The Beauty of Geometry

Twelve Essays

Author: H. S. M. Coxeter,Harold Scott Macdonald Coxeter

Publisher: Courier Corporation

ISBN: 0486409198

Category: Mathematics

Page: 274

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Absorbing essays demonstrate the charms of mathematics. Stimulating and thought-provoking treatment of geometry's crucial role in a wide range of mathematical applications, for students and mathematicians.

Beautiful Geometry

Author: Eli Maor,Eugen Jost

Publisher: Princeton University Press

ISBN: 1400848334

Category: Mathematics

Page: 208

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If you've ever thought that mathematics and art don't mix, this stunning visual history of geometry will change your mind. As much a work of art as a book about mathematics, Beautiful Geometry presents more than sixty exquisite color plates illustrating a wide range of geometric patterns and theorems, accompanied by brief accounts of the fascinating history and people behind each. With artwork by Swiss artist Eugen Jost and text by math historian Eli Maor, this unique celebration of geometry covers numerous subjects, from straightedge-and-compass constructions to intriguing configurations involving infinity. The result is a delightful and informative illustrated tour through the 2,500-year-old history of one of the most important branches of mathematics.

Shapes, Space, and Symmetry

Author: Alan Holden

Publisher: Courier Corporation

ISBN: 9780486268514

Category: Mathematics

Page: 200

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Explains structure of nine regular solids and many semiregular solids and demonstrates how they can be used to explain mathematics. Instructions for cardboard models. Over 300 illustrations. 1971 edition.

King of Infinite Space

Donald Coxeter, the Man Who Saved Geometry

Author: Siobhan Roberts

Publisher: Bloomsbury Publishing USA

ISBN: 9780802718327

Category: Biography & Autobiography

Page: 416

View: 8301

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"There is perhaps no better way to prepare for the scientific breakthroughs of tomorrow than to learn the language of geometry." -Brian Greene, author of The Elegant Universe The word "geometry" brings to mind an array of mathematical images: circles, triangles, the Pythagorean Theorem. Yet geometry is so much more than shapes and numbers; indeed, it governs much of our lives-from architecture and microchips to car design, animated movies, the molecules of food, even our own body chemistry. And as Siobhan Roberts elegantly conveys in The King of Infinite Space, there can be no better guide to the majesty of geometry than Donald Coxeter, perhaps the greatest geometer of the twentieth century. Many of the greatest names in intellectual history-Pythagoras, Plato, Archimedes, Euclid- were geometers, and their creativity and achievements illuminate those of Coxeter, revealing geometry to be a living, ever-evolving endeavor, an intellectual adventure that has always been a building block of civilization. Coxeter's special contributions-his famed Coxeter groups and Coxeter diagrams-have been called by other mathematicians "tools as essential as numbers themselves," but his greatest achievement was to almost single-handedly preserve the tradition of classical geometry when it was under attack in a mathematical era that valued all things austere and rational. Coxeter also inspired many outside the field of mathematics. Artist M. C. Escher credited Coxeter with triggering his legendary Circle Limit patterns, while futurist/inventor Buckminster Fuller acknowledged that his famed geodesic dome owed much to Coxeter's vision. The King of Infinite Space is an elegant portal into the fascinating, arcane world of geometry.

Perspectives on Projective Geometry

A Guided Tour Through Real and Complex Geometry

Author: Jürgen Richter-Gebert

Publisher: Springer Science & Business Media

ISBN: 9783642172861

Category: Mathematics

Page: 571

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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.

Excursions in Geometry

Author: Charles Stanley Ogilvy

Publisher: Courier Corporation

ISBN: 0486265307

Category: Mathematics

Page: 178

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A straightedge, compass, and a little thought are all that's needed to discover the intellectual excitement of geometry. Harmonic division and Apollonian circles, inversive geometry, hexlet, Golden Section, more. 132 illustrations.

Geometry and the Visual Arts

Author: Daniel Pedoe

Publisher: Courier Corporation

ISBN: 9780486244587

Category: Mathematics

Page: 296

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This survey traces the effects of geometry on artistic achievement and clearly discusses its importance to artists and scientists. It also surveys projective geometry, mathematical curves, theories of perspective, architectural form, and concepts of space.

Geometry: A Comprehensive Course

Author: Dan Pedoe

Publisher: Courier Corporation

ISBN: 0486131734

Category: Mathematics

Page: 464

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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.

The Real Projective Plane

Author: H.S.M. Coxeter

Publisher: Springer Science & Business Media

ISBN: 1461227348

Category: Mathematics

Page: 227

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Along with many small improvements, this revised edition contains van Yzeren's new proof of Pascal's theorem (§1.7) and, in Chapter 2, an improved treatment of order and sense. The Sylvester-Gallai theorem, instead of being introduced as a curiosity, is now used as an essential step in the theory of harmonic separation (§3.34). This makes the logi cal development self-contained: the footnotes involving the References (pp. 214-216) are for comparison with earlier treatments, and to give credit where it is due, not to fill gaps in the argument. H.S.M.C. November 1992 v Preface to the Second Edition Why should one study the real plane? To this question, put by those who advocate the complex plane, or geometry over a general field, I would reply that the real plane is an easy first step. Most of the prop erties are closely analogous, and the real field has the advantage of intuitive accessibility. Moreover, real geometry is exactly what is needed for the projective approach to non· Euclidean geometry. Instead of introducing the affine and Euclidean metrics as in Chapters 8 and 9, we could just as well take the locus of 'points at infinity' to be a conic, or replace the absolute involution by an absolute polarity.

A Modern View of Geometry

Author: Leonard M. Blumenthal

Publisher: Courier Dover Publications

ISBN: 0486821137

Category: Mathematics

Page: 208

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Elegant exposition of postulation geometry of planes offers rigorous, lucid treatment of coordination of affine and projective planes, set theory, propositional calculus, affine planes with Desargues and Pappus properties, more. 1961 edition.

Famous Problems of Geometry and How to Solve Them

Author: Benjamin Bold

Publisher: Courier Corporation

ISBN: 0486137635

Category: Science

Page: 144

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Delve into the development of modern mathematics and match wits with Euclid, Newton, Descartes, and others. Each chapter explores an individual type of challenge, with commentary and practice problems. Solutions.

Proof in Geometry

With "Mistakes in Geometric Proofs"

Author: A. I. Fetisov,Ya. S. Dubnov

Publisher: Courier Corporation

ISBN: 0486154920

Category: Mathematics

Page: 128

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This single-volume compilation of 2 books explores the construction of geometric proofs. It offers useful criteria for determining correctness and presents examples of faulty proofs that illustrate common errors. 1963 editions.

Non-Euclidean Geometry

Author: H. S. M. Coxeter

Publisher: Cambridge University Press

ISBN: 9780883855225

Category: Mathematics

Page: 336

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A reissue of Professor Coxeter's classic text on non-Euclidean geometry. It surveys real projective geometry, and elliptic geometry. After this the Euclidean and hyperbolic geometries are built up axiomatically as special cases. This is essential reading for anybody with an interest in geometry.

The Divine Proportion

Author: H. E. Huntley

Publisher: Courier Corporation

ISBN: 0486131874

Category: Mathematics

Page: 208

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Discussion ranges from theories of biological growth to intervals and tones in music, Pythagorean numerology, conic sections, Pascal's triangle, the Fibonnacci series, and much more. Excellent bridge between science and art. Features 58 figures.

The Beauty of Numbers in Nature

Mathematical Patterns and Principles from the Natural World

Author: Ian Stewart

Publisher: N.A

ISBN: 9781782404712

Category:

Page: 224

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Think of a zebra's stripes, the complexities of a spider's web, the uniformity of desert dunes, or the spirals in a sunflower head ... think of a snowflake. The Beauty of Numbers in Nature shows how life on Earth forms the principles of mathematics. Starting with the simplest patterns, each chapter looks at a different kind of patterning system and the mathematics that underlies it. In doing so the book also uncovers some universal patterns, both in nature and man-made, from the basic geometry of ancient Greece to the visually startling fractals that we are familiar with today. Elegantly illustrated, The Beauty of Numbers in Nature is an illuminating and engaging vision of how the apparently cold laws of mathematics find expression in the beauty of nature.

Lessons in Geometry: Plane geometry

Author: Jacques Hadamard

Publisher: American Mathematical Soc.

ISBN: 0821843672

Category: Mathematics

Page: 330

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This is a work in the tradition of Euclidean synthetic geometry written by one of the 20th century's great mathematicians. The text starts where Euclid starts, and covers all the basics of plane Euclidean geometry.

Regular Polytopes

Author: H. S. M. Coxeter

Publisher: Courier Corporation

ISBN: 0486141586

Category: Mathematics

Page: 368

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Foremost book available on polytopes, incorporating ancient Greek and most modern work. Discusses polygons, polyhedrons, and multi-dimensional polytopes. Definitions of symbols. Includes 8 tables plus many diagrams and examples. 1963 edition.