General Investigations of Curved Surfaces of 1827 and 1825 PDF Download

Author: Carl Friedrich Gauss
Publisher:
ISBN:
Category : Surfaces
Languages : en
Pages : 144

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Author: Karl Friedrich Gauss
Publisher: Courier Corporation
ISBN: 0486154815
Category : Mathematics
Languages : en
Pages : 146

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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.

Author: Karl Friedrich Gauss
Publisher: Legare Street Press
ISBN: 9781015823617
Category : Education
Languages : en
Pages : 0

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Book Description
This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

Author: Art Knoebel
Publisher: Springer Science & Business Media
ISBN: 0387330623
Category : Mathematics
Languages : en
Pages : 346

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Book Description
Intended for juniors and seniors majoring in mathematics, as well as anyone pursuing independent study, this book traces the historical development of four different mathematical concepts by presenting readers with the original sources. Each chapter showcases a masterpiece of mathematical achievement, anchored to a sequence of selected primary sources. The authors examine the interplay between the discrete and continuous, with a focus on sums of powers. They then delineate the development of algorithms by Newton, Simpson and Smale. Next they explore our modern understanding of curvature, and finally they look at the properties of prime numbers. The book includes exercises, numerous photographs, and an annotated bibliography.

Author: Brian A. Barsky
Publisher: Springer
ISBN: 364272292X
Category : Computers
Languages : en
Pages : 154

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Author: Renhong Wang
Publisher: American Mathematical Soc.
ISBN: 9780821820445
Category : Mathematics
Languages : en
Pages : 252

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Computational geometry is a borderline subject related to pure and applied mathematics, computer science, and engineering. The book contains articles on various topics in computational geometry based on invited lectures and contributed papers presented during the program on computational geometry at the Morningside Center of Mathematics at the Chinese Academy of Sciences (Beijing). The opening article by R.-H. Wang gives a nice survey of various aspects of computational geometry, many of which are discussed in detail in the volume. Topics of the other articles include problems of optimal triangulation, splines, data interpolation, problems of curve and surface design, problems of shape control, quantum teleportation, and more. The book is suitable for graduate students and researchers interested in computational geometry and specialists in theoretical computer science.

Author: Leonor Godinho
Publisher: Springer
ISBN: 3319086669
Category : Mathematics
Languages : en
Pages : 476

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Book Description
Unlike many other texts on differential geometry, this textbook also offers interesting applications to geometric mechanics and general relativity. The first part is a concise and self-contained introduction to the basics of manifolds, differential forms, metrics and curvature. The second part studies applications to mechanics and relativity including the proofs of the Hawking and Penrose singularity theorems. It can be independently used for one-semester courses in either of these subjects. The main ideas are illustrated and further developed by numerous examples and over 300 exercises. Detailed solutions are provided for many of these exercises, making An Introduction to Riemannian Geometry ideal for self-study.

Author: Jagdish Mehra
Publisher: Springer
ISBN: 9401026025
Category : Science
Languages : en
Pages : 853

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Book Description
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).

Author: A. D. Aleksandrov
Publisher: Courier Corporation
ISBN: 0486157873
Category : Mathematics
Languages : en
Pages : 1123

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Book Description
Major survey offers comprehensive, coherent discussions of analytic geometry, algebra, differential equations, calculus of variations, functions of a complex variable, prime numbers, linear and non-Euclidean geometry, topology, functional analysis, more. 1963 edition.

Author: Eberhard Zeidler
Publisher: Springer Science & Business Media
ISBN: 3642224210
Category : Mathematics
Languages : en
Pages : 1141

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Book Description
In this third volume of his modern introduction to quantum field theory, Eberhard Zeidler examines the mathematical and physical aspects of gauge theory as a principle tool for describing the four fundamental forces which act in the universe: gravitative, electromagnetic, weak interaction and strong interaction. Volume III concentrates on the classical aspects of gauge theory, describing the four fundamental forces by the curvature of appropriate fiber bundles. This must be supplemented by the crucial, but elusive quantization procedure. The book is arranged in four sections, devoted to realizing the universal principle force equals curvature: Part I: The Euclidean Manifold as a Paradigm Part II: Ariadne's Thread in Gauge Theory Part III: Einstein's Theory of Special Relativity Part IV: Ariadne's Thread in Cohomology For students of mathematics the book is designed to demonstrate that detailed knowledge of the physical background helps to reveal interesting interrelationships among diverse mathematical topics. Physics students will be exposed to a fairly advanced mathematics, beyond the level covered in the typical physics curriculum. Quantum Field Theory builds a bridge between mathematicians and physicists, based on challenging questions about the fundamental forces in the universe (macrocosmos), and in the world of elementary particles (microcosmos).