Search Results for "beautiful-geometry"

Beautiful Geometry

Beautiful Geometry

  • Author: Eli Maor,Eugen Jost
  • Publisher: Princeton University Press
  • ISBN: 1400848334
  • Category: Mathematics
  • Page: 208
  • View: 6692
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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.

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

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

  • Author: Paulus Gerdes
  • Publisher: Lulu.com
  • ISBN: 1435726294
  • Category:
  • Page: 202
  • View: 7470
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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

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: 6933
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​​​​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.

Matroids: A Geometric Introduction

Matroids: A Geometric Introduction

  • Author: Gary Gordon,Jennifer McNulty
  • Publisher: Cambridge University Press
  • ISBN: 0521145686
  • Category: Language Arts & Disciplines
  • Page: 393
  • View: 6263
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This friendly introduction helps undergraduate students understand and appreciate matroid theory and its connections to geometry.

Models of the Real Projective Plane

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: 1695
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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.

The Geometry of Infinite-Dimensional Groups

The Geometry of Infinite-Dimensional Groups

  • Author: Boris Khesin,Robert Wendt
  • Publisher: Springer Science & Business Media
  • ISBN: 3540772634
  • Category: Mathematics
  • Page: 304
  • View: 9446
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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.

Differentialgeometrie

Differentialgeometrie

Kurven - Flächen - Mannigfaltigkeiten

  • Author: Wolfgang Kühnel
  • Publisher: Springer-Verlag
  • ISBN: 3834896551
  • Category: Mathematics
  • Page: 280
  • View: 6914
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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.

Classical Algebraic Geometry

Classical Algebraic Geometry

A Modern View

  • Author: Igor V. Dolgachev
  • Publisher: Cambridge University Press
  • ISBN: 1107017653
  • Category: Mathematics
  • Page: 639
  • View: 8624
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Makes classical algebraic geometry accessible to the modern mathematician.

Some Adventures in Euclidean Geometry

Some Adventures in Euclidean Geometry

  • Author: Michael de Villiers
  • Publisher: Dynamic Mathematics Learning
  • ISBN: 0557102952
  • Category: Euclid's Elements
  • Page: 219
  • View: 1368
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This book seeks to actively involve the reader in the heuristic processes of conjecturing, discovering, formulating, classifying, defining, refuting, proving, etc. within the context of Euclidean geometry. The book deals with many interesting and beautiful geometric results, which have only been discovered during the past 300 years such as the Euler line, the theorems of Ceva, Napoleon, Morley, Miquel, Varignon, etc. Extensive attention is also given to the classification of the quadrilaterals from the symmetry of a side-angle duality. Many examples lend themselves excellently for exploration on computer with dynamic geometry programs such as Sketchpad. The book is addressed primarily to university or college lecturers involved in the under-graduate or in-service training of high school mathematics teachers, but may also interest teachers who are looking for enrichment material, and gifted high school mathematics pupils.

Riemannian Geometry

Riemannian Geometry

  • Author: Sylvestre Gallot,Dominique Hulin,Jacques Lafontaine
  • Publisher: Springer Science & Business Media
  • ISBN: 9783540204930
  • Category: Mathematics
  • Page: 322
  • View: 6350
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Many years have passed since the ?rst edition. However, the encouragements of various readers and friends have persuaded us to write this third edition. During these years, Riemannian Geometry has undergone many dramatic - velopments. Here is not the place to relate them. The reader can consult for instance the recent book [Br5]. of our “mentor” Marcel Berger. However,R- mannian Geometry is not only a fascinating ?eld in itself. It has proved to be a precious tool in other parts of mathematics. In this respect, we can quote the major breakthroughs in four-dimensional topology which occurred in the eighties and the nineties of the last century (see for instance [L2]). These have been followed, quite recently, by a possibly successful approach to the Poincar ́ e conjecture. In another direction, Geometric Group Theory, a very active ?eld nowadays (cf. [Gr6]), borrows many ideas from Riemannian or metric geometry. Butletusstophoggingthelimelight.Thisisjustatextbook.Wehopethatour point of view of working intrinsically with manifolds as early as possible, and testingeverynewnotiononaseriesofrecurrentexamples(seetheintroduction to the ?rst edition for a detailed description), can be useful both to beginners and to mathematicians from other ?elds, wanting to acquire some feeling for the subject.

Computer Graphics and Geometric Modelling

Computer Graphics and Geometric Modelling

Mathematics

  • Author: Max K. Agoston
  • Publisher: Springer Science & Business Media
  • ISBN: 9781852338176
  • Category: Computers
  • Page: 959
  • View: 9282
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The second book of a two-volume work in which the author presents an overview of computer graphics as seen in the context of geometric modeling and the mathematics required to understand the subject.

The Geometry of Syzygies

The Geometry of Syzygies

A Second Course in Algebraic Geometry and Commutative Algebra

  • Author: David Eisenbud
  • Publisher: Springer Science & Business Media
  • ISBN: 0387264566
  • Category: Mathematics
  • Page: 246
  • View: 300
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First textbook-level account of basic examples and techniques in this area. Suitable for self-study by a reader who knows a little commutative algebra and algebraic geometry already. David Eisenbud is a well-known mathematician and current president of the American Mathematical Society, as well as a successful Springer author.

Flavors of Geometry

Flavors of Geometry

  • Author: Silvio Levy
  • Publisher: Cambridge University Press
  • ISBN: 9780521629621
  • Category: Mathematics
  • Page: 194
  • View: 6670
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Lectures on hyperbolic geometry, dynamics in several complex variables, convex geometry, and volume estimation.

Advances in Analysis and Geometry

Advances in Analysis and Geometry

New Developments Using Clifford Algebras

  • Author: Tao Qian,Thomas Hempfling,Alan McIntosh,Franciscus Sommen
  • Publisher: Birkhäuser
  • ISBN: 3034878389
  • Category: Mathematics
  • Page: 376
  • View: 398
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At the heart of Clifford analysis is the study of systems of special partial differential operators that arise naturally from the use of Clifford algebra as a calculus tool. This book focuses on the study of Dirac operators and related ones, together with applications in mathematics, physics and engineering. This book collects refereed papers from a satellite conference to the ICM 2002, plus invited contributions. All articles contain unpublished new results.

Non-Euclidean Geometries

Non-Euclidean Geometries

János Bolyai Memorial Volume

  • Author: András Prékopa,Emil Molnár
  • Publisher: Springer Science & Business Media
  • ISBN: 0387295550
  • Category: Mathematics
  • Page: 506
  • View: 4155
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"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.

The Beautiful Necessity

The Beautiful Necessity

  • Author: Claude Fayette Bragdon
  • Publisher: Simon and Schuster
  • ISBN: 1627936513
  • Category: Philosophy
  • Page: 64
  • View: 7457
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Written in 1910, The Beautiful Necessity discusses architectural theory by American architect and writer, Claude Fayette Bragdon.

A Celebration of the Mathematical Legacy of Raoul Bott

A Celebration of the Mathematical Legacy of Raoul Bott

  • Author: Peter Robert Kotiuga
  • Publisher: American Mathematical Soc.
  • ISBN: 082188381X
  • Category: Mathematics
  • Page: 403
  • View: 5519
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Noble Numbers, Subtle Words

Noble Numbers, Subtle Words

The Art of Mathematics in the Science of Storytelling

  • Author: Barbara Milberg Fisher
  • Publisher: Fairleigh Dickinson Univ Press
  • ISBN: 9780838637401
  • Category: Literary Criticism
  • Page: 168
  • View: 7911
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This study approaches the use of mathematics in fiction in an entirely new way, as a potent instrument of language. Following Wittgenstein's description of mathematical constructs as a component of ordinary language, Fisher shows how number, geometric figuration, algebraic coding, and transcendent abstractions have been made to function as practical narrative tools. Far from rehearsing the various paradigms of numerology, whether Pythagorean, Elizabethan, or Cabalistic, this book explores the tactical deployment of mathematical objects as shaping and framing agents. It reveals how mathematical objects may be subordinated to the storyteller's art.

Sacred Mathematics

Sacred Mathematics

Japanese Temple Geometry

  • Author: Hidetoshi Fukagawa,Tony Rothman
  • Publisher: Princeton University Press
  • ISBN: 9780691127453
  • Category: Art
  • Page: 348
  • View: 5427
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Between the seventeenth and nineteenth centuries Japan was totally isolated from the West by imperial decree. During that time, a unique brand of homegrown mathematics flourished, one that was completely uninfluenced by developments in Western mathematics. People from all walks of life--samurai, farmers, and merchants--inscribed a wide variety of geometry problems on wooden tablets called sangaku and hung them in Buddhist temples and Shinto shrines throughout Japan. Sacred Mathematics is the first book published in the West to fully examine this tantalizing--and incredibly beautiful--mathematical tradition. Fukagawa Hidetoshi and Tony Rothman present for the first time in English excerpts from the travel diary of a nineteenth-century Japanese mathematician, Yamaguchi Kanzan, who journeyed on foot throughout Japan to collect temple geometry problems. The authors set this fascinating travel narrative--and almost everything else that is known about temple geometry--within the broader cultural and historical context of the period. They explain the sacred and devotional aspects of sangaku, and reveal how Japanese folk mathematicians discovered many well-known theorems independently of mathematicians in the West--and in some cases much earlier. The book is generously illustrated with photographs of the tablets and stunning artwork of the period. Then there are the geometry problems themselves, nearly two hundred of them, fully illustrated and ranging from the utterly simple to the virtually impossible. Solutions for most are provided. A unique book in every respect, Sacred Mathematics demonstrates how mathematical thinking can vary by culture yet transcend cultural and geographic boundaries.

An Introduction to Families, Deformations and Moduli

An Introduction to Families, Deformations and Moduli

  • Author: T. E. Venkata Balaji
  • Publisher: Universitätsverlag Göttingen
  • ISBN: 3941875329
  • Category: Complex manifolds
  • Page: 208
  • View: 3040
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