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Perspectives on Projective Geometry

Perspectives on Projective Geometry PDF Author: Jürgen Richter-Gebert
Publisher: Springer
ISBN: 9783642172854
Category : Mathematics
Languages : en
Pages : 571

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Book Description
Projective geometry is one of the most fundamental and at the same time most beautiful branches of geometry. It can be considered the common foundation of many other geometric disciplines like Euclidean geometry, hyperbolic and elliptic geometry or even relativistic space-time geometry. This book offers a comprehensive introduction to this fascinating field and its applications. In particular, it explains how metric concepts may be best understood in projective terms. One of the major themes that appears throughout this book is the beauty of the interplay between geometry, algebra and combinatorics. This book can especially be used as a guide that explains how geometric objects and operations may be most elegantly expressed in algebraic terms, making it a valuable resource for mathematicians, as well as for computer scientists and physicists. The book is based on the author’s experience in implementing geometric software and includes hundreds of high-quality illustrations.

Perspectives on Projective Geometry

Perspectives on Projective Geometry PDF Author: Jürgen Richter-Gebert
Publisher: Springer
ISBN: 9783642172854
Category : Mathematics
Languages : en
Pages : 571

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Book Description
Projective geometry is one of the most fundamental and at the same time most beautiful branches of geometry. It can be considered the common foundation of many other geometric disciplines like Euclidean geometry, hyperbolic and elliptic geometry or even relativistic space-time geometry. This book offers a comprehensive introduction to this fascinating field and its applications. In particular, it explains how metric concepts may be best understood in projective terms. One of the major themes that appears throughout this book is the beauty of the interplay between geometry, algebra and combinatorics. This book can especially be used as a guide that explains how geometric objects and operations may be most elegantly expressed in algebraic terms, making it a valuable resource for mathematicians, as well as for computer scientists and physicists. The book is based on the author’s experience in implementing geometric software and includes hundreds of high-quality illustrations.

Projective Geometry

Projective Geometry PDF Author: H.S.M. Coxeter
Publisher: Springer Science & Business Media
ISBN: 9780387406237
Category : Mathematics
Languages : en
Pages : 162

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Book Description
In Euclidean geometry, constructions are made with ruler and compass. Projective geometry is simpler: its constructions require only a ruler. In projective geometry one never measures anything, instead, one relates one set of points to another by a projectivity. The first two chapters of this book introduce the important concepts of the subject and provide the logical foundations. The third and fourth chapters introduce the famous theorems of Desargues and Pappus. Chapters 5 and 6 make use of projectivities on a line and plane, respectively. The next three chapters develop a self-contained account of von Staudt's approach to the theory of conics. The modern approach used in that development is exploited in Chapter 10, which deals with the simplest finite geometry that is rich enough to illustrate all the theorems nontrivially. The concluding chapters show the connections among projective, Euclidean, and analytic geometry.

Perspective and Projective Geometries

Perspective and Projective Geometries PDF Author: James C. Morehead
Publisher:
ISBN:
Category : Geometry, Projective
Languages : en
Pages : 25

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Lumen Naturae

Lumen Naturae PDF Author: Matilde Marcolli
Publisher: MIT Press
ISBN: 0262358328
Category : Mathematics
Languages : en
Pages : 400

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Book Description
Exploring common themes in modern art, mathematics, and science, including the concept of space, the notion of randomness, and the shape of the cosmos. This is a book about art—and a book about mathematics and physics. In Lumen Naturae (the title refers to a purely immanent, non-supernatural form of enlightenment), mathematical physicist Matilde Marcolli explores common themes in modern art and modern science—the concept of space, the notion of randomness, the shape of the cosmos, and other puzzles of the universe—while mapping convergences with the work of such artists as Paul Cezanne, Mark Rothko, Sol LeWitt, and Lee Krasner. Her account, focusing on questions she has investigated in her own scientific work, is illustrated by more than two hundred color images of artworks by modern and contemporary artists. Thus Marcolli finds in still life paintings broad and deep philosophical reflections on space and time, and connects notions of space in mathematics to works by Paul Klee, Salvador Dalí, and others. She considers the relation of entropy and art and how notions of entropy have been expressed by such artists as Hans Arp and Fernand Léger; and traces the evolution of randomness as a mode of artistic expression. She analyzes the relation between graphical illustration and scientific text, and offers her own watercolor-decorated mathematical notebooks. Throughout, she balances discussions of science with explorations of art, using one to inform the other. (She employs some formal notation, which can easily be skipped by general readers.) Marcolli is not simply explaining art to scientists and science to artists; she charts unexpected interdependencies that illuminate the universe.

Handbook of Mathematics

Handbook of Mathematics PDF Author: Vialar Thierry
Publisher: BoD - Books on Demand
ISBN: 295519901X
Category :
Languages : en
Pages : 1132

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Book Description
The book consists of XI Parts and 28 Chapters covering all areas of mathematics. It is a tool for students, scientists, engineers, students of many disciplines, teachers, professionals, writers and also for a general reader with an interest in mathematics and in science. It provides a wide range of mathematical concepts, definitions, propositions, theorems, proofs, examples, and numerous illustrations. The difficulty level can vary depending on chapters, and sustained attention will be required for some. The structure and list of Parts are quite classical: I. Foundations of Mathematics, II. Algebra, III. Number Theory, IV. Geometry, V. Analytic Geometry, VI. Topology, VII .Algebraic Topology, VIII. Analysis, IX. Category Theory, X. Probability and Statistics, XI. Applied Mathematics. Appendices provide useful lists of symbols and tables for ready reference. The publisher’s hope is that this book, slightly revised and in a convenient format, will serve the needs of readers, be it for study, teaching, exploration, work, or research.

The Beauty of Physics: Patterns, Principles, and Perspectives

The Beauty of Physics: Patterns, Principles, and Perspectives PDF Author: A. R. P. Rau
Publisher: OUP Oxford
ISBN: 0191019887
Category : Science
Languages : en
Pages : 256

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Book Description
The beauty of physics lies in its coherence in terms of a few fundamental concepts and principles. Even physicists have occasion to marvel at the overarching reach of basic principles and their ability to account for features stretching from the microscopic sub-atomic world to the cosmological expanses of the Universe. While mathematics is its natural language, physics is mostly about patterns, connections, and relations between objects and phenomena, and it is this aspect that is emphasized in this book. Since science tries to connect phenomena that at first sight appear widely different, while boiling them down to a small set of essential principles and laws, metaphor and analogy pervade our subject. Consider the pendulum, its swing from one extreme to the other often invoked in social or economic contexts. In molecular vibrations, such as in the CO2 molecule, the quantum motions of electrons and nuclei are metaphorically the pendulums. In electromagnetic radiation, including the visible light we observe, there are not even any concrete material particles, only electric and magnetic fields executing simple harmonic motion. But, to a physicist, they are all "just a pendulum". The selection of topics reflects the author's own four-decade career in research physics and his resultant perspective on the subject. While aimed primarily at physicists, including junior students, this book also addresses other readers who are willing to think with symbols and simple algebra in understanding the physical world around us. Each chapter, on themes such as dimensions, transformations, symmetries, or maps, begins with simple examples accessible to all while connecting them later to more sophisticated realizations in more advanced topics of physics.

Martin Kneser Collected Works

Martin Kneser Collected Works PDF Author: Ulf Rehmann
Publisher: Birkhäuser
ISBN: 9783030816247
Category : Mathematics
Languages : en
Pages : 749

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Book Description
This volume presents the collection of mathematical articles by Martin Kneser, reprinted in the original language – mostly German –, including one yet unpublished. Moreover, also included is an article by Raman Parimala, discussing Kneser’s work concerning algebraic groups and the Hasse principle, which has been written especially for this volume, as well as an article by Rudolf Scharlau about Kneser’s work on quadratic forms, published elsewhere before. Another commentary article, written by Günter M. Ziegler especially for this volume, describes the astounding influence on the field of combinatorics of what was published as “Aufgabe 360” and its subsequent solution in 1955 resp. 1957 in the “Jahresbericht der Deutschen Mathematiker-Vereinigung”. However, as the titles of the articles show, Kneser’s mathematical interests were much broader, which is beautifully discussed in an obituary by Ulrich Stuhler, included as well in this volume.

Handbook of Geometric Constraint Systems Principles

Handbook of Geometric Constraint Systems Principles PDF Author: Meera Sitharam
Publisher: CRC Press
ISBN: 1351647431
Category : Mathematics
Languages : en
Pages : 578

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Book Description
The Handbook of Geometric Constraint Systems Principles is an entry point to the currently used principal mathematical and computational tools and techniques of the geometric constraint system (GCS). It functions as a single source containing the core principles and results, accessible to both beginners and experts. The handbook provides a guide for students learning basic concepts, as well as experts looking to pinpoint specific results or approaches in the broad landscape. As such, the editors created this handbook to serve as a useful tool for navigating the varied concepts, approaches and results found in GCS research. Key Features: A comprehensive reference handbook authored by top researchers Includes fundamentals and techniques from multiple perspectives that span several research communities Provides recent results and a graded program of open problems and conjectures Can be used for senior undergraduate or graduate topics course introduction to the area Detailed list of figures and tables About the Editors: Meera Sitharam is currently an Associate Professor at the University of Florida’s Department of Computer & Information Science and Engineering. She received her Ph.D. at the University of Wisconsin, Madison. Audrey St. John is an Associate Professor of Computer Science at Mount Holyoke College, who received her Ph. D. from UMass Amherst. Jessica Sidman is a Professor of Mathematics on the John S. Kennedy Foundation at Mount Holyoke College. She received her Ph.D. from the University of Michigan.

The Principles of Projective Geometry

The Principles of Projective Geometry PDF Author:
Publisher: CUP Archive
ISBN:
Category :
Languages : en
Pages :

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Synthetic Projective Geometry

Synthetic Projective Geometry PDF Author: George Bruce Halsted
Publisher:
ISBN:
Category : Geometry, Projective
Languages : en
Pages : 62

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