Gems of Geometry

Author: John Barnes

Publisher: Springer Science & Business Media

ISBN: 364230964X

Category: Mathematics

Page: 325

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Based on a series of lectures for adult students, this lively and entertaining book proves that, far from being a dusty, dull subject, geometry is in fact full of beauty and fascination. The author's infectious enthusiasm is put to use in explaining many of the key concepts in the field, starting with the Golden Number and taking the reader on a geometrical journey via Shapes and Solids, through the Fourth Dimension, finishing up with Einstein's Theories of Relativity. Equally suitable as a gift for a youngster or as a nostalgic journey back into the world of mathematics for older readers, John Barnes' book is the perfect antidote for anyone whose maths lessons at school are a source of painful memories. Where once geometry was a source of confusion and frustration, Barnes brings enlightenment and entertainment. In this second edition, stimulated by recent lectures at Oxford, further material and extra illustrations have been added on many topics including Coloured Cubes, Chaos and Crystals.

Six gems of geometry

Author: Thomas Reale

Publisher: PSIpress

ISBN: 1935638025

Category: Geometry

Page: 137

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Six gems of geometry is an introductory geometry textbook for general audiences. The book focuses mainly on the teachings of Euclid. It contains a story inspired by William Blake's painting, Newton the Measurer, where an encounter is imagined between Euclid and Newton, suggesting a deep influence the former may have had on the latter.

Applied Computational Geometry. Towards Geometric Engineering

FCRC '96 Workshop, WACG '96, Philadelphia, PA, May 27 - 28, 1996, Selected Papers

Author: Acm Workshop on Applied Computational Geometry 1996 Philadelphia, Pa,Ming C. Lin

Publisher: Springer Science & Business Media

ISBN: 9783540617853

Category: Computers

Page: 222

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Content Description #Anthology selected from contributions to the First ACM Workshop on Applied Computational Geometry.#Includes bibliographical references and index.

Computational Geometry in C

Author: Joseph O'Rourke

Publisher: Cambridge University Press

ISBN: 9780521649766

Category: Computers

Page: 376

View: 4522

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This is the newly revised and expanded edition of the popular introduction to the design and implementation of geometry algorithms arising in areas such as computer graphics, robotics, and engineering design. The second edition contains material on several new topics, such as randomized algorithms for polygon triangulation, planar point location, 3D convex hull construction, intersection algorithms for ray-segment and ray-triangle, and point-in-polyhedron. A new "Sources" chapter points to supplemental literature for readers needing more information on any topic. A novel aspect is the inclusion of working C code for many of the algorithms, with discussion of practical implementation issues. The self-contained treatment presumes only an elementary knowledge of mathematics, but reaches topics on the frontier of current research, making it a useful reference for practitioners at all levels. The code in this new edition is significantly improved from the first edition, and four new routines are included. Java versions for this new edition are also available. All code is accessible from the book's Web site (http://cs.smith.edu/~orourke/) or by anonymous ftp.

The Foundations of Geometry and the Non-Euclidean Plane

Author: G.E. Martin

Publisher: Springer Science & Business Media

ISBN: 9780387906942

Category: Mathematics

Page: 512

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This book is a text for junior, senior, or first-year graduate courses traditionally titled Foundations of Geometry and/or Non Euclidean Geometry. The first 29 chapters are for a semester or year course on the foundations of geometry. The remaining chap ters may then be used for either a regular course or independent study courses. Another possibility, which is also especially suited for in-service teachers of high school geometry, is to survey the the fundamentals of absolute geometry (Chapters 1 -20) very quickly and begin earnest study with the theory of parallels and isometries (Chapters 21 -30). The text is self-contained, except that the elementary calculus is assumed for some parts of the material on advanced hyperbolic geometry (Chapters 31 -34). There are over 650 exercises, 30 of which are 10-part true-or-false questions. A rigorous ruler-and-protractor axiomatic development of the Euclidean and hyperbolic planes, including the classification of the isometries of these planes, is balanced by the discussion about this development. Models, such as Taxicab Geometry, are used exten sively to illustrate theory. Historical aspects and alternatives to the selected axioms are prominent. The classical axiom systems of Euclid and Hilbert are discussed, as are axiom systems for three and four-dimensional absolute geometry and Pieri's system based on rigid motions. The text is divided into three parts. The Introduction (Chapters 1 -4) is to be read as quickly as possible and then used for ref erence if necessary.

The Warring States

The Wave Trilogy

Author: Aidan Harte

Publisher: Hachette UK

ISBN: 0857389025

Category: Fiction

Page: 512

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The second book in the Wave Trilogy, set in a darkly original alternative Renaissance Italy. After the rout at Rasenna, Concord faces enemies on all fronts, and nobody believes that the last surviving Apprentice is equal to these crises - but Torbidda didn't become Apprentice by letting himself be manipulated. While Sofia is struggling to understand her miraculous pregnancy, the City of Towers grows wealthy. But it's not long before the people of Rasenna start arguing again, and as the city falls apart once more, Sofia realises she must escape Etruria to save her baby. When prophecy leads her to another cesspit of treachery, the decadent Crusader kingdom of Oltremare, Sofia begins to despair, for this time she can see no way out...

The Heart of Mathematics

An invitation to effective thinking

Author: Edward B. Burger,Michael Starbird

Publisher: Springer Science & Business Media

ISBN: 9781931914413

Category: Mathematics

Page: 760

View: 9872

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Hallmark features include: * A focus on the important ideas of mathematics that students will retain long after their formal studies are complete. * An engaging and humorous style, written to be read and enjoyed. * Ten Life Lessons that readers will apply beyond their study of mathematics. * Use of a variety of visualization techniques that direct students to model their thinking and to actively explore the world around them. New to this Edition: * A new chapter, Deciding Wisely: Applications of Rigorous Thought, provides a thought-provoking capstone. * Expanded and improved statistics and probability content in Chapter 7, Taming Uncertainty. * Enhanced Mindscapes at the end of each section which ask the reader to review, apply and think deeply about the ideas presented in the chapter. * Radically superior ancillary package.

Nice Numbers

Author: John Barnes

Publisher: Birkhäuser

ISBN: 3319468316

Category: Mathematics

Page: 329

View: 9473

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In this intriguing book, John Barnes takes us on a journey through aspects of numbers much as he took us on a geometrical journey in Gems of Geometry. Similarly originating from a series of lectures for adult students at Reading and Oxford University, this book touches a variety of amusing and fascinating topics regarding numbers and their uses both ancient and modern. The author informs and intrigues his audience with both fundamental number topics such as prime numbers and cryptography, and themes of daily needs and pleasures such as counting one's assets, keeping track of time, and enjoying music. Puzzles and exercises at the end of each lecture offer additional inspiration, and numerous illustrations accompany the reader. Furthermore, a number of appendices provides in-depth insights into diverse topics such as Pascal's triangle, the Rubik cube, Mersenne's curious keyboards, and many others. A theme running through is the thought of what is our favourite number. Written in an engaging and witty style and requiring only basic school mathematical knowledge, this book will appeal to both young and mature readers fascinated by the curiosities of numbers.

Graphics Gems V (Macintosh Version)

Author: Alan W. Paeth

Publisher: Academic Press

ISBN: 1483296695

Category: Computers

Page: 438

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Graphics Gems V is the newest volume in The Graphics Gems Series. It is intended to provide the graphics community with a set of practical tools for implementing new ideas and techniques, and to offer working solutions to real programming problems. These tools are written by a wide variety of graphics programmers from industry, academia, and research. The books in the series have become essential, time-saving tools for many programmers. Latest collection of graphics tips in The Graphics Gems Series written by the leading programmers in the field. Contains over 50 new gems displaying some of the most recent and innovative techniques in graphics programming. Includes gems covering ellipses, splines, Bezier curves, and ray tracing. Disk included containing source code from the gems available in both IBM and Macintosh versions.

Topics in Elementary Geometry

Author: O. Bottema

Publisher: Springer Science & Business Media

ISBN: 9780387781310

Category: Mathematics

Page: 142

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This small book, translated into English for the first time, has long been a unique place to find classical results from geometry, such as Pythagoras' theorem, the nine-point circle, Morley's triangle, and many other subjects. In addition, this book contains recent, geometric theorems which have been obtained over the past years. There are 27 independent chapters on a wide range of topics in elementary plane Euclidean geometry, at a level just beyond what is usually taught in a good high school or college geometry course. The selection of topics is intelligent, varied, and stimulating, and the author provides many thought-provoking ideas.

Analytic Hyperbolic Geometry

Mathematical Foundations and Applications

Author: Abraham A. Ungar

Publisher: World Scientific

ISBN: 9812703276

Category: Mathematics

Page: 463

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This is the first book on analytic hyperbolic geometry, fully analogous to analytic Euclidean geometry. Analytic hyperbolic geometry regulates relativistic mechanics just as analytic Euclidean geometry regulates classical mechanics. The book presents a novel gyrovector space approach to analytic hyperbolic geometry, fully analogous to the well-known vector space approach to Euclidean geometry. A gyrovector is a hyperbolic vector. In the resulting "gyrolanguage" of the book, one attaches the prefix "gyro" to a classical term to mean the analogous term in hyperbolic geometry. The book begins with the definition of gyrogroups, which is fully analogous to the definition of groups. Gyrogroups, both gyrocommutative and nongyrocommutative, abound in group theory. Surprisingly, the seemingly structureless Einstein velocity addition of special relativity turns out to be a gyrocommutative gyrogroup operation. Introducing scalar multiplication, some gyrocommutative gyrogroups of gyrovectors become gyrovector spaces. The latter, in turn, form the setting for analytic hyperbolic geometry just as vector spaces form the setting for analytic Euclidean geometry. By hybrid techniques of differential geometry and gyrovector spaces, it is shown that Einstein (Mobius) gyrovector spaces form the setting for Beltrami-Klein (Poincare) ball models of hyperbolic geometry. Finally, novel applications of Mobius gyrovector spaces in quantum computation, and of Einstein gyrovector spaces in special relativity, are presented.

Lectures on the Geometry of Manifolds

Author: Liviu I. Nicolaescu

Publisher: World Scientific

ISBN: 9812708537

Category: Mathematics

Page: 589

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The goal of this book is to introduce the reader to some of the most frequently used techniques in modern global geometry. Suited to the beginning graduate student willing to specialize in this very challenging field, the necessary prerequisite is a good knowledge of several variables calculus, linear algebra and point-set topology.The book's guiding philosophy is, in the words of Newton, that ?in learning the sciences examples are of more use than precepts?. We support all the new concepts by examples and, whenever possible, we tried to present several facets of the same issue.While we present most of the local aspects of classical differential geometry, the book has a ?global and analytical bias?. We develop many algebraic-topological techniques in the special context of smooth manifolds such as Poincar‚ duality, Thom isomorphism, intersection theory, characteristic classes and the Gauss-;Bonnet theorem.We devoted quite a substantial part of the book to describing the analytic techniques which have played an increasingly important role during the past decades. Thus, the last part of the book discusses elliptic equations, including elliptic Lpand H”lder estimates, Fredholm theory, spectral theory, Hodge theory, and applications of these. The last chapter is an in-depth investigation of a very special, but fundamental class of elliptic operators, namely, the Dirac type operators.The second edition has many new examples and exercises, and an entirely new chapter on classical integral geometry where we describe some mathematical gems which, undeservedly, seem to have disappeared from the contemporary mathematical limelight.

The Geometry of Moduli Spaces of Sheaves

A Publication of the Max-Planck-Institut für Mathematik, Bonn

Author: Daniel Huybrechts,Manfred Lehn

Publisher: Vieweg+Teubner Verlag

ISBN: 9783663116257

Category: Technology & Engineering

Page: 270

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This book is intended to serve as an introduction to the theory of semistable sheaves and at the same time to provide a survey of recent research results on the geometry of moduli spaces. The first part introduces the basic concepts in the theory: Hilbert polynomial, slope, stability, Harder-Narasimhan filtration, Grothendieck's Quot-scheme. It presents detailed proofs of the Grauert-Mülich Theorem, the Bogomolov Inequality, the semistability of tensor products, and the boundedness of the family of semistable sheaves. It also gives a self-contained account of the construction of moduli spaces of semistable sheaves on a projective variety à la Gieseker, Maruyama, and Simpson. The second part presents some of the recent results of the geometry of moduli spaces of sheaves on an algebraic surface, following work of Mukai, O'Grady, Gieseker, Li and many others. In particular, moduli spaces of sheaves on K3 surfaces and determinant line bundles on the moduli spaces are treated in some detail. Other topics include the Serre correspondence, restriction of stable bundles to curves, symplectic structures, irreducibility and Kodaira-dimension of moduli spaces.

Graphics Gems II

Author: James Arvo

Publisher: Elsevier

ISBN: 0080507549

Category: Computers

Page: 672

View: 4882

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Graphics Gems II is a collection of articles shared by a diverse group of people that reflect ideas and approaches in graphics programming which can benefit other computer graphics programmers. This volume presents techniques for doing well-known graphics operations faster or easier. The book contains chapters devoted to topics on two-dimensional and three-dimensional geometry and algorithms, image processing, frame buffer techniques, and ray tracing techniques. The radiosity approach, matrix techniques, and numerical and programming techniques are likewise discussed. Graphics artists and computer programmers will find the book invaluable.

On the Topology of Isolated Singularities in Analytic Spaces

Author: José Seade

Publisher: Springer Science & Business Media

ISBN: 9783764373221

Category: Mathematics

Page: 238

View: 7584

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This book has been awarded the Ferran Sunyer i Balaguer 2005 prize. The aim of this book is to give an overview of selected topics on the topology of real and complex isolated singularities, with emphasis on its relations to other branches of geometry and topology. The first chapters are mostly devoted to complex singularities and a myriad of results spread in a vast literature, which are presented here in a unified way, accessible to non-specialists. Among the topics are the fibration theorems of Milnor; the relation with 3-dimensional Lie groups; exotic spheres; spin structures and 3-manifold invariants; the geometry of quadrics and Arnold's theorem which states that the complex projective plane modulo conjugation is the 4-sphere. The second part of the book studies pioneer work about real analytic singularities which arise from the topological and geometric study of holomorphic vector fields and foliations. In the low dimensional case these turn out to be related to fibred links in the 3-sphere defined by meromorphic functions. This provides new methods for constructing manifolds equipped with a rich geometry. The book is largely self-contained and serves a wide audience of graduate students, mathematicians and researchers interested in geometry and topology.