Beautiful Geometry

Author: Eli Maor,Eugen Jost

Publisher: Princeton University Press

ISBN: 1400848334

Category: Mathematics

Page: 208

View: 6114

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.

Lunda Geometry: Mirror Curves, Designs, Knots, Polyominoes, Patterns, Symmetries

Author: Paulus Gerdes


ISBN: 1435726294


Page: 202

View: 6434

The book "Lunda Geometry" explains how the mathematical concepts of mirror curves and Lunda-designs were discovered in the context of the author's research of 'sona', illustrations traditionally made in the sand by Cokwe storytellers from eastern Angola (a region called Lunda) and neighboring regions of Congo and Zambia. Examples of mirror curves from several cultures are presented. Lunda-designs are aesthetically attractive and display interesting symmetry properties. Examples of Lunda-patterns and Lunda-polyominoes are presented. Some generalizations of the concept of Lunda-design are discussed, like hexagonal Lunda-designs, Lunda-k-designs, Lunda-fractals, and circular Lunda-designs. Lunda-designs of Celtic knot designs are constructed.Several chapters were published in journals like 'Computers & Graphics' (Oxford), 'Visual Mathematics' (Belgrade), and 'Mathematics in School' (UK).

Birational Geometry, Rational Curves, and Arithmetic

Author: Fedor Bogomolov,Brendan Hassett,Yuri Tschinkel

Publisher: Springer Science & Business Media

ISBN: 146146482X

Category: Mathematics

Page: 319

View: 700

​​​​This book features recent developments in a rapidly growing area at the interface of higher-dimensional birational geometry and arithmetic geometry. It focuses on the geometry of spaces of rational curves, with an emphasis on applications to arithmetic questions. Classically, arithmetic is the study of rational or integral solutions of diophantine equations and geometry is the study of lines and conics. From the modern standpoint, arithmetic is the study of rational and integral points on algebraic varieties over nonclosed fields. A major insight of the 20th century was that arithmetic properties of an algebraic variety are tightly linked to the geometry of rational curves on the variety and how they vary in families. This collection of solicited survey and research papers is intended to serve as an introduction for graduate students and researchers interested in entering the field, and as a source of reference for experts working on related problems. Topics that will be addressed include: birational properties such as rationality, unirationality, and rational connectedness, existence of rational curves in prescribed homology classes, cones of rational curves on rationally connected and Calabi-Yau varieties, as well as related questions within the framework of the Minimal Model Program.

The Natural philosophy of Emanuel Swedenborg

A Study in the Conceptual Metaphors of the Mechanistic World-View

Author: David Duner

Publisher: Springer Science & Business Media

ISBN: 9400745605

Category: Philosophy

Page: 476

View: 8766

Although Emanuel Swedenborg (1688–1772) is commonly known for his spiritual philosophy, his early career was focused unnatural science. During this period, Swedenborg thought of the world was like a gigantic machine, following the laws of mechanics and geometry. This volume analyzes this mechanistic worldview from the cognitive perspective, by means of a study of the metaphors in Swedenborg’s texts. The author argues that these conceptual metaphors are vital skills of the creative mind and scientific thinking, used to create visual analogies and abstract ideas. This means that Swedenborg’s mechanistic and geometrical worldview, allowed him to perceive the world as mechanical and geometrical. Swedenborg thought ”with” books and pens. The reading gave him associations and clues, forced him to interpret, and gave him material for his intellectual development.

The Geometry of Infinite-Dimensional Groups

Author: Boris Khesin,Robert Wendt

Publisher: Springer Science & Business Media

ISBN: 3540772634

Category: Mathematics

Page: 304

View: 3227

This monograph gives an overview of various classes of infinite-dimensional Lie groups and their applications in Hamiltonian mechanics, fluid dynamics, integrable systems, gauge theory, and complex geometry. The text includes many exercises and open questions.


Kurven - Flächen - Mannigfaltigkeiten

Author: Wolfgang Kühnel

Publisher: Springer-Verlag

ISBN: 3834896551

Category: Mathematics

Page: 280

View: 4649

Dieses Buch ist eine Einführung in die Differentialgeometrie. Zunächst geht es um die klassischen Aspekte wie die Geometrie von Kurven und Flächen, bevor dann höherdimensionale Flächen sowie abstrakte Mannigfaltigkeiten betrachtet werden. Die Nahtstelle ist dabei das zentrale Kapitel "Die innere Geometrie von Flächen". Dieses führt den Leser bis hin zu dem berühmten Satz von Gauß-Bonnet, der ein entscheidendes Bindeglied zwischen lokaler und globaler Geometrie darstellt. Die zweite Hälfte des Buches ist der Riemannschen Geometrie gewidmet. Den Abschluss bildet ein Kapitel über "Einstein-Räume", die eine große Bedeutung sowohl in der "Reinen Mathematik" als auch in der Allgemeinen Relativitätstheorie von A. Einstein haben. Es wird großer Wert auf Anschaulichkeit gelegt, was durch zahlreiche Abbildungen unterstützt wird. Im Laufe der Neuauflagen wurde der Text erweitert, neue Aufgaben wurden hinzugefügt und am Ende des Buches wurden zusätzliche Hinweise zur Lösung der Übungsaufgaben ergänzt. Der Text wurde für die fünfte Auflage gründlich durchgesehen und an einigen Stellen verbessert.

Non-Euclidean Geometries

János Bolyai Memorial Volume

Author: András Prékopa,Emil Molnár

Publisher: Springer Science & Business Media

ISBN: 0387295550

Category: Mathematics

Page: 506

View: 8551

"From nothing I have created a new different world," wrote János Bolyai to his father, Wolgang Bolyai, on November 3, 1823, to let him know his discovery of non-Euclidean geometry, as we call it today. The results of Bolyai and the co-discoverer, the Russian Lobachevskii, changed the course of mathematics, opened the way for modern physical theories of the twentieth century, and had an impact on the history of human culture. The papers in this volume, which commemorates the 200th anniversary of the birth of János Bolyai, were written by leading scientists of non-Euclidean geometry, its history, and its applications. Some of the papers present new discoveries about the life and works of János Bolyai and the history of non-Euclidean geometry, others deal with geometrical axiomatics; polyhedra; fractals; hyperbolic, Riemannian and discrete geometry; tilings; visualization; and applications in physics.

Lectures on Curves on an Algebraic Surface

Author: David Mumford

Publisher: Princeton University Press

ISBN: 9780691079936

Category: Mathematics

Page: 200

View: 8496

These lectures, delivered by Professor Mumford at Harvard in 1963-1964, are devoted to a study of properties of families of algebraic curves, on a non-singular projective algebraic curve defined over an algebraically closed field of arbitrary characteristic. The methods and techniques of Grothendieck, which have so changed the character of algebraic geometry in recent years, are used systematically throughout. Thus the classical material is presented from a new viewpoint.

The Works of Sir William Jones

With the Life of the Author by Lord Teignmouth

Author: William Jones,Lord Teignmouth

Publisher: Cambridge University Press

ISBN: 1108055702

Category: History

Page: 466

View: 560

A renowned Enlightenment polymath, Sir William Jones (1746-94) was a lawyer, translator and poet who wrote authoritatively on politics, comparative linguistics and oriental literature. Known initially for his Persian translations and political radicalism, Jones became further celebrated for his study and translation of ancient Sanskrit texts following his appointment to the supreme court in Calcutta in 1783. He spent the next eleven years introducing Europe to the mysticism and rationality of Hinduism through works such as his nine 'Hymns' to Hindu deities and his translation of the Sanskrit classic Sacontalá, influencing Romantic writers from William Blake to August Wilhelm Schlegel. Volume 3 of his thirteen-volume works, published in 1807, contains Jones' 'Anniversary Discourses' (1784-94) addressed to the Asiatick Society as its president - including 'On the Hindus' (1786), a seminal work of comparative linguistics. It also contains his landmark essay of cultural comparison, 'On the Gods of Greece, Italy, and India' (1784).

Models of the Real Projective Plane

Computer Graphics of Steiner and Boy Surfaces

Author: Francois Apery

Publisher: Springer-Verlag

ISBN: 3322895696

Category: Technology & Engineering

Page: 156

View: 1985

In the present time, objects generated by computers are replacing models made from wood, wire, and plaster. It is interesting to see how computer graphics can help us to understand the geometry of surfaces and illustrate some recent results on representations of the real projective plane.

Linear Algebra and Geometry

Author: David M. Bloom

Publisher: CUP Archive

ISBN: 9780521293242

Category: Mathematics

Page: 625

View: 4104

The Beautiful Necessity

Author: Claude Fayette Bragdon

Publisher: Simon and Schuster

ISBN: 1627936513

Category: Philosophy

Page: 64

View: 2427

Written in 1910, The Beautiful Necessity discusses architectural theory by American architect and writer, Claude Fayette Bragdon.

Analytic Hyperbolic Geometry

Mathematical Foundations and Applications

Author: Abraham A. Ungar

Publisher: World Scientific

ISBN: 9812703276

Category: Mathematics

Page: 463

View: 6476

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.

Designer's Apprentice

Automating Photoshop, Illustrator, and InDesign in Adobe Creative Suite 3, The

Author: Rick Ralston

Publisher: Adobe Press

ISBN: 9780132701396

Category: Computers

Page: 256

View: 9397

Adobe Creative Suite 3 has fantastic tools for minimizing the drudgery of graphics production work: The key is to make your computer and Photoshop, Illustrator, and InDesign do rote tasks for you. And although the concept of automation may sound intimidating, it doesn’t have to be. Learn what automation is, why it’s as natural as breathing, and how it can take over routine work, freeing you up to be creative. · Combine customer data with graphics for personalized communications · Customize hundreds or even thousands of illustrations or layouts in one pass · Record tasks with macro-like Actions in Photoshop and Illustrator, then reuse them with multiple files · Learn how scripting languages like AppleScript and JavaScript can automate complex workflows, even ones with varying conditions


Author: Robert C. West

Publisher: Elsevier

ISBN: 0323159168

Category: Science

Page: 248

View: 8276

Oxocarbons is a 10-chapter text that covers chemical-physical aspects, reaction chemistry, and spectroscopic investigations of oxocarbons. This book starts with a discussion on the early history of the oxocarbons. The subsequent seven chapters are devoted to the reactions, synthesis, and chemistry of substituted derivatives of cyclic polycarbonyls, called ""pseudooxocarbons"". The remaining chapters describe the structural phase transition and dielectric properties of squaric acid. This book will be of value to organic chemists and researchers who are interested in the synthesis of oxocarbons and related derivatives.

Getting Started in 3D with Maya

Create a Project from Start to Finish—Model, Texture, Rig, Animate, and Render in Maya

Author: Adam Watkins

Publisher: Taylor & Francis

ISBN: 1136147098

Category: Art

Page: 448

View: 7593

Deliver professional-level 3D content in no time with this comprehensive guide to 3D animation with Maya. With over 12 years of training experience, plus several award winning students under his belt, author Adam Watkins is the ideal mentor to get you up to speed with 3D in Maya. Using a structured and pragmatic approach Getting Started in 3D with Maya begins with basic theory of fundamental techniques, then builds on this knowledge using practical examples and projects to put your new skills to the test. Prepared so that you can learn in an organic fashion, each chapter builds on the knowledge gained in the previous chapter, showing you all the essentials of 3D in Maya, from modeling and UV layout, to texture creation, rigging animating and rendering. As you go from project to project you'll develop a strong arsenal of skills that combined will form a complete end to end process to creating complete projects in Maya. The accompanying website provides all the tools you need to develop your skills. Project files to accompany the practical examples used throughout the text, so you can work along with the examples. Additional textures and models will give you all the resources you need to start making your own projects in no time at all.

Martinis And Roses

Author: H. Levitt

Publisher: iUniverse

ISBN: 0595382754

Category: Fiction

Page: 248

View: 1198

An obsessive womanizer, a wealthy poet, an Iranian philanthropist, and a New York abstract expressionist painter fiercely compete for the attentions of Eleanor von Schroeder, a self-assured, beautiful woman in her twenties in the hectic Madison Avenue world of the 1960's. Eleanor has them believe she loves each of them simply by being the even-tempered, gracious, good-humored girl she is. But though she is compliant and fun-loving to a degree she is unconquerable in ways that count. Her would-be lovers will not give up and Eleanor will not give in, until circumstances change and a difficult solution occurs.

The Abyss Beyond Dreams

Author: Peter F. Hamilton

Publisher: Pan Macmillan

ISBN: 0230769470

Category: Fiction

Page: N.A

View: 8559

The first volume in the Chronicles of the Fallers, The Abyss Beyond Dreams by Peter F. Hamilton, is an exceptional novel exploring the mystery at the heart of the Commonwealth Universe. Fitting between the events of the Commonwealth Saga and the Void Trilogy, The Abyss Beyond Dreams is the first in an expansive duology, from the master of space opera. To save their civilization he must destroy it . . . When images of a lost civilization are 'dreamed' by a self-proclaimed prophet of the age, Nigel Sheldon, inventor of wormhole technology and creator of the Commonwealth society, is asked to investigate. Especially as the dreams seem to be coming from the Void - a mysterious area of living space monitored and controlled because of its hugely destructive capabilities. With it being the greatest threat to the known universe, Nigel is committed to finding out what really lies within the Void and if there's any truth to the visions they've received. Does human life really exist inside its boundary? But when Nigel crash lands inside the Void, on a planet he didn't even know existed, he finds so much more than he expected. Bienvenido: a world populated by the ancestors of survivors from Commonwealth colony ships that disappeared centuries ago. Since then they've been fighting an increasingly desperate battle against the Fallers, a space-born predator artificially evolved to conquer worlds. Their sole purpose is to commit genocide against every species they encounter. With their powerful telepathic lure - that tempts any who stray across their path to a slow and painful death - they are by far the greatest threat to humanity's continued existence on this planet. But Nigel soon realizes that the Fallers also hold the key to something he'd never hoped to find - the destruction of the Void itself. If only he can survive long enough to work out how to use it . . .