Download or read book Metrical Geometry written by George Bruce Halsted and published by . This book was released on 1881 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Course in Metric Geometry written by Dmitri Burago and published by American Mathematical Society. This book was released on 2022-01-27 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: “Metric geometry” is an approach to geometry based on the notion of length on a topological space. This approach experienced a very fast development in the last few decades and penetrated into many other mathematical disciplines, such as group theory, dynamical systems, and partial differential equations. The objective of this graduate textbook is twofold: to give a detailed exposition of basic notions and techniques used in the theory of length spaces, and, more generally, to offer an elementary introduction into a broad variety of geometrical topics related to the notion of distance, including Riemannian and Carnot-Carathéodory metrics, the hyperbolic plane, distance-volume inequalities, asymptotic geometry (large scale, coarse), Gromov hyperbolic spaces, convergence of metric spaces, and Alexandrov spaces (non-positively and non-negatively curved spaces). The authors tend to work with “easy-to-touch” mathematical objects using “easy-to-visualize” methods. The authors set a challenging goal of making the core parts of the book accessible to first-year graduate students. Most new concepts and methods are introduced and illustrated using simplest cases and avoiding technicalities. The book contains many exercises, which form a vital part of the exposition.
Download or read book A Course in Metric Geometry written by Dmitri Burago and published by American Mathematical Soc.. This book was released on 2001 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Metric geometry" is an approach to geometry based on the notion of length on a topological space. This approach experienced a very fast development in the last few decades and penetrated into many other mathematical disciplines, such as group theory, dynamical systems, and partial differential equations. The objective of this graduate textbook is twofold: to give a detailed exposition of basic notions and techniques used in the theory of length spaces, and, more generally, to offer an elementary introduction into a broad variety of geometrical topics related to the notion of distance, including Riemannian and Carnot-Caratheodory metrics, the hyperbolic plane, distance-volume inequalities, asymptotic geometry (large scale, coarse), Gromov hyperbolic spaces, convergence of metric spaces, and Alexandrov spaces (non-positively and non-negatively curved spaces).
Download or read book An Elementary Treatise on Mensuration written by George Bruce Halsted and published by . This book was released on 1881 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Geometry written by Richard S. Millman and published by Springer Science & Business Media. This book was released on 1993-05-07 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometry: A Metric Approach with Models, imparts a real feeling for Euclidean and non-Euclidean (in particular, hyperbolic) geometry. Intended as a rigorous first course, the book introduces and develops the various axioms slowly, and then, in a departure from other texts, continually illustrates the major definitions and axioms with two or three models, enabling the reader to picture the idea more clearly. The second edition has been expanded to include a selection of expository exercises. Additionally, the authors have designed software with computational problems to accompany the text. This software may be obtained from George Parker.
Download or read book Geometry written by R.S. Millman and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended as a first rigorous course in geometry. As the title indicates, we have adopted Birkhoff's metric approach (i.e., through use of real numbers) rather than Hilbert's synthetic approach to the subject. Throughout the text we illustrate the various axioms, definitions, and theorems with models ranging from the familiar Cartesian plane to the Poincare upper half plane, the Taxicab plane, and the Moulton plane. We hope that through an intimate acquaintance with examples (and a model is just an example), the reader will obtain a real feeling and intuition for non Euclidean (and in particular, hyperbolic) geometry. From a pedagogical viewpoint this approach has the advantage of reducing the reader's tendency to reason from a picture. In addition, our students have found the strange new world of the non-Euclidean geometries both interesting and exciting. Our basic approach is to introduce and develop the various axioms slowly, and then, in a departure from other texts, illustrate major definitions and axioms with two or three models. This has the twin advantages of showing the richness of the concept being discussed and of enabling the reader to picture the idea more clearly. Furthermore, encountering models which do not satisfy the axiom being introduced or the hypothesis of the theorem being proved often sheds more light on the relevant concept than a myriad of cases which do.
Download or read book An Essay on the Foundations of Geometry written by Bertrand Russell and published by . This book was released on 1897 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Metrical Geometry written by George Bruce Halsted and published by Forgotten Books. This book was released on 2017-09-16 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from Metrical Geometry: An Elementary Treatise on Mensuration Mensuration is that branch of mathematics Which has for its object the measurement Of geometrical magnitudes. It has been called, that branch Of applied geometry which gives rules for finding the length Of lines, the area Of sur faces, and the volume Of solids, from certain data Of lines and angles. A Magnitude is anything Which can be conceived of as added to itself, or of Which we can form multiples. The measurement Of a magnitude consists in finding how many times it contains another magnitude Of the same kind, taken as a unit of measure. Measurement, then, is the pro cess of ascertaining the ratio which one magnitude bears to some other chosen as the standard; and the measure of a magnitude is this ratio expressed in numbers. Hence, We must refer to some concrete standard, some actual Object, to give our measures their absolute meaning. The concrete standard is arbitrary in point of theory, and its selection a question Of practical convenience. A discrete aggregate, such as a pile of cannon-balls, or a number, has a natural unit, one of them. 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.
Download or read book Metrical Geometry written by George Bruce Halsted and published by . This book was released on 1883 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On Certain Properties of the Metrical and Generalized Metrical Groups in Linear Spaces of N Dimensions written by Sergei Alexander Schelkunoff and published by . This book was released on 1927 with total page 58 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Projective Geometry written by T. Ewan Faulkner and published by Courier Corporation. This book was released on 2013-02-20 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: Highlighted by numerous examples, this book explores methods of the projective geometry of the plane. Examines the conic, the general equation of the 2nd degree, and the relationship between Euclidean and projective geometry. 1960 edition.
Download or read book Geometry and Chronometry in Philosophical Perspective written by Adolf Grunbaum and published by U of Minnesota Press. This book was released on 1968-06-01 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometry and Chronometry in Philosophical Perspective was first published in 1968. Minnesota Archive Editions uses digital technology to make long-unavailable books once again accessible, and are published unaltered from the original University of Minnesota Press editions. In this volume Professor Grünbaum substantially extends and comments upon his essay "Geometry, Chronometry, and Empiricism," which was first published in Volume III of the Minnesota Studies in the Philosophy of Science. Commenting on the essay when it first appeared J. J. C. Smart wrote in Mind (England): "In my opinion Adolf Grünbaum's paper ... supersedes nearly all that has been written on the logical status of physical geometry and chronometry." The full text of the essay is given here with the author's extension of it and his discussion of some of the critical comment it has evoked, particularly, a critique published by Hilary Putnam. Adolph Grünbaum is Andrew Mellon Professor of Philosophy at the University of Pittsburgh and the current president of the Philosophy of Science Association.
Download or read book Metrical Geometry written by George Bruce Halsted and published by Forgotten Books. This book was released on 2015-06-26 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from Metrical Geometry: An Elementary Treatise on Mensuration This book is primarily the outcome of work on the subject while teaching it to large classes. The competent critic may recognize signs of a Berlin residence; but a considerable part, it is believed, is entirely new. Special mention must be made of the book's indebtedness to Dr. J. W. Davis, a classmate with me at Columbia School of Mines; also to Prof. G. A. Wentworth, who has kindly looked over the proofs. But if the book be found especially accurate, this is due to the pains taking care of my friend H. B. Fine, Fellow of Princeton. Any corrections or suggestions relating to the work will be thank fully received. 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.
Download or read book The Axioms of Descriptive Geometry written by Alfred North Whitehead and published by . This book was released on 1907 with total page 74 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Pure Metric Geometry written by Anton Petrunin and published by Springer. This book was released on 2023-11-19 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book serves as an introductory asset for learning metric geometry by delivering an in-depth examination of key constructions and providing an analysis of universal spaces, injective spaces, the Gromov-Hausdorff convergence, and ultralimits. This book illustrates basic examples of domestic affairs of metric spaces, this includes Alexandrov geometry, geometric group theory, metric-measure spaces and optimal transport. Researchers in metric geometry will find this book appealing and helpful, in addition to graduate students in mathematics, and advanced undergraduate students in need of an introduction to metric geometry. Any previous knowledge of classical geometry, differential geometry, topology, and real analysis will be useful in understanding the presented topics.
Download or read book Russell s Philosophy of Logical Analysis 1897 1905 written by J. Galaugher and published by Springer. This book was released on 2013-11-07 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: This systematic and historical treatment of Russell's contributions to analytic philosophy, from his embrace of analysis in 1898 to his landmark theory of descriptions in 1905, draws important connections between his philosophically motivated conception of analysis and the technical apparatus he devised to facilitate analyses in mathematics
Download or read book Anachronisms in the History of Mathematics written by Niccol- Guicciardini and published by Cambridge University Press. This book was released on 2021-07-22 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discover essays by leading scholars on the history of mathematics from ancient to modern times in European and non-European cultures.
