Euclid S Heritage Is Space Three Dimensional
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Euclid S Heritage Is Space Three Dimensional
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Author : P. Janich
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Euclid S Heritage Is Space Three Dimensional written by P. Janich and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Science categories.
We live in a space, we get about in it. We also quantify it, we think of it as having dimensions. Ever since Euclid's ancient geometry, we have thought of bodies occupying parts of this space (including our own bodies), the space of our practical orientations (our 'moving abouts'), as having three dimensions. Bodies have volume specified by measures of length, breadth and height. But how do we know that the space we live in has just these three dimensions? It is theoreti cally possible that some spaces might exist that are not correctly described by Euclidean geometry. After all, there are the non Euclidian geometries, descriptions of spaces not conforming to the axioms and theorems of Euclid's geometry. As one might expect, there is a history of philosophers' attempts to 'prove' that space is three-dimensional. The present volume surveys these attempts from Aristotle, through Leibniz and Kant, to more recent philosophy. As you will learn, the historical theories are rife with terminology, with language, already tainted by the as sumed, but by no means obvious, clarity of terms like 'dimension', 'line', 'point' and others. Prior to that language there are actions, ways of getting around in the world, building things, being interested in things, in the more specific case of dimensionality, cutting things. It is to these actions that we must eventually appeal if we are to understand how science is grounded.
Foundations Of Three Dimensional Euclidean Geometry
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Author : Izu Vaisman
language : en
Publisher: CRC Press
Release Date : 2020-11-26
Foundations Of Three Dimensional Euclidean Geometry written by Izu Vaisman and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-26 with Mathematics categories.
This book presents to the reader a modern axiomatic construction of three-dimensional Euclidean geometry in a rigorous and accessible form. It is helpful for high school teachers who are interested in the modernization of the teaching of geometry.
Progress In Physics Vol 1 2011
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Author : Dmitri Rabounski
language : en
Publisher: Infinite Study
Release Date :
Progress In Physics Vol 1 2011 written by Dmitri Rabounski and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
The Journal on Advanced Studies in Theoretical and Experimental Physics, including Related Themes from Mathematics
International Tables For Crystallography Mathematical Physical And Chemical Tables
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Author : E. Prince
language : en
Publisher: John Wiley & Sons
Release Date : 2004-01-16
International Tables For Crystallography Mathematical Physical And Chemical Tables written by E. Prince 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 2004-01-16 with Science categories.
International Tables for Crystallography is the definitive resource and reference work for crystallography and structural science. Each of the volumes in the series contains articles and tables of data relevant to crystallographic research and to applications of crystallographic methods in all sciences concerned with the structure and properties of materials. Emphasis is given to symmetry, diffraction methods and techniques of crystal-structure determination, and the physical and chemical properties of crystals. The data are accompanied by discussions of theory, practical explanations and examples, all of which are useful for teaching. Volume C provides the mathematical, physical and chemical information needed for experimental studies in structural crystallography. This volume covers all aspects of experimental techniques, using all three principal radiation types (X-ray, electron and neutron), from the selection and mounting of crystals and production of radiation, through data collection and analysis, to interpretation of results. Each chapter is supported by a substantial collection of references, and the volume ends with a section on precautions against radiation injury. Eleven chapters have been revised, corrected or updated for the third edition of Volume C. More information on the series can be found at: http://it.iucr.org
The Elements Of Non Euclidean Geometry
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Author : D. M.Y. Sommerville
language : en
Publisher: Courier Corporation
Release Date : 2012-05-24
The Elements Of Non Euclidean Geometry written by D. M.Y. Sommerville and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-24 with Mathematics categories.
Renowned for its lucid yet meticulous exposition, this classic allows students to follow the development of non-Euclidean geometry from a fundamental analysis of the concept of parallelism to more advanced topics. 1914 edition. Includes 133 figures.
Three Dimensional Geometry And Topology Volume 1
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Author : William P. Thurston
language : en
Publisher: Princeton University Press
Release Date : 2014-10-31
Three Dimensional Geometry And Topology Volume 1 written by William P. Thurston 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 2014-10-31 with Mathematics categories.
This book develops some of the extraordinary richness, beauty, and power of geometry in two and three dimensions, and the strong connection of geometry with topology. Hyperbolic geometry is the star. A strong effort has been made to convey not just denatured formal reasoning (definitions, theorems, and proofs), but a living feeling for the subject. There are many figures, examples, and exercises of varying difficulty. This book was the origin of a grand scheme developed by Thurston that is now coming to fruition. In the 1920s and 1930s the mathematics of two-dimensional spaces was formalized. It was Thurston's goal to do the same for three-dimensional spaces. To do this, he had to establish the strong connection of geometry to topology--the study of qualitative questions about geometrical structures. The author created a new set of concepts, and the expression "Thurston-type geometry" has become a commonplace. Three-Dimensional Geometry and Topology had its origins in the form of notes for a graduate course the author taught at Princeton University between 1978 and 1980. Thurston shared his notes, duplicating and sending them to whoever requested them. Eventually, the mailing list grew to more than one thousand names. The book is the culmination of two decades of research and has become the most important and influential text in the field. Its content also provided the methods needed to solve one of mathematics' oldest unsolved problems--the Poincaré Conjecture. In 2005 Thurston won the first AMS Book Prize, for Three-dimensional Geometry and Topology. The prize recognizes an outstanding research book that makes a seminal contribution to the research literature. Thurston received the Fields Medal, the mathematical equivalent of the Nobel Prize, in 1982 for the depth and originality of his contributions to mathematics. In 1979 he was awarded the Alan T. Waterman Award, which recognizes an outstanding young researcher in any field of science or engineering supported by the National Science Foundation.
Spaces Of Constant Curvature
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Author : Joseph Albert Wolf
language : en
Publisher: American Mathematical Soc.
Release Date : 2011
Spaces Of Constant Curvature written by Joseph Albert Wolf and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
This book is the sixth edition of the classic Spaces of Constant Curvature, first published in 1967, with the previous (fifth) edition published in 1984. It illustrates the high degree of interplay between group theory and geometry. The reader will benefit from the very concise treatments of riemannian and pseudo-riemannian manifolds and their curvatures, of the representation theory of finite groups, and of indications of recent progress in discrete subgroups of Lie groups. Part I is a brief introduction to differentiable manifolds, covering spaces, and riemannian and pseudo-riemannian geometry. It also contains a certain amount of introductory material on symmetry groups and space forms, indicating the direction of the later chapters. Part II is an updated treatment of euclidean space form. Part III is Wolf's classic solution to the Clifford-Klein Spherical Space Form Problem. It starts with an exposition of the representation theory of finite groups. Part IV introduces riemannian symmetric spaces and extends considerations of spherical space forms to space forms of riemannian symmetric spaces. Finally, Part V examines space form problems on pseudo-riemannian symmetric spaces. At the end of Chapter 12 there is a new appendix describing some of the recent work on discrete subgroups of Lie groups with application to space forms of pseudo-riemannian symmetric spaces. Additional references have been added to this sixth edition as well.
Prolegomena To Analytical Geometry In Anisotropic Euclidean Space Of Three Dimensions
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Author : Eric Harold Neville
language : en
Publisher:
Release Date : 1922
Prolegomena To Analytical Geometry In Anisotropic Euclidean Space Of Three Dimensions written by Eric Harold Neville and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1922 with Geometry, Analytic categories.
Linear Order In Three Dimensional Euclidean And Double Elliptic Spaces
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Author : George Hervey Hallett
language : en
Publisher:
Release Date : 1920
Linear Order In Three Dimensional Euclidean And Double Elliptic Spaces written by George Hervey Hallett and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1920 with Geometry categories.
Geometry In Space
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Author : R. C. J. Nixon
language : en
Publisher: Forgotten Books
Release Date : 2015-06-26
Geometry In Space written by R. C. J. Nixon and has been published by Forgotten Books this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-26 with Mathematics categories.
Excerpt from Geometry in Space: Containing Parts of Euclid's Eleventh and Twelfth Books; And Some Properties of Polyhedra and Solids of Revolution, With Exercises This little volume would have had its natural place as Part III of Euclid Revised, had not that Book extended to a quite sufficient size in its present form. But, mindful of the maxim - 'Great book, great evil' - the Editor thought that it would be better to make a separate volume of those parts of Euclid's Eleventh and Twelfth Books, which are, by common consent, desirable for a student; with such analogous additional matter as it might seem advisable to treat from a purely geometrical standpoint. There is too the additional reason for taking this course, that the number of those who extend the study of Geometry from two to three dimensions is few compared with the number who content themselves with what can be done in one plane. No doubt the conception of solid figures, beyond the very simplest, is difficult; and the graphic exhibition of them is perhaps more difficult still. Yet there can be no doubt also that the study of Pure Geometry in Space is of immense value, whether considered as a mental discipline, or with regard to its utility for other purposes. Respecting the range and amount of matter that should be included in a treatise designed to give an introduction to the purely geometrical treatment of figures in space, the Editor has had difficulty in coming to a decision ; and he would put forward what is here given as, to a considerable extent, tentative. Thus, for example, it was originally intended that there should be a separate chapter on Surface Spherics; but, on reflection, it appeared dubious whether such a chapter would not be a 'game not worth the candle'-adding to the expense of the book, and not really wanted. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.