The Foundations of Geometry PDF Download
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Author: David Hilbert
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 190
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Book Description
Author: David Hilbert
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 190
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Book Description
Author: Karol Borsuk
Publisher: Courier Dover Publications
ISBN: 0486828093
Category : Mathematics
Languages : en
Pages : 465
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Book Description
In Part One of this comprehensive and frequently cited treatment, the authors develop Euclidean and Bolyai-Lobachevskian geometry on the basis of an axiom system due, in principle, to the work of David Hilbert. Part Two develops projective geometry in much the same way. An Introduction provides background on topological space, analytic geometry, and other relevant topics, and rigorous proofs appear throughout the text. Topics covered by Part One include axioms of incidence and order, axioms of congruence, the axiom of continuity, models of absolute geometry, and Euclidean geometry, culminating in the treatment of Bolyai-Lobachevskian geometry. Part Two examines axioms of incidents and order and the axiom of continuity, concluding with an exploration of models of projective geometry.
Author: G.E. Martin
Publisher: Springer Science & Business Media
ISBN: 1461257255
Category : Mathematics
Languages : en
Pages : 525
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Book Description
This book is a text for junior, senior, or first-year graduate courses traditionally titled Foundations of Geometry and/or Non Euclidean Geometry. The first 29 chapters are for a semester or year course on the foundations of geometry. The remaining chap ters may then be used for either a regular course or independent study courses. Another possibility, which is also especially suited for in-service teachers of high school geometry, is to survey the the fundamentals of absolute geometry (Chapters 1 -20) very quickly and begin earnest study with the theory of parallels and isometries (Chapters 21 -30). The text is self-contained, except that the elementary calculus is assumed for some parts of the material on advanced hyperbolic geometry (Chapters 31 -34). There are over 650 exercises, 30 of which are 10-part true-or-false questions. A rigorous ruler-and-protractor axiomatic development of the Euclidean and hyperbolic planes, including the classification of the isometries of these planes, is balanced by the discussion about this development. Models, such as Taxicab Geometry, are used exten sively to illustrate theory. Historical aspects and alternatives to the selected axioms are prominent. The classical axiom systems of Euclid and Hilbert are discussed, as are axiom systems for three and four-dimensional absolute geometry and Pieri's system based on rigid motions. The text is divided into three parts. The Introduction (Chapters 1 -4) is to be read as quickly as possible and then used for ref erence if necessary.
Author: C. R. Wylie
Publisher: Courier Corporation
ISBN: 0486472140
Category : Mathematics
Languages : en
Pages : 352
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Book Description
Explains geometric theories and shows many examples.
Author: Bertrand Russell
Publisher:
ISBN:
Category : Geometry
Languages : en
Pages : 228
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Book Description
Author: Tim Maudlin
Publisher:
ISBN: 0198701306
Category : Mathematics
Languages : en
Pages : 374
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Book Description
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.
Author: Gerard Venema
Publisher:
ISBN: 9780136020585
Category : Geometry
Languages : en
Pages : 0
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Book Description
Normal 0 false false false Foundations of Geometry, Second Edition is written to help enrich the education of all mathematics majors and facilitate a smooth transition into more advanced mathematics courses. The text also implements the latest national standards and recommendations regarding geometry for the preparation of high school mathematics teachers--and encourages students to make connections between their college courses and classes they will later teach. This text's coverage begins with Euclid's Elements, lays out a system of axioms for geometry, and then moves on to neutral geometry, Euclidian and hyperbolic geometries from an axiomatic point of view, and then non-Euclidean geometry. Good proof-writing skills are emphasized, along with a historical development of geometry. The Second Edition streamlines and reorganizes material in order to reach coverage of neutral geometry as early as possible, adds more exercises throughout, and facilitates use of the open-source software Geogebra. This text is ideal for an undergraduate course in axiomatic geometry for future high school geometry teachers, or for any student who has not yet encountered upper-level math, such as real analysis or abstract algebra. It assumes calculus and linear algebra as prerequisites.
Author: Nikolai I. Lobachevsky
Publisher:
ISBN: 9781927763247
Category : Mathematics
Languages : en
Pages : 212
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Book Description
Neither general relativity (which revealed that gravity is merely manifestation of the non-Euclidean geometry of spacetime) nor modern cosmology would have been possible without the almost simultaneous and independent discovery of non-Euclidean geometry in the 19th century by three great mathematicians - Nikolai Ivanovich Lobachevsky, János Bolyai and Carl Friedrich Gauss (whose ideas were later further developed by Georg Friedrich Bernhard Riemann).This volume contains three works by Lobachevsky on the foundations of geometry and non-Euclidean geometry: "Geometry", "Geometrical investigations on the theory of parallel lines" and "Pangeometry". It will be of interest not only to experts and students in mathematics, physics, history and philosophy of science, but also to anyone who is not intimidated by the magnitude of one of the greatest discoveries of our civilization and would attempt to follow (and learn from) Lobachevsky's line of thought, helpfully illustrated by over 130 figures, that led him to the discovery.
Author: Michel Serres
Publisher: Bloomsbury Publishing
ISBN: 1474281419
Category : Philosophy
Languages : en
Pages : 224
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Book Description
In this third installment of his classic 'Foundations' trilogy, Michel Serres takes on the history of geometry and mathematics. Even more broadly, Geometry is the beginnings of things and also how these beginnings have shaped how we continue to think philosophically and critically. Serres rejects a traditional history of mathematics which unfolds in a linear manner, and argues for the need to delve into the past of maths and identify a series of ruptures which can help shed light on how this discipline has developed and how, in turn, the way we think has been shaped and formed. This meticulous and lyrical translation marks the first ever English translation of this key text in the history of ideas.
Author: Alexandru Buium
Publisher: American Mathematical Soc.
ISBN: 147043623X
Category : Mathematics
Languages : en
Pages : 357
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Book Description
The aim of this book is to introduce and develop an arithmetic analogue of classical differential geometry. In this new geometry the ring of integers plays the role of a ring of functions on an infinite dimensional manifold. The role of coordinate functions on this manifold is played by the prime numbers. The role of partial derivatives of functions with respect to the coordinates is played by the Fermat quotients of integers with respect to the primes. The role of metrics is played by symmetric matrices with integer coefficients. The role of connections (respectively curvature) attached to metrics is played by certain adelic (respectively global) objects attached to the corresponding matrices. One of the main conclusions of the theory is that the spectrum of the integers is “intrinsically curved”; the study of this curvature is then the main task of the theory. The book follows, and builds upon, a series of recent research papers. A significant part of the material has never been published before.
