On The Hypotheses Which Lie At The Bases Of Geometry
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On The Hypotheses Which Lie At The Bases Of Geometry
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Author : Bernhard Riemann
language : en
Publisher: Birkhäuser
Release Date : 2016-04-19
On The Hypotheses Which Lie At The Bases Of Geometry written by Bernhard Riemann and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-19 with Mathematics categories.
This book presents William Clifford’s English translation of Bernhard Riemann’s classic text together with detailed mathematical, historical and philosophical commentary. The basic concepts and ideas, as well as their mathematical background, are provided, putting Riemann’s reasoning into the more general and systematic perspective achieved by later mathematicians and physicists (including Helmholtz, Ricci, Weyl, and Einstein) on the basis of his seminal ideas. Following a historical introduction that positions Riemann’s work in the context of his times, the history of the concept of space in philosophy, physics and mathematics is systematically presented. A subsequent chapter on the reception and influence of the text accompanies the reader from Riemann’s times to contemporary research. Not only mathematicians and historians of the mathematical sciences, but also readers from other disciplines or those with an interest in physics or philosophy will find this work both appealing and insightful.
Bernhard Riemann On The Hypotheses Which Lie At The Bases Of Geometry
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Author : Jürgen Jost
language : en
Publisher: Birkhäuser
Release Date : 2025-07-09
Bernhard Riemann On The Hypotheses Which Lie At The Bases Of Geometry written by Jürgen Jost and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-07-09 with Mathematics categories.
This book presents William Clifford’s English translation of Bernhard Riemann’s seminal text, accompanied by detailed mathematical, historical, and philosophical commentary. It explores Riemann’s revolutionary ideas on space, placing them within the broader framework developed by later thinkers such as Helmholtz, Ricci, Weyl, and Einstein. A historical introduction situates Riemann’s work in its 19th-century context, while subsequent chapters trace the evolution of the concept of space across philosophy, physics, and mathematics, and examine its enduring influence up to modern research. The second edition includes expanded mathematical commentary, a new section on metric geometry and machine learning, a systematic bibliography, and numerous updates throughout. Appealing to mathematicians, historians, and readers with an interest in physics or philosophy, this book provides a comprehensive perspective on Riemann’s groundbreaking contributions and their lasting impact.
Mathematical Papers
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Author : William Kingdon Clifford
language : en
Publisher:
Release Date : 1882
Mathematical Papers written by William Kingdon Clifford and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1882 with Mathematics categories.
The Development Of Peirce S Philosophy
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Author : Murray G. Murphey
language : en
Publisher: Hackett Publishing
Release Date : 1993-01-01
The Development Of Peirce S Philosophy written by Murray G. Murphey and has been published by Hackett Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-01-01 with Philosophy categories.
A reprint of the Harvard University Press edition of 1961. Includes a new preface and a new appendix with footnotes keyed to the manuscript classifications by Max Fisch.
Revolutions Of Geometry
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Author : Michael L. O'Leary
language : en
Publisher: John Wiley & Sons
Release Date : 2010-02-22
Revolutions Of Geometry written by Michael L. O'Leary and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-02-22 with Mathematics categories.
Guides readers through the development of geometry and basic proof writing using a historical approach to the topic In an effort to fully appreciate the logic and structure of geometric proofs, Revolutions of Geometry places proofs into the context of geometry's history, helping readers to understand that proof writing is crucial to the job of a mathematician. Written for students and educators of mathematics alike, the book guides readers through the rich history and influential works, from ancient times to the present, behind the development of geometry. As a result, readers are successfully equipped with the necessary logic to develop a full understanding of geometric theorems. Following a presentation of the geometry of ancient Egypt, Babylon, and China, the author addresses mathematical philosophy and logic within the context of works by Thales, Plato, and Aristotle. Next, the mathematics of the classical Greeks is discussed, incorporating the teachings of Pythagoras and his followers along with an overview of lower-level geometry using Euclid's Elements. Subsequent chapters explore the work of Archimedes, Viete's revolutionary contributions to algebra, Descartes' merging of algebra and geometry to solve the Pappus problem, and Desargues' development of projective geometry. The author also supplies an excursion into non-Euclidean geometry, including the three hypotheses of Saccheri and Lambert and the near simultaneous discoveries of Lobachevski and Bolyai. Finally, modern geometry is addressed within the study of manifolds and elliptic geometry inspired by Riemann's work, Poncelet's return to projective geometry, and Klein's use of group theory to characterize different geometries. The book promotes the belief that in order to learn how to write proofs, one needs to read finished proofs, studying both their logic and grammar. Each chapter features a concise introduction to the presented topic, and chapter sections conclude with exercises that are designed to reinforce the material and provide readers with ample practice in writing proofs. In addition, the overall presentation of topics in the book is in chronological order, helping readers appreciate the relevance of geometry within the historical development of mathematics. Well organized and clearly written, Revolutions of Geometry is a valuable book for courses on modern geometry and the history of mathematics at the upper-undergraduate level. It is also a valuable reference for educators in the field of mathematics.
Beyond Geometry
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Author : Peter Pesic
language : en
Publisher: Courier Corporation
Release Date : 2007-01-01
Beyond Geometry written by Peter Pesic and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-01-01 with Mathematics categories.
Eight essays trace seminal ideas about the foundations of geometry that led to the development of Einstein's general theory of relativity. This is the only English-language collection of these important papers, some of which are extremely hard to find. Contributors include Helmholtz, Klein, Clifford, Poincaré, and Cartan.
The Emergence Of The Fourth Dimension
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Author : Mark Blacklock
language : en
Publisher: Oxford University Press
Release Date : 2018-04-05
The Emergence Of The Fourth Dimension written by Mark Blacklock 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 2018-04-05 with Literary Criticism categories.
The Emergence of the Fourth Dimension describes the development and proliferation of the idea of higher dimensional space in the late nineteenth- and early twentieth-centuries. An idea from mathematics that was appropriated by occultist thought, it emerged in the fin de siècle as a staple of genre fiction and influenced a number of important Modernist writers and artists. Providing a context for thinking of space in dimensional terms, the volume describes an active interplay between self-fashioning disciplines and a key moment in the popularisation of science. It offers new research into spiritualism and the Theosophical Society and studies a series of curious hybrid texts. Examining works by Joseph Conrad, Ford Madox Ford, H.G. Wells, Henry James, H. P. Lovecraft, and others, the volume explores how new theories of the possibilities of time and space influenced fiction writers of the period, and how literature shaped, and was in turn shaped by, the reconfiguration of imaginative space occasioned by the n-dimensional turn. A timely study of the interplay between philosophy, literature, culture, and mathematics, it offers a rich resource for readers interested in nineteenth century literature, Modernist studies, science fiction, and gothic scholarship.
Negative Math
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Author : Alberto A. Martínez
language : en
Publisher: Princeton University Press
Release Date : 2018-06-05
Negative Math written by Alberto A. Martínez and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-05 with Mathematics categories.
A student in class asks the math teacher: "Shouldn't minus times minus make minus?" Teachers soon convince most students that it does not. Yet the innocent question brings with it a germ of mathematical creativity. What happens if we encourage that thought, odd and ungrounded though it may seem? Few books in the field of mathematics encourage such creative thinking. Fewer still are engagingly written and fun to read. This book succeeds on both counts. Alberto Martinez shows us how many of the mathematical concepts that we take for granted were once considered contrived, imaginary, absurd, or just plain wrong. Even today, he writes, not all parts of math correspond to things, relations, or operations that we can actually observe or carry out in everyday life. Negative Math ponders such issues by exploring controversies in the history of numbers, especially the so-called negative and "impossible" numbers. It uses history, puzzles, and lively debates to demonstrate how it is still possible to devise new artificial systems of mathematical rules. In fact, the book contends, departures from traditional rules can even be the basis for new applications. For example, by using an algebra in which minus times minus makes minus, mathematicians can describe curves or trajectories that are not represented by traditional coordinate geometry. Clear and accessible, Negative Math expects from its readers only a passing acquaintance with basic high school algebra. It will prove pleasurable reading not only for those who enjoy popular math, but also for historians, philosophers, and educators. Key Features? Uses history, puzzles, and lively debates to devise new mathematical systems Shows how departures from rules can underlie new practical applications Clear and accessible Requires a background only in basic high school algebra
The Age Of Scientific Naturalism
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Author : Bernard Lightman
language : en
Publisher: University of Pittsburgh Press
Release Date : 2016-02-19
The Age Of Scientific Naturalism written by Bernard Lightman and has been published by University of Pittsburgh Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-02-19 with Science categories.
Physicist John Tyndall and his contemporaries were at the forefront of developing the cosmology of scientific naturalism during the Victorian period. They rejected all but physical laws as having any impact on the operations of human life and the universe. Contributors focus on the way Tyndall and his correspondents developed their ideas through letters, periodicals and scientific journals and challenge previously held assumptions about who gained authority, and how they attained and defended their position within the scientific community.
The Victorian Supernatural
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Author : Nicola Bown
language : en
Publisher: Cambridge University Press
Release Date : 2004-02-05
The Victorian Supernatural written by Nicola Bown 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 2004-02-05 with Art categories.
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