Download or read book New Foundations for Physical Geometry written by Tim Maudlin and published by . This book was released on 2014-02 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tim Maudlin sets out a completely new method for describing the geometrical structure of spaces, and thus a better mathematical tool for describing and understanding space-time. He presents a historical review of the development of geometry and topology, and then his original Theory of Linear Structures.
Download or read book Space and Geometry in the Light of Physiological Psychological and Physical Inquiry written by Ernst Mach and published by . This book was released on 1906 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Simple Non Euclidean Geometry and Its Physical Basis written by I.M. Yaglom and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: There are many technical and popular accounts, both in Russian and in other languages, of the non-Euclidean geometry of Lobachevsky and Bolyai, a few of which are listed in the Bibliography. This geometry, also called hyperbolic geometry, is part of the required subject matter of many mathematics departments in universities and teachers' colleges-a reflec tion of the view that familiarity with the elements of hyperbolic geometry is a useful part of the background of future high school teachers. Much attention is paid to hyperbolic geometry by school mathematics clubs. Some mathematicians and educators concerned with reform of the high school curriculum believe that the required part of the curriculum should include elements of hyperbolic geometry, and that the optional part of the curriculum should include a topic related to hyperbolic geometry. I The broad interest in hyperbolic geometry is not surprising. This interest has little to do with mathematical and scientific applications of hyperbolic geometry, since the applications (for instance, in the theory of automorphic functions) are rather specialized, and are likely to be encountered by very few of the many students who conscientiously study (and then present to examiners) the definition of parallels in hyperbolic geometry and the special features of configurations of lines in the hyperbolic plane. The principal reason for the interest in hyperbolic geometry is the important fact of "non-uniqueness" of geometry; of the existence of many geometric systems.
Download or read book Differential Geometry For Physicists written by Bo-yu Hou and published by World Scientific Publishing Company. This book was released on 1997-10-31 with total page 561 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is divided into fourteen chapters, with 18 appendices as introduction to prerequisite topological and algebraic knowledge, etc. The first seven chapters focus on local analysis. This part can be used as a fundamental textbook for graduate students of theoretical physics. Chapters 8-10 discuss geometry on fibre bundles, which facilitates further reference for researchers. The last four chapters deal with the Atiyah-Singer index theorem, its generalization and its application, quantum anomaly, cohomology field theory and noncommutative geometry, giving the reader a glimpse of the frontier of current research in theoretical physics.
Download or read book An Introduction to Noncommutative Differential Geometry and Its Physical Applications written by J. Madore and published by Cambridge University Press. This book was released on 1999-06-24 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: A thoroughly revised introduction to non-commutative geometry.
Download or read book On the Hypotheses Which Lie at the Bases of Geometry written by Bernhard Riemann and published by Birkhäuser. This book was released on 2016-04-19 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Relativity and Geometry written by Roberto Torretti and published by Elsevier. This book was released on 2014-05-20 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: Relativity and Geometry aims to elucidate the motivation and significance of the changes in physical geometry brought about by Einstein, in both the first and the second phases of relativity. The book contains seven chapters and a mathematical appendix. The first two chapters review a historical background of relativity. Chapter 3 centers on Einstein's first Relativity paper of 1905. Subsequent chapter presents the Minkowskian formulation of special relativity. Chapters 5 and 6 deal with Einstein's search for general relativity from 1907 to 1915, as well as some aspects and subsequent developments of the theory. The last chapter explores the concept of simultaneity, geometric conventionalism, and a few other questions concerning space time structure, causality, and time.
Download or read book Linear Algebra and Analytic Geometry for Physical Sciences written by Giovanni Landi and published by Springer. This book was released on 2018-05-12 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained introduction to finite dimensional vector spaces, matrices, systems of linear equations, spectral analysis on euclidean and hermitian spaces, affine euclidean geometry, quadratic forms and conic sections. The mathematical formalism is motivated and introduced by problems from physics, notably mechanics (including celestial) and electro-magnetism, with more than two hundreds examples and solved exercises.Topics include: The group of orthogonal transformations on euclidean spaces, in particular rotations, with Euler angles and angular velocity. The rigid body with its inertia matrix. The unitary group. Lie algebras and exponential map. The Dirac’s bra-ket formalism. Spectral theory for self-adjoint endomorphisms on euclidean and hermitian spaces. The Minkowski spacetime from special relativity and the Maxwell equations. Conic sections with the use of eccentricity and Keplerian motions. An appendix collects basic algebraic notions like group, ring and field; and complex numbers and integers modulo a prime number.The book will be useful to students taking a physics or engineer degree for a basic education as well as for students who wish to be competent in the subject and who may want to pursue a post-graduate qualification.
Download or read book Physical Geometry written by Gustavo R Gonz Lez-Mart N and published by CreateSpace. This book was released on 2011-09-24 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is generally recognized that there exist problems in Physics. In particular, A. Einstein remained critical of some theoretical ideas in modern physics until his death. He was unsatisfied with his own gravitation and advocated the need for a fundamental unified theory which would include relativity, electromagnetism and gravitation from the beginning. He stated that the concepts of parallelism and differentiation are important. Furthermore, present models for Particle Physics are expressed in terms of a very large number of empirical parameters and a high number of dimensions. They are not clearly related to a fundamental underlying physical interaction. Gravitation and Electrodynamics are faced with serious theoretical challenges, particularly in Cosmic Physics due to the possible existence of dark matter and energy. Differential geometry offers the appropriate mathematical structure to accomplish Einstein's physical ideas. The key is "how to differentiate." In the book we use an Ehresmann connection, a concept related to groups. The group is determined from electrodynamics and relativity as the automorphisms of the space-time geometric algebra. Matter and fields are represented by generator-valued tensors. Unification is given by the fundamental nonlinear equation associated to the group. Microscopic physics is the study of linear excitations, which are group representations characterized by discrete numbers. Results obtained indicate that gravitation and electromagnetism are unified in a nontrivial manner. Odd generators represent non classical interactions. The equation of motion determines a geodesic motion with the Lorentz force term. The Einstein field equation with a purely geometric energy momentum tensor is obtained. In the newtonian limit, the constant geometric energy density of a hyperbolic symmetric solution is related to the gravitational constant G. Far from the limit the parameter G would be variable. This effect may be interpreted as dark matter. In vacuum, the known gravitational solutions are obtained. Electromagnetism is related to an SU(2) subgroup. If we restrict to the even U(1) subgroup we obtain Maxwell's equations. The equation of motion is a geometric generalization of Dirac's equation. This geometry is the germ of quantum physics including its probabilistic aspects. The geometric nature of Planck's constant h and of light speed c is determined by their relations to the connection and the metric. The alpha coupling constant is also determined geometrically. Mass is defined in terms of energy. The geometry shows various physical triple structures. The geometric excitations have quanta of charge, flux and spin which determine the fractional quantum Hall effect. The bare-mass quotients of the three stable particles are calculated giving a geometric expression for the proton-electron mass ratio, previously known but physically unexplained. There are connection excitations whose masses correspond to the weak boson masses and allow a geometric interpretation of Weinberg's angle. The equation of motion determines the anomalous bare magnetic moments of the proton, the electron and the neutron. The "strong" electromagnetic odd SU(2) part, generates short range attractive magnetic potentials which are sufficiently strong to determine the binding energy of the deuteron and other light nuclides. The bare masses of the leptons in the three families are calculated as topological excitations of the electron. The masses of these excitations increase under the action of a strong connection and are related to meson and quark masses. The mass spectrum for low masses agrees with the physical particle mass spectrum. The proton shows a triple structure that may be related to a quark structure. The combinations of the three fundamental geometric excitations (proton, electron and neutrino) form other excitations and may be used to represent particles showing a symmetry under the group SU(3)xSU(2)XU(1).
Download or read book The Geometry of an Art written by Kirsti Andersen and published by Springer Science & Business Media. This book was released on 2008-11-23 with total page 837 pages. Available in PDF, EPUB and Kindle. Book excerpt: This review of literature on perspective constructions from the Renaissance through the 18th century covers 175 authors, emphasizing Peiro della Francesca, Guidobaldo del Monte, Simon Stevin, Brook Taylor, and Johann Heinrich. It treats such topics as the various methods of constructing perspective, the development of theories underlying the constructions, and the communication between mathematicians and artisans in these developments.
Download or read book Philosophy and Geometry written by L. Magnani and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: Philosophers have studied geometry since ancient times. Geometrical knowledge has often played the role of a laboratory for the philosopher's conceptual experiments dedicated to the ideation of powerful theories of knowledge. Lorenzo Magnani's new book Philosophy and Geometry illustrates the rich intrigue of this fascinating story of human knowledge, providing a new analysis of the ideas of many scholars (including Plato, Proclus, Kant, and Poincaré), and discussing conventionalist and neopositivist perspectives and the problem of the origins of geometry. The book also ties together the concerns of philosophers of science and cognitive scientists, showing, for example, the connections between geometrical reasoning and cognition as well as the results of recent logical and computational models of geometrical reasoning. All the topics are dealt with using a novel combination of both historical and contemporary perspectives. Philosophy and Geometry is a valuable contribution to the renaissance of research in the field.
Download or read book A History of Non Euclidean Geometry written by Boris A. Rosenfeld and published by Springer Science & Business Media. This book was released on 2012-09-08 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Russian edition of this book appeared in 1976 on the hundred-and-fiftieth anniversary of the historic day of February 23, 1826, when LobaeevskiI delivered his famous lecture on his discovery of non-Euclidean geometry. The importance of the discovery of non-Euclidean geometry goes far beyond the limits of geometry itself. It is safe to say that it was a turning point in the history of all mathematics. The scientific revolution of the seventeenth century marked the transition from "mathematics of constant magnitudes" to "mathematics of variable magnitudes. " During the seventies of the last century there occurred another scientific revolution. By that time mathematicians had become familiar with the ideas of non-Euclidean geometry and the algebraic ideas of group and field (all of which appeared at about the same time), and the (later) ideas of set theory. This gave rise to many geometries in addition to the Euclidean geometry previously regarded as the only conceivable possibility, to the arithmetics and algebras of many groups and fields in addition to the arith metic and algebra of real and complex numbers, and, finally, to new mathe matical systems, i. e. , sets furnished with various structures having no classical analogues. Thus in the 1870's there began a new mathematical era usually called, until the middle of the twentieth century, the era of modern mathe matics.
Download or read book The Determinate World written by David Jalal Hyder and published by Walter de Gruyter. This book was released on 2009 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a new interpretation of Hermann von Helmholtz's work on the epistemology of geometry. A detailed analysis of the philosophical arguments of Helmholtz's Erhaltung der Kraft shows that he took physical theories to be constrained by a regulative ideal. They must render nature "completely comprehensible", which implies that all physical magnitudes must be relations among empirically given phenomena. This conviction eventually forced Helmholtz to explain how geometry itself could be so construed. Hyder shows how Helmholtz answered this question by drawing on the theory of magnitudes developed in his research on the colour-space. He argues against the dominant interpretation of Helmholtz's work by suggesting that for the latter, it is less the inductive character of geometry that makes it empirical, and rather the regulative requirement that the system of natural science be empirically closed.
Download or read book Modern Differential Geometry in Gauge Theories written by Anastasios Mallios and published by Springer Science & Business Media. This book was released on 2006-07-27 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is original, well-written work of interest Presents for the first time (physical) field theories written in sheaf-theoretic language Contains a wealth of minutely detailed, rigorous computations, ususally absent from standard physical treatments Author's mastery of the subject and the rigorous treatment of this text make it invaluable
Download or read book Axiomatic Characterization of Physical Geometry written by H.J. Schmidt and published by Springer. This book was released on 1979-11-01 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Differential Sheaves And Connections A Natural Approach To Physical Geometry written by Anastasios Mallios and published by World Scientific. This book was released on 2015-09-17 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique book provides a self-contained conceptual and technical introduction to the theory of differential sheaves. This serves both the newcomer and the experienced researcher in undertaking a background-independent, natural and relational approach to 'physical geometry'. In this manner, this book is situated at the crossroads between the foundations of mathematical analysis with a view toward differential geometry and the foundations of theoretical physics with a view toward quantum mechanics and quantum gravity. The unifying thread is provided by the theory of adjoint functors in category theory and the elucidation of the concepts of sheaf theory and homological algebra in relation to the description and analysis of dynamically constituted physical geometric spectrums.
Download or read book Brook Taylor s Work on Linear Perspective written by Kirsti Andersen and published by Springer Science & Business Media. This book was released on 1992 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Study of Taylors Role in the History of Perspective Geometry. Including Facsimiles of Taylors̀ Two Books on Perspective.
