general investigations of curved surfaces dover books on mathematics

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General Investigations Of Curved Surfaces

Author : Karl Friedrich Gauss
ISBN : 9780486154817
Genre : Mathematics
File Size : 28. 65 MB
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This influential work defines the concept of surface curvature and presents the important theorem stating that the "Gauss curvature" is invariant under arbitrary isometric deformation of a curved surface. 1902 edition.

Beyond Geometry

Author : Peter Pesic
ISBN : 9780486453507
Genre : Mathematics
File Size : 66. 36 MB
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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.

Non Euclidean Geometry And Curvature Two Dimensional Spaces Volume 3

Author : James W. Cannon
ISBN : 9781470437169
Genre : Geometry
File Size : 86. 52 MB
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This is the final volume of a three volume collection devoted to the geometry, topology, and curvature of 2-dimensional spaces. The collection provides a guided tour through a wide range of topics by one of the twentieth century's masters of geometric topology. The books are accessible to college and graduate students and provide perspective and insight to mathematicians at all levels who are interested in geometry and topology. Einstein showed how to interpret gravity as the dynamic response to the curvature of space-time. Bill Thurston showed us that non-Euclidean geometries and curvature are essential to the understanding of low-dimensional spaces. This third and final volume aims to give the reader a firm intuitive understanding of these concepts in dimension 2. The volume first demonstrates a number of the most important properties of non-Euclidean geometry by means of simple infinite graphs that approximate that geometry. This is followed by a long chapter taken from lectures the author gave at MSRI, which explains a more classical view of hyperbolic non-Euclidean geometry in all dimensions. Finally, the author explains a natural intrinsic obstruction to flattening a triangulated polyhedral surface into the plane without distorting the constituent triangles. That obstruction extends intrinsically to smooth surfaces by approximation and is called curvature. Gauss's original definition of curvature is extrinsic rather than intrinsic. The final two chapters show that the book's intrinsic definition is equivalent to Gauss's extrinsic definition (Gauss's “Theorema Egregium” (“Great Theorem”)).

The Mechanics Of Ribbons And M Bius Bands

Author : Roger Fosdick
ISBN : 9789401773003
Genre : Technology & Engineering
File Size : 78. 79 MB
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Recent developments in biology and nanotechnology have stimulated a rapidly growing interest in the mechanics of thin, flexible ribbons and Mobius bands. This edited volume contains English translations of four seminal papers on this topic, all originally written in German; of these, Michael A. Sadowsky published the first in 1929, followed by two others in 1930, and Walter Wunderlich published the last in 1962. The volume also contains invited, peer-reviewed, original research articles on related topics. Previously published in the Journal of Elasticity, Volume 119, Issue 1-2, 2015.

Differential Equations With Applications And Historical Notes Third Edition

Author : George F. Simmons
ISBN : 9781498702621
Genre : Mathematics
File Size : 32. 66 MB
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Fads are as common in mathematics as in any other human activity, and it is always difficult to separate the enduring from the ephemeral in the achievements of one’s own time. An unfortunate effect of the predominance of fads is that if a student doesn’t learn about such worthwhile topics as the wave equation, Gauss’s hypergeometric function, the gamma function, and the basic problems of the calculus of variations—among others—as an undergraduate, then he/she is unlikely to do so later. The natural place for an informal acquaintance with such ideas is a leisurely introductory course on differential equations. Specially designed for just such a course, Differential Equations with Applications and Historical Notes takes great pleasure in the journey into the world of differential equations and their wide range of applications. The author—a highly respected educator—advocates a careful approach, using explicit explanation to ensure students fully comprehend the subject matter. With an emphasis on modeling and applications, the long-awaited Third Edition of this classic textbook presents a substantial new section on Gauss’s bell curve and improves coverage of Fourier analysis, numerical methods, and linear algebra. Relating the development of mathematics to human activity—i.e., identifying why and how mathematics is used—the text includes a wealth of unique examples and exercises, as well as the author’s distinctive historical notes, throughout. A solutions manual is available upon qualifying course adoption. Provides an ideal text for a one- or two-semester introductory course on differential equations Emphasizes modeling and applications Presents a substantial new section on Gauss’s bell curve Improves coverage of Fourier analysis, numerical methods, and linear algebra Relates the development of mathematics to human activity—i.e., identifying why and how mathematics is used Includes a wealth of unique examples and exercises, as well as the author’s distinctive historical notes, throughout Uses explicit explanation to ensure students fully comprehend the subject matter Solutions manual available upon qualifying course adoption

Einstein Hilbert And The Theory Of Gravitation

Author : Jagdish Mehra
ISBN : 9789401021944
Genre : Science
File Size : 54. 55 MB
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Some time ago I published a small piece * dealing with a charming little essay on 'the state of ether in magnetic fields', which the sixteen-year-old Einstein had written while he was awaiting admission to the E. T. H. in Zurich. This paper sought to trace the continuity between Einstein's early interest in electrodynamics and his later work on the special and general relativity theories. On reading this paper, Professor Eugene Wigner asked me whether David Hilbert had not independently discovered the field equations of gravitation. ** His impression from his stay in Gottingen (where Wigner had been Hilbert's assistant for one year in the late nineteen-twenties) was that Hilbert had indeed done so, and he asked me if it was true. I replied to Professor Wigner about Hilbert's contribution to the theory of gravitation. t He kindly encouraged me to expand my account to deal with the intricate and exciting details of the early years in the formulation of the general relativity theory of gravitation. This is what I have sought to do in this study. Albert Einstein created the general relativity theory of gravitation and dominated its development through the rest of his life. His early work on the theory of gravitation, from 1912 to 1916, had the drama of high adventure. It culminated in the establishment of its foundations which have remained unassailed by the theoretical and experimental work of succeeding decades.

The Physicist S Conception Of Nature

Author : Jagdish Mehra
ISBN : 9789401026024
Genre : Science
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The fundamental conceptions of twentieth-century physics have profoundly influenced almost every field of modern thought and activity. Quantum Theory, Relativity, and the modern ideas on the Structure of Matter have contributed to a deeper understand ing of Nature, and they will probably rank in history among the greatest intellectual achievements of all time. The purpose of our symposium was to review, in historical perspective, the current horizons of the major conceptual structures of the physics of this century. Professors Abdus Salam and Hendrik Casimir, in their remarks at the opening of the symposium, have referred to its origin and planning. Our original plan was to hold a two-week symposium on the different aspects of five principal themes: 1. Space, Time and Geometry (including the structure of the universe and the theory of gravita tion),2. Quantum Theory (including the development of quantum mechanics and quantum field theory), 3. Statistical Description of Nature (including the discussion of equilibrium and non-equilibrium phenomena, and the application of these ideas to the evolution of biological structure), 4. The Structure of Matter (including the discus sion, in a unified perspective, of atoms, molecules, nuclei, elementary particles, and the physics of condensed matter), and finally, 5. Physical Description and Epistemo logy (including the distinction between classical and quantum descriptions, and the epistemological and philosophical problems raised by them).

The Golden Age Of Theoretical Physics

Author : Jagdish Mehra
ISBN : 9789814492850
Genre : Science
File Size : 84. 75 MB
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The Golden Age of Theoretical Physics brings together 37 selected essays. Many of these essays were first presented as lectures at various universities in Europe and the USA, and then published as reports or articles. Their enlarged, final versions were published in the joint work of Jagdish Mehra and Helmut Rechenberg, The Historical Development of Quantum Theory, while the other essays were published as articles in scientific journals or in edited books. Here they are published together as a tribute to the Mehra-Rechenberg collaboration sustained for several decades, and cover various aspects of quantum theory, the special and general theories of relativity, the foundations of statistical mechanics, and some of their fundamental applications. Two essays, ‘Albert Einstein's “First” Paper’ (Essay 1) and ‘The Dream of Leonardo da Vinci’ (Essay 37), lie outside the major themes treated in this book, but are included here because of their historical interest. The origin of each essay is explained in a footnote. This book deals with the most important themes developed in the first 40 years of the twentieth century by some of the greatest pioneers and architects of modern physics. It is a vital source of information about what can veritably be described as ‘the golden age of theoretical physics’. Contents: Volume 1:Albert Einstein's ‘First’ PaperMax Planck and the Law of Blackbody RadiationPlanck's Half-Quanta: A History of the Concept of Zero-Point EnergyJosiah Willard Gibbs and the Foundations of Statistical MechanicsEinstein and the Foundation of Statistical MechanicsAlbert Einstein and Marian von Smoluchowski: Early History of the Theory of Fluctuation PhenomenaThe Historical Origins of the Special Theory of RelativityThe Historical Origins of the General Theory of RelativityAlbert Einstein and the Origin of Light-Quantum TheoryNiels Bohr and the Quantum Theory of the AtomArnold Sommerfeld and Atoms as Conditionally Periodic SystemsThe Göttingen Tradition of Mathematics and Physics from Gauss to Hilbert and Born and FranckThe Bohr Festival in Göttingen: Bohr's Wolfskehl Lectures and the Theory of the Periodic System of ElementsSatyendra Nath Bose, Bose–Einstein Statistics, and the Quantum Theory of an Ideal GasLouis de Broglie and the Phase Waves Associated with MatterWolfgang Pauli and the Discovery of the Exclusion PrincipleThe Discovery of Electron SpinThe Discovery of the Fermi–Dirac StatisticsVolume 2:Werner Heisenberg and the Birth of Quantum Mechanics‘The Golden Age of Theoretical Physics’: PAM Dirac's Scientific Work from 1924 to 1933Erwin Schrödinger and the Rise of Wave Mechanics. I. Schrödinger's Scientific Work Before the Creation of Wave MechanicsErwin Schrödinger and the Rise of Wave Mechanics. II. The Creation of Wave MechanicsErwin Schrödinger and the Rise of Wave Mechanics. III. Early Response and ApplicationsNiels Bohr's Discussions with Albert Einstein, Werner Heisenberg, and Erwin Schrödinger: The Origins of the Principles of Uncertainty and ComplementarityEugene Paul Wigner: Aspects of His Life Work, and PersonalityLev Davidovich Landau: Some Aspects of His Life and PersonalityThe Origin of Quantum Field TheoryThe Solvay Conferences of 1927 and 1930 and the Consistency DebateRelativistic Electrons and Quantum FieldsNew Elementary Particles in Nuclear and Cosmic-Ray PhysicsBetween Hope and Despair: Quantum Electrodynamics in the 1930sUniversal Nuclear Forces and Yukawa's New Intermediate Mass Particle (1933–1937)New Fields Describing Elementary Particles, Their Properties and InteractionsEnergy Generation in Stars and the Origins of Nuclear FissionThe Einstein–Bohr Debate on the Completion of Quantum Mechanics and Its Description of Reality (1931–1936)The Quantum Principle: Its Interpretation and EpistemologyThe Dream of Leonardo da Vinci Readership: Physicists, historians and philosophers of science. Keywords:The Golden Age of Theoretical Physics;Max Planck, J Willard Gibbs, Albert Einstein, Arnold Sommerfeld, David Hilbert, Henri Poincare, Hendrik Antoon Lorentz, Niels Bohr, Max Born, Wolfgang Pauli, Werner Heisenberg, PAM Dirac, Pascual Jordan, Erwin Schrodinger, Eugene Wigner, Enrico Fermi, John Von Neumann, Hans A Bethe, Hideki Yukawa, and Their Collaborators;The Dream of Leonardo Da Vinci: Man's Changing Vision of the Universe from Pythagoras to Kinstein;The Creation of Quantum Theory and Quantum Mechanics, and Quantum Field Theory;The Creation of Statistical Mechanics;The Solvay Conferences on Physics;The Interpretation of Quantum MechanicsReviews:“Whatever subject Mehra writes about, he does it concisely and authoritatively, and with great technical competence. He covers an incredible amount of information and yet he manages to present his material in a clear and highly readable way.”Physics World

General Investigations Of Curved Surfaces Of 1827 And 1825

Author : Carl Friedrich Gauss
ISBN : WISC:89057165953
Genre : Surfaces
File Size : 60. 14 MB
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The Fifth Postulate

Author : Jason Socrates Bardi
ISBN : 0470149094
Genre : Mathematics
File Size : 77. 96 MB
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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

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