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Geometry

Geometry Book
Author : David A. Brannan,Matthew F. Esplen,Jeremy J. Gray
Publisher : Cambridge University Press
Release : 2011-12-22
ISBN : 1139503707
Language : En, Es, Fr & De

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Book Description :

This richly illustrated and clearly written undergraduate textbook captures the excitement and beauty of geometry. The approach is that of Klein in his Erlangen programme: a geometry is a space together with a set of transformations of the space. The authors explore various geometries: affine, projective, inversive, hyperbolic and elliptic. In each case they carefully explain the key results and discuss the relationships between the geometries. New features in this second edition include concise end-of-chapter summaries to aid student revision, a list of further reading and a list of special symbols. The authors have also revised many of the end-of-chapter exercises to make them more challenging and to include some interesting new results. Full solutions to the 200 problems are included in the text, while complete solutions to all of the end-of-chapter exercises are available in a new Instructors' Manual, which can be downloaded from www.cambridge.org/9781107647831.

Handbook of Differential Geometry

Handbook of Differential Geometry Book
Author : Franki J.E. Dillen,Leopold C.A. Verstraelen
Publisher : Elsevier
Release : 2005-11-29
ISBN : 9780080461205
Language : En, Es, Fr & De

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Book Description :

In the series of volumes which together will constitute the "Handbook of Differential Geometry" we try to give a rather complete survey of the field of differential geometry. The different chapters will both deal with the basic material of differential geometry and with research results (old and recent). All chapters are written by experts in the area and contain a large bibliography. In this second volume a wide range of areas in the very broad field of differential geometry is discussed, as there are Riemannian geometry, Lorentzian geometry, Finsler geometry, symplectic geometry, contact geometry, complex geometry, Lagrange geometry and the geometry of foliations. Although this does not cover the whole of differential geometry, the reader will be provided with an overview of some its most important areas. . Written by experts and covering recent research . Extensive bibliography . Dealing with a diverse range of areas . Starting from the basics

Geometry A Comprehensive Course

Geometry  A Comprehensive Course Book
Author : Dan Pedoe
Publisher : Courier Corporation
Release : 2013-04-02
ISBN : 0486131734
Language : En, Es, Fr & De

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Book Description :

Introduction to vector algebra in the plane; circles and coaxial systems; mappings of the Euclidean plane; similitudes, isometries, Moebius transformations, much more. Includes over 500 exercises.

Stochastic Geometry

Stochastic Geometry Book
Author : David Coupier
Publisher : Springer
Release : 2019-04-09
ISBN : 3030135470
Language : En, Es, Fr & De

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Book Description :

This volume offers a unique and accessible overview of the most active fields in Stochastic Geometry, up to the frontiers of recent research. Since 2014, the yearly meeting of the French research structure GDR GeoSto has been preceded by two introductory courses. This book contains five of these introductory lectures. The first chapter is a historically motivated introduction to Stochastic Geometry which relates four classical problems (the Buffon needle problem, the Bertrand paradox, the Sylvester four-point problem and the bicycle wheel problem) to current topics. The remaining chapters give an application motivated introduction to contemporary Stochastic Geometry, each one devoted to a particular branch of the subject: understanding spatial point patterns through intensity and conditional intensities; stochastic methods for image analysis; random fields and scale invariance; and the theory of Gibbs point processes. Exposing readers to a rich theory, this book will encourage further exploration of the subject and its wide applications.

Nonlinear Computational Geometry

Nonlinear Computational Geometry Book
Author : Ioannis Z. Emiris,Frank Sottile,Thorsten Theobald
Publisher : Springer Science & Business Media
Release : 2009-10-28
ISBN : 1441909990
Language : En, Es, Fr & De

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Book Description :

An original motivation for algebraic geometry was to understand curves and surfaces in three dimensions. Recent theoretical and technological advances in areas such as robotics, computer vision, computer-aided geometric design and molecular biology, together with the increased availability of computational resources, have brought these original questions once more into the forefront of research. One particular challenge is to combine applicable methods from algebraic geometry with proven techniques from piecewise-linear computational geometry (such as Voronoi diagrams and hyperplane arrangements) to develop tools for treating curved objects. These research efforts may be summarized under the term nonlinear computational geometry. This volume grew out of an IMA workshop on Nonlinear Computational Geometry in May/June 2007 (organized by I.Z. Emiris, R. Goldman, F. Sottile, T. Theobald) which gathered leading experts in this emerging field. The research and expository articles in the volume are intended to provide an overview of nonlinear computational geometry. Since the topic involves computational geometry, algebraic geometry, and geometric modeling, the volume has contributions from all of these areas. By addressing a broad range of issues from purely theoretical and algorithmic problems, to implementation and practical applications this volume conveys the spirit of the IMA workshop.

Geometry Intuition and Concepts

Geometry   Intuition and Concepts Book
Author : Jost-Hinrich Eschenburg
Publisher : Springer Nature
Release : 2022-12-02
ISBN : 3658386401
Language : En, Es, Fr & De

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Book Description :

This book deals with the geometry of visual space in all its aspects. As in any branch of mathematics, the aim is to trace the hidden to the obvious; the peculiarity of geometry is that the obvious is sometimes literally before one's eyes.Starting from intuition, spatial concepts are embedded in the pre-existing mathematical framework of linear algebra and calculus. The path from visualization to mathematically exact language is itself the learning content of this book. This is intended to close an often lamented gap in understanding between descriptive preschool and school geometry and the abstract concepts of linear algebra and calculus. At the same time, descriptive geometric modes of argumentation are justified because their embedding in the strict mathematical language has been clarified. The concepts of geometry are of a very different nature; they denote, so to speak, different layers of geometric thinking: some arguments use only concepts such as point, straight line, and incidence, others require angles and distances, still others symmetry considerations. Each of these conceptual fields determines a separate subfield of geometry and a separate chapter of this book, with the exception of the last-mentioned conceptual field "symmetry", which runs through all the others: - Incidence: Projective geometry - Parallelism: Affine geometry - Angle: Conformal Geometry - Distance: Metric Geometry - Curvature: Differential Geometry - Angle as distance measure: Spherical and Hyperbolic Geometry - Symmetry: Mapping Geometry. The mathematical experience acquired in the visual space can be easily transferred to much more abstract situations with the help of the vector space notion. The generalizations beyond the visual dimension point in two directions: Extension of the number concept and transcending the three illustrative dimensions. This book is a translation of the original German 1st edition Geometrie – Anschauung und Begriffe by Jost-Hinrich Eschenburg, published by Springer Fachmedien Wiesbaden GmbH, part of Springer Nature in 2020. The translation was done with the help of artificial intelligence (machine translation by the service DeepL.com). A subsequent human revision was done primarily in terms of content, so that the book will read stylistically differently from a conventional translation. Springer Nature works continuously to further the development of tools for the production of books and on the related technologies to support the authors.

The Wonder Book of Geometry

The Wonder Book of Geometry Book
Author : David Acheson
Publisher : Oxford University Press, USA
Release : 2020-10-14
ISBN : 019884638X
Language : En, Es, Fr & De

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Book Description :

David Acheson transports us into the world of geometry, one of the oldest branches of mathematics. He describes its history, from ancient Greece to the present day, and its emphasis on proofs. With its elegant deduction and practical applications, he demonstrates how geometry offers the quickest route to the spirit of mathematics at its best.

Giordano Bruno and the Geometry of Language

Giordano Bruno and the Geometry of Language Book
Author : Arielle Saiber
Publisher : Routledge
Release : 2017-03-02
ISBN : 1351933671
Language : En, Es, Fr & De

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Book Description :

Giordano Bruno and the Geometry of Language brings to the fore a sixteenth-century philosopher's role in early modern Europe as a bridge between science and literature, or more specifically, between the spatial paradigm of geometry and that of language. Arielle Saiber examines how, to invite what Bruno believed to be an infinite universe-its qualities and vicissitudes-into the world of language, Bruno forged a system of 'figurative' vocabularies: number, form, space, and word. This verbal and symbolic system in which geometric figures are seen to underlie rhetorical figures, is what Saiber calls 'geometric rhetoric.' Through analysis of Bruno's writings, Saiber shows how Bruno's writing necessitates a crafting of space, and is, in essence, a lexicon of spatial concepts. This study constitutes an original contribution both to scholarship on Bruno and to the fields of early modern scientific and literary studies. It also addresses the broader question of what role geometry has in the formation of any language and literature of any place and time.

Commutative Algebra and Noncommutative Algebraic Geometry

Commutative Algebra and Noncommutative Algebraic Geometry Book
Author : David Eisenbud,Srikanth B. Iyengar,Anurag K. Singh,Michel Van den Bergh,J. Toby Stafford
Publisher : Cambridge University Press
Release : 2015-11-19
ISBN : 110714972X
Language : En, Es, Fr & De

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Book Description :

This book surveys fundamental current topics in these two areas of research, emphasising the lively interaction between them. Volume 2 focuses on the most recent research.

Combinatorial Algebraic Geometry

Combinatorial Algebraic Geometry Book
Author : Gregory G. Smith,Bernd Sturmfels
Publisher : Springer
Release : 2017-11-17
ISBN : 1493974866
Language : En, Es, Fr & De

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Book Description :

This volume consolidates selected articles from the 2016 Apprenticeship Program at the Fields Institute, part of the larger program on Combinatorial Algebraic Geometry that ran from July through December of 2016. Written primarily by junior mathematicians, the articles cover a range of topics in combinatorial algebraic geometry including curves, surfaces, Grassmannians, convexity, abelian varieties, and moduli spaces. This book bridges the gap between graduate courses and cutting-edge research by connecting historical sources, computation, explicit examples, and new results.

An Invitation To Noncommutative Geometry

An Invitation To Noncommutative Geometry Book
Author : Matilde Marcolli,Masoud Khalkhali
Publisher : World Scientific
Release : 2008-02-11
ISBN : 9814475629
Language : En, Es, Fr & De

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Book Description :

This is the first existing volume that collects lectures on this important and fast developing subject in mathematics. The lectures are given by leading experts in the field and the range of topics is kept as broad as possible by including both the algebraic and the differential aspects of noncommutative geometry as well as recent applications to theoretical physics and number theory.

Foundations of Three Dimensional Euclidean Geometry

Foundations of Three Dimensional Euclidean Geometry Book
Author : Izu Vaisman
Publisher : CRC Press
Release : 2020-11-25
ISBN : 1000110494
Language : En, Es, Fr & De

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Book Description :

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.

Complex Projective Geometry

Complex Projective Geometry Book
Author : G. Ellingsrud,C. Peskine,G. Sacchiero,S. A. Stromme
Publisher : Cambridge University Press
Release : 1992-07-30
ISBN : 0521433525
Language : En, Es, Fr & De

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Book Description :

A volume of papers describing new methods in algebraic geometry.

Algebraic Geometry and Singularities

Algebraic Geometry and Singularities Book
Author : Antonio Campillo Lopez,Luis Narvaez Macarro
Publisher : Springer Science & Business Media
Release : 1995-01-26
ISBN : 9783764353346
Language : En, Es, Fr & De

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Book Description :

The volume contains both general and research papers. Among the first ones are papers showing recent and original developments or methods in subjects such as resolution of singularities, D-module theory, singularities of maps and geometry of curves. The research papers deal on topics related to, or close to, those listed_above. The contributions are organized in three parts according to their contents. Part I presents a set of papers on resolution of singularities, a topic of renewed activity. It deals with important topics of current interest, such as canonical, algorithmic, combinatorial and graphical procedures (Villamayor, Oka, Marijmin), as well as special results on desingularization in characteristic p (Cossart, Moh), and connections between resolution and structure of the space of arcs through a singularity (Gonz81ez-Sprinberg-Lejeune-Jalabert). Part II contains a series of papers on the study~of singularities and its connections with differential systems and deformation or perturbation theo­ ries. Two expository papers (Maisonobe-Briam;on, :'vlebkhout) describe, in an algebro-geometric way, the interaction between singularities and D-module t.he­ ory including recent progress on Bernstein polynomials and Newton polygon techniques. Geometry of foliations (Henaut, Garcfa-Reguera), polar varieties and stratifications (Hajto) are also topics treated here. Two other papers (Wall, Greuel-Pfister) deal with quasihomogeneous singularities in the contexts of per­ turbations and moduli spaces. Globalization of deformations of singularities (de Jong) and determination of complex topology from the real one (~10nd) com­ plete this series of papers. Part III consists of papers on algebraic geometry of curves and surfaces.

Advances in Geometry and Lie Algebras from Supergravity

Advances in Geometry and Lie Algebras from Supergravity Book
Author : Pietro Giuseppe Frè
Publisher : Springer
Release : 2018-02-24
ISBN : 3319744917
Language : En, Es, Fr & De

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Book Description :

This book aims to provide an overview of several topics in advanced differential geometry and Lie group theory, all of them stemming from mathematical problems in supersymmetric physical theories. It presents a mathematical illustration of the main development in geometry and symmetry theory that occurred under the fertilizing influence of supersymmetry/supergravity. The contents are mainly of mathematical nature, but each topic is introduced by historical information and enriched with motivations from high energy physics, which help the reader in getting a deeper comprehension of the subject.

Differential Geometry and Relativity Theory

Differential Geometry and Relativity Theory Book
Author : RichardL. Faber
Publisher : Routledge
Release : 2017-10-19
ISBN : 1351455141
Language : En, Es, Fr & De

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Book Description :

Differentilil Geometry and Relativity Theory: An Introduction approaches relativity asa geometric theory of space and time in which gravity is a manifestation of space-timecurvature, rathe1 than a force. Uniting differential geometry and both special and generalrelativity in a single source, this easy-to-understand text opens the general theory of relativityto mathematics majors having a backgr.ound only in multivariable calculus and linearalgebra.The book offers a broad overview of the physical foundations and mathematical details ofrelativity, and presents concrete physical interpretations of numerous abstract concepts inRiemannian geometry. The work is profusely illustrated with diagrams aiding in the understandingof proofs and explanations. Appendices feature important material on vectoranalysis and hyperbolic functions.Differential Geometry and Relativity Theory: An Introduction serves as the ideal textfor high-level undergraduate couues in mathematics and physics, and includes a solutionsmanual augmenting classroom study. It is an invaluable reference for mathematicians interestedin differential and IUemannian geometry, or the special and general theories ofrelativity

Introduction to Geometric Computing

Introduction to Geometric Computing Book
Author : Sherif Ghali
Publisher : Springer Science & Business Media
Release : 2008-07-05
ISBN : 1848001150
Language : En, Es, Fr & De

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Book Description :

Computing is quickly making much of geometry intriguing not only for philosophers and mathematicians, but also for scientists and engineers. What is the core set of topics that a practitioner needs to study before embarking on the design and implementation of a geometric system in a specialized discipline? This book attempts to find the answer. Every programmer tackling a geometric computing problem encounters design decisions that need to be solved. This book reviews the geometric theory then applies it in an attempt to find that elusive "right" design.

Geometry and Algebra in Ancient Civilizations

Geometry and Algebra in Ancient Civilizations Book
Author : Bartel L. van der Waerden
Publisher : Springer Science & Business Media
Release : 2012-12-06
ISBN : 3642617794
Language : En, Es, Fr & De

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Book Description :

Originally, my intention was to write a "History of Algebra", in two or three volumes. In preparing the first volume I saw that in ancient civiliza tions geometry and algebra cannot well be separated: more and more sec tions on ancient geometry were added. Hence the new title of the book: "Geometry and Algebra in Ancient Civilizations". A subsequent volume on the history of modem algebra is in preparation. It will deal mainly with field theory, Galois theory and theory of groups. I want to express my deeply felt gratitude to all those who helped me in shaping this volume. In particular, I want to thank Donald Blackmore Wagner (Berkeley) who put at my disposal his English translation of the most interesting parts of the Chinese "Nine Chapters of the Art of Arith metic" and of Liu Hui's commentary to this classic, and also Jacques Se siano (Geneva), who kindly allowed me to use his translation of the re cently discovered Arabic text of four books of Diophantos not extant in Greek. Warm thanks are also due to Wyllis Bandler (Colchester, England) who read my English text very carefully and suggested several improve ments, and to Annemarie Fellmann (Frankfurt) and Erwin Neuenschwan der (Zurich) who helped me in correcting the proof sheets. Miss Fellmann also typed the manuscript and drew the figures. I also want to thank the editorial staff and production department of Springer-Verlag for their nice cooperation.

Analytic Geometry

Analytic Geometry Book
Author : Murray H. Protter,Charles Bradfield Morrey
Publisher : Unknown
Release : 1966
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Analytic Geometry book written by Murray H. Protter,Charles Bradfield Morrey, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

The Teaching of Geometry

The Teaching of Geometry Book
Author : National Council of Teachers of Mathematics
Publisher : Unknown
Release : 1966
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download The Teaching of Geometry book written by National Council of Teachers of Mathematics, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.