Eighteen Essays In Non Euclidean Geometry
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Eighteen Essays In Non Euclidean Geometry
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Author : Vincent Alberge
language : en
Publisher:
Release Date : 2019
Eighteen Essays In Non Euclidean Geometry written by Vincent Alberge and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with categories.
18 Unconventional Essays On The Nature Of Mathematics
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Author : Reuben Hersh
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-01-16
18 Unconventional Essays On The Nature Of Mathematics written by Reuben Hersh 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 2006-01-16 with Mathematics categories.
Collection of the most interesting recent writings on the philosophy of mathematics written by highly respected researchers from philosophy, mathematics, physics, and chemistry Interdisciplinary book that will be useful in several fields—with a cross-disciplinary subject area, and contributions from researchers of various disciplines
Mathematical Geography In The Eighteenth Century Euler Lagrange And Lambert
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Author : Renzo Caddeo
language : en
Publisher: Springer Nature
Release Date : 2022-10-31
Mathematical Geography In The Eighteenth Century Euler Lagrange And Lambert written by Renzo Caddeo and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-10-31 with Mathematics categories.
This volume presents the beautiful memoirs of Euler, Lagrange and Lambert on geography, translated into English and put into perspective through explanatory and historical essays as well as commentaries and mathematical notes. These works had a major impact on the development of the differential geometry of surfaces and they deserve to be studied, not only as historical documents, but most of all as a rich source of ideas.
Topological Differential And Conformal Geometry Of Surfaces
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Author : Norbert A'Campo
language : en
Publisher: Springer Nature
Release Date : 2021-10-27
Topological Differential And Conformal Geometry Of Surfaces written by Norbert A'Campo and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-27 with Mathematics categories.
This book provides an introduction to the main geometric structures that are carried by compact surfaces, with an emphasis on the classical theory of Riemann surfaces. It first covers the prerequisites, including the basics of differential forms, the Poincaré Lemma, the Morse Lemma, the classification of compact connected oriented surfaces, Stokes’ Theorem, fixed point theorems and rigidity theorems. There is also a novel presentation of planar hyperbolic geometry. Moving on to more advanced concepts, it covers topics such as Riemannian metrics, the isometric torsion-free connection on vector fields, the Ansatz of Koszul, the Gauss–Bonnet Theorem, and integrability. These concepts are then used for the study of Riemann surfaces. One of the focal points is the Uniformization Theorem for compact surfaces, an elementary proof of which is given via a property of the energy functional. Among numerous other results, there is also a proof of Chow’s Theorem on compact holomorphic submanifolds in complex projective spaces. Based on lecture courses given by the author, the book will be accessible to undergraduates and graduates interested in the analytic theory of Riemann surfaces.
Circles Spheres And Spherical Geometry
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Author : Hiroshi Maehara
language : en
Publisher: Springer Nature
Release Date : 2024-08-09
Circles Spheres And Spherical Geometry written by Hiroshi Maehara and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-08-09 with Mathematics categories.
This textbook focuses on the geometry of circles, spheres, and spherical geometry. Various classic themes are used as introductory and motivating topics. The book begins very simply for the reader in the first chapter discussing the notions of inversion and stereographic projection. Here, various classical topics and theorems such as Steiner cycles, inversion, Soddy's hexlet, stereographic projection and Poncelet's porism are discussed. The book then delves into Bend formulas and the relation of radii of circles, focusing on Steiner circles, mutually tangent four circles in the plane and other related notions. Next, some fundamental concepts of graph theory are explained. The book then proceeds to explore orthogonal-cycle representation of quadrangulations, giving detailed discussions of the Brightwell-Scheinerman theorem (an extension of the Koebe-Andreev-Thurston theorem), Newton’s 13-balls-problem, Casey’s theorem (an extension of Ptolemy’s theorem) and its generalizations. The remainder of the book is devoted to spherical geometry including a chapter focusing on geometric probability on the sphere. The book also contains new results of the authors and insightful notes on the existing literature, bringing the reader closer to the research front. Each chapter concludes with related exercises of varying levels of difficulty. Solutions to selected exercises are provided. This book is suitable to be used as textbook for a geometry course or alternatively as basis for a seminar for both advanced undergraduate and graduate students alike.
In The Tradition Of Thurston
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Author : Ken’ichi Ohshika
language : en
Publisher: Springer Nature
Release Date : 2020-12-07
In The Tradition Of Thurston written by Ken’ichi Ohshika and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-07 with Mathematics categories.
This book consists of 16 surveys on Thurston's work and its later development. The authors are mathematicians who were strongly influenced by Thurston's publications and ideas. The subjects discussed include, among others, knot theory, the topology of 3-manifolds, circle packings, complex projective structures, hyperbolic geometry, Kleinian groups, foliations, mapping class groups, Teichmüller theory, anti-de Sitter geometry, and co-Minkowski geometry. The book is addressed to researchers and students who want to learn about Thurston’s wide-ranging mathematical ideas and their impact. At the same time, it is a tribute to Thurston, one of the greatest geometers of all time, whose work extended over many fields in mathematics and who had a unique way of perceiving forms and patterns, and of communicating and writing mathematics.
Convexity From The Geometric Point Of View
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Author : Vitor Balestro
language : en
Publisher: Springer Nature
Release Date : 2024-07-14
Convexity From The Geometric Point Of View written by Vitor Balestro and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-14 with Mathematics categories.
This text gives a comprehensive introduction to the “common core” of convex geometry. Basic concepts and tools which are present in all branches of that field are presented with a highly didactic approach. Mainly directed to graduate and advanced undergraduates, the book is self-contained in such a way that it can be read by anyone who has standard undergraduate knowledge of analysis and of linear algebra. Additionally, it can be used as a single reference for a complete introduction to convex geometry, and the content coverage is sufficiently broad that the reader may gain a glimpse of the entire breadth of the field and various subfields. The book is suitable as a primary text for courses in convex geometry and also in discrete geometry (including polytopes). It is also appropriate for survey type courses in Banach space theory, convex analysis, differential geometry, and applications of measure theory. Solutions to all exercises are available to instructors who adopt the text for coursework. Most chapters use the same structure with the first part presenting theory and the next containing a healthy range of exercises. Some of the exercises may even be considered as short introductions to ideas which are not covered in the theory portion. Each chapter has a notes section offering a rich narrative to accompany the theory, illuminating the development of ideas, and providing overviews to the literature concerning the covered topics. In most cases, these notes bring the reader to the research front. The text includes many figures that illustrate concepts and some parts of the proofs, enabling the reader to have a better understanding of the geometric meaning of the ideas. An appendix containing basic (and geometric) measure theory collects useful information for convex geometers.
Dynamics Of Discrete Group Action
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Author : Boris N. Apanasov
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2024-07-22
Dynamics Of Discrete Group Action written by Boris N. Apanasov and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-22 with Mathematics categories.
Provides the first systematic study of geometry and topology of locally symmetric rank one manifolds and dynamics of discrete action of their fundamental groups. In addition to geometry and topology, this study involves several other areas of Mathematics – from algebra of varieties of groups representations and geometric group theory, to geometric analysis including classical questions from function theory.
Mus Mathematimus Hyperelliptical Geometry
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Author : Stenio Musich
language : en
Publisher: Stenio Musich
Release Date : 2024-03-25
Mus Mathematimus Hyperelliptical Geometry written by Stenio Musich and has been published by Stenio Musich this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-03-25 with Mathematics categories.
M.U.S. (Mathematical Uniform Space) is a new number of π (pi), representing the reality of the Universe in which we live. With this number, we created a new geometry, Hyperelliptical Geometry, which will provide the unification of physics, thus uniting the Theory of Relativity and Quantum Theory. A new geometry for a new Mathematics and a new Physics. (ISBN 978-65-00-98107-0).
Conformally Invariant Metrics And Quasiconformal Mappings
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Author : Parisa Hariri
language : en
Publisher: Springer Nature
Release Date : 2020-04-11
Conformally Invariant Metrics And Quasiconformal Mappings written by Parisa Hariri and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-11 with Mathematics categories.
This book is an introduction to the theory of quasiconformal and quasiregular mappings in the euclidean n-dimensional space, (where n is greater than 2). There are many ways to develop this theory as the literature shows. The authors' approach is based on the use of metrics, in particular conformally invariant metrics, which will have a key role throughout the whole book. The intended readership consists of mathematicians from beginning graduate students to researchers. The prerequisite requirements are modest: only some familiarity with basic ideas of real and complex analysis is expected.