessitates a crafting of space, and is, in essence, a lexicon of spatial concepts. This study constitutes an original contribution both to scholarship on Bruno and to the fields of early modern scientific and literary studies. It also addresses the broader question of what role geometry has in the formation of any language and literature of any place and time.
The Popularization Of Mathematics
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Author : A. G. Howson
language : en
Publisher: Cambridge University Press
Release Date : 1990-11-22
The Popularization Of Mathematics written by A. G. Howson 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 1990-11-22 with Mathematics categories.
The papers arising from the ICMI study seminar on the popularization of mathematics held at the University of Leeds, UK, 17-22 September 1989.
Galileo Unbound
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Author : David D. Nolte
language : en
Publisher: Oxford University Press
Release Date : 2018-07-12
Galileo Unbound written by David D. Nolte and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-12 with Science categories.
Galileo Unbound traces the journey that brought us from Galileo's law of free fall to today's geneticists measuring evolutionary drift, entangled quantum particles moving among many worlds, and our lives as trajectories traversing a health space with thousands of dimensions. Remarkably, common themes persist that predict the evolution of species as readily as the orbits of planets or the collapse of stars into black holes. This book tells the history of spaces of expanding dimension and increasing abstraction and how they continue today to give new insight into the physics of complex systems. Galileo published the first modern law of motion, the Law of Fall, that was ideal and simple, laying the foundation upon which Newton built the first theory of dynamics. Early in the twentieth century, geometry became the cause of motion rather than the result when Einstein envisioned the fabric of space-time warped by mass and energy, forcing light rays to bend past the Sun. Possibly more radical was Feynman's dilemma of quantum particles taking all paths at once — setting the stage for the modern fields of quantum field theory and quantum computing. Yet as concepts of motion have evolved, one thing has remained constant, the need to track ever more complex changes and to capture their essence, to find patterns in the chaos as we try to predict and control our world.
Analytic Hyperbolic Geometry
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Author : Abraham A. Ungar
language : en
Publisher: World Scientific
Release Date : 2005
Analytic Hyperbolic Geometry written by Abraham A. Ungar and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
This is the first book on analytic hyperbolic geometry, fully analogous to analytic Euclidean geometry. Analytic hyperbolic geometry regulates relativistic mechanics just as analytic Euclidean geometry regulates classical mechanics. The book presents a novel gyrovector space approach to analytic hyperbolic geometry, fully analogous to the well-known vector space approach to Euclidean geometry. A gyrovector is a hyperbolic vector. Gyrovectors are equivalence classes of directed gyrosegments that add according to the gyroparallelogram law just as vectors are equivalence classes of directed segments that add according to the parallelogram law. In the resulting ?gyrolanguage? of the book one attaches the prefix ?gyro? to a classical term to mean the analogous term in hyperbolic geometry. The prefix stems from Thomas gyration, which is the mathematical abstraction of the relativistic effect known as Thomas precession. Gyrolanguage turns out to be the language one needs to articulate novel analogies that the classical and the modern in this book share.The scope of analytic hyperbolic geometry that the book presents is cross-disciplinary, involving nonassociative algebra, geometry and physics. As such, it is naturally compatible with the special theory of relativity and, particularly, with the nonassociativity of Einstein velocity addition law. Along with analogies with classical results that the book emphasizes, there are remarkable disanalogies as well. Thus, for instance, unlike Euclidean triangles, the sides of a hyperbolic triangle are uniquely determined by its hyperbolic angles. Elegant formulas for calculating the hyperbolic side-lengths of a hyperbolic triangle in terms of its hyperbolic angles are presented in the book.The book begins with the definition of gyrogroups, which is fully analogous to the definition of groups. Gyrogroups, both gyrocommutative and non-gyrocommutative, abound in group theory. Surprisingly, the seemingly structureless Einstein velocity addition of special relativity turns out to be a gyrocommutative gyrogroup operation. Introducing scalar multiplication, some gyrocommutative gyrogroups of gyrovectors become gyrovector spaces. The latter, in turn, form the setting for analytic hyperbolic geometry just as vector spaces form the setting for analytic Euclidean geometry. By hybrid techniques of differential geometry and gyrovector spaces, it is shown that Einstein (Mbius) gyrovector spaces form the setting for Beltrami-Klein (Poincar) ball models of hyperbolic geometry. Finally, novel applications of Mbius gyrovector spaces in quantum computation, and of Einstein gyrovector spaces in special relativity, are presented.
The Fifth Postulate
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Author : Jason Socrates Bardi
language : en
Publisher: Turner Publishing Company
Release Date : 2008-12-01
The Fifth Postulate written by Jason Socrates Bardi and has been published by Turner Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-12-01 with Mathematics categories.
The great discovery that no one wanted to make It's the dawn of the Industrial Revolution, and Euclidean geometry has been profoundly influential for centuries. One mystery remains, however: Euclid's fifth postulate has eluded for two thousand years all attempts to prove it. What happens when three nineteenth-century mathematicians realize that there is no way to prove the fifth postulate and that it ought to be discarded—along with everything they'd come to know about geometry? Jason Socrates Bardi shares the dramatic story of the moment when the tangible and easily understood world we live in gave way to the strange, mind-blowing world of relativity, curved space-time, and more. "Jason Socrates Bardi tells the story of the discovery of non-Euclidian geometry—one of the greatest intellectual advances of all time—with tremendous clarity and verve. I loved this book." —John Horgan, author, The End of Science and Rational Mysticism "An accessible and engrossing blend of micro-biography, history and mathematics, woven together to reveal a blockbuster discovery." —David Wolman, author of Righting the Mother Tongue and A Left-Hand Turn around the World
Thinking Things Through
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Author : Clark N. Glymour
language : en
Publisher: MIT Press
Release Date : 1997
Thinking Things Through written by Clark N. Glymour and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Philosophy categories.
Thinking Things Through provides a broad, historical, and rigorous introduction to the logical tradition in philosophy and to its contemporary significance. The presentation is centered around three of the most fruitful issues in Western thought: What are proofs, and why do they provide knowledge? How can experience be used to gain knowledge or to alter beliefs in a rational way? What is the nature of mind and of mental events and mental states? In a clear and lively style, Glymour describes these key philosophical problems and traces attempts to solve them, from ancient Greece to the present. Thinking Things Through reveals the philosophical sources of modern work in logic, the theory of computation, Bayesian statistics, cognitive psychology, and artificial intelligence, and it connects these subjects with contemporary problems in epistemology and metaphysics. The text is full of examples and problems, and an instructor's manual is available.Clark Glymour is Alumni Professor of Philosophy at Carnegie-Mellon University and Adjunct Professor of History and Philosophy of Science at the University of Pittsburgh.
Thinking Things Through Second Edition
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Author : Clark Glymour
language : en
Publisher: MIT Press
Release Date : 2015-04-10
Thinking Things Through Second Edition written by Clark Glymour and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-04-10 with Philosophy categories.
The second edition of a unique introductory text, offering an account of the logical tradition in philosophy and its influence on contemporary scientific disciplines. Thinking Things Through offers a broad, historical, and rigorous introduction to the logical tradition in philosophy and its contemporary significance. It is unique among introductory philosophy texts in that it considers both the historical development and modern fruition of a few central questions. It traces the influence of philosophical ideas and arguments on modern logic, statistics, decision theory, computer science, cognitive science, and public policy. The text offers an account of the history of speculation and argument, and the development of theories of deductive and probabilistic reasoning. It considers whether and how new knowledge of the world is possible at all, investigates rational decision making and causality, explores the nature of mind, and considers ethical theories. Suggestions for reading, both historical and contemporary, accompany most chapters. This second edition includes four new chapters, on decision theory and causal relations, moral and political theories, “moral tools” such as game theory and voting theory, and ethical theories and their relation to real-world issues. Examples have been updated throughout, and some new material has been added. It is suitable for use in advanced undergraduate and beginning graduate classes in philosophy, and as an ancillary text for students in computer science and the natural sciences.