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: 6278
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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.

Beautiful Geometry

Beautiful Geometry

  • Author: Eli Maor,Eugen Jost
  • Publisher: N.A
  • ISBN: 9780691175881
  • Category: Art
  • Page: 208
  • View: 387
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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 acclaimed 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 and beautiful branches of mathematics"--

Beautiful Geometry

Beautiful Geometry

  • Author: Eli Maor,Eugen Jost
  • Publisher: N.A
  • ISBN: 9780691150994
  • Category: Mathematics
  • Page: 187
  • View: 3982
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"Mathematicians always claim their subject is beautiful. Eli Maor and Eugen Jost prove it. This is geometry as you've never seen it before. A feast for the eyes."--Ian Stewart, author of Visions of Infinity "This book shows that math is more than theorems and proofs--it is full of history, philosophy, and glimpses of different cultures. I was immediately attracted by the book's intriguing and beautiful illustrations, and once I started reading the text, I could not stop following its fascinating stories about the origins of geometrical theorems."--Carlo H. Sequin, University of California, Berkeley "Reading Beautiful Geometry is like touring a personal art collection, except the masterpieces here are elegantly presented theorems and constructions by ancient and modern mathematicians. Eli Maor teaches the thought process of a geometry connoisseur as he highlights important details in each of these gems, and Eugen Jost illustrates these ideas with colorful and creative artworks. Readers who like to see real math in their math books will enjoy how Beautiful Geometry brings these enduring mathematical achievements to life."--George Hart, mathematical sculptor "Beautiful Geometry teaches and delights with its marriage of art and mathematics. The lovely illustrations range from conversation starters to dazzling Proofs Without Words--clever diagrams that explain why something is true. A feast for the eye and mind."--Frank Farris, Santa Clara University "A beautiful book that is as delightful to see as to read. Once you start you are compelled to read the next subject, and the next, and the next."--Zentralblatt MATH "

New Horizons in Geometry

New Horizons in Geometry

  • Author: Tom M. Apostol,Mamikon Mnatsakanian
  • Publisher: MAA
  • ISBN: 088385354X
  • Category: Mathematics
  • Page: 513
  • View: 9127
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New Horizons in Geometry represents the fruits of 15 years of work in geometry by a remarkable team of prize-winning authors—Tom Apostol and Mamikon Mnatsakanian. It serves as a capstone to an amazing collaboration. Apostol and Mamikon provide fresh and powerful insights into geometry that requires only a modest background in mathematics. Using new and intuitively rich methods, they give beautifully illustrated proofs of results, the majority of which are new, and frequently develop extensions of familiar theorems that are often surprising and sometimes astounding. It is mathematical exposition of the highest order. The hundreds of full color illustrations by Mamikon are visually enticing and provide great motivation to read further and savor the wonderful results. Lengths, areas, and volumes of curves, surfaces, and solids are explored from a visually captivating perspective. It is an understatement to say that Apostol and Mamikon have breathed new life into geometry.

Sacred Mathematics

Sacred Mathematics

Japanese Temple Geometry

  • Author: Hidetoshi Fukagawa,Tony Rothman
  • Publisher: Princeton University Press
  • ISBN: 9780691127453
  • Category: Art
  • Page: 348
  • View: 7662
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"An enchanting history of Japanese geometry--of a time and place where 'geometers did not cede place to poets.' This intersection of science and culture, of the mathematical, the artistic, and the spiritual, is packed, like circles within circles, with rewarding Aha! epiphanies that drive a mathematician's curiosity."--Siobhan Roberts, author of "King of Infinite Space" "Teachers will welcome this remarkable collection of mathematical problems, history, and art, which will enrich their curriculum and promote both logical thinking and critical evaluation. It is especially important that we maintain an interest in geometry, which needs, and for once gets, more than its share."--Richard Guy, coauthor of "The Book of Numbers" "This remarkable book provides a novel insight into the Japanese mathematics of the past few hundred years. It is fascinating to see the difference in mathematical style from that which we are used to in the Western world, but the book also elegantly illustrates the cross-cultural Platonic nature and profound beauty of mathematics itself."--Roger Penrose, author of "The Road to Reality" "A significant contribution to the history of mathematics. The wealth of mathematical problems--from the very simple to quite complex ones--will keep the interested reader busy for years. And the beautiful illustrations make this book a work of art as much as of science. Destined to become a classic!"--Eli Maor, author of "The Pythagorean Theorem: A 4,000-Year History" "A pleasure to read. "Sacred Mathematics" brings to light the unique style and character of geometry in the traditional Japanese sources--in particular the "sangaku" problems. These problems range from trivial to utterly devilish. I found myself captivated by them, and regularly astounded by the ingenuity and sophistication of many of the traditional solutions."--Glen Van Brummelen, coeditor of "Mathematics and the Historian's Craft"

Mathematical Problems and Proofs

Mathematical Problems and Proofs

Combinatorics, Number Theory, and Geometry

  • Author: Branislav Kisacanin
  • Publisher: Springer Science & Business Media
  • ISBN: 0306469634
  • Category: Mathematics
  • Page: 220
  • View: 9006
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A gentle introduction to the highly sophisticated world of discrete mathematics, Mathematical Problems and Proofs presents topics ranging from elementary definitions and theorems to advanced topics -- such as cardinal numbers, generating functions, properties of Fibonacci numbers, and Euclidean algorithm. This excellent primer illustrates more than 150 solutions and proofs, thoroughly explained in clear language. The generous historical references and anecdotes interspersed throughout the text create interesting intermissions that will fuel readers' eagerness to inquire further about the topics and some of our greatest mathematicians. The author guides readers through the process of solving enigmatic proofs and problems, and assists them in making the transition from problem solving to theorem proving. At once a requisite text and an enjoyable read, Mathematical Problems and Proofs is an excellent entrée to discrete mathematics for advanced students interested in mathematics, engineering, and science.

Crocheting Adventures with Hyperbolic Planes

Crocheting Adventures with Hyperbolic Planes

Tactile Mathematics, Art and Craft for all to Explore, Second Edition

  • Author: Daina Taimina
  • Publisher: CRC Press
  • ISBN: 1351402196
  • Category: Mathematics
  • Page: 200
  • View: 2880
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Winner, Euler Book Prize, awarded by the Mathematical Association of America. With over 200 full color photographs, this non-traditional, tactile introduction to non-Euclidean geometries also covers early development of geometry and connections between geometry, art, nature, and sciences. For the crafter or would-be crafter, there are detailed instructions for how to crochet various geometric models and how to use them in explorations. New to the 2nd Edition; Daina Taimina discusses her own adventures with the hyperbolic planes as well as the experiences of some of her readers. Includes recent applications of hyperbolic geometry such as medicine, architecture, fashion & quantum computing.

Excursions in Geometry

Excursions in Geometry

  • Author: Charles Stanley Ogilvy
  • Publisher: Courier Corporation
  • ISBN: 0486265307
  • Category: Mathematics
  • Page: 178
  • View: 8726
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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: A Comprehensive Course

Geometry: A Comprehensive Course

  • Author: Dan Pedoe
  • Publisher: Courier Corporation
  • ISBN: 0486131734
  • Category: Mathematics
  • Page: 464
  • View: 2341
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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.

Geometry of Design

Geometry of Design

Studies in Proportion and Composition

  • Author: Kimberly Elam
  • Publisher: Princeton Architectural Press
  • ISBN: 9781568982496
  • Category: Design
  • Page: 107
  • View: 7350
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This work takes a close look at a broad range of 20th-century examples of design, architecture and illustration, revealing underlying geometric structures in their compositions.

Geometry

Geometry

  • Author: V. V. Prasolov, V. M. Tikhomirov
  • Publisher: American Mathematical Soc.
  • ISBN: 1470425432
  • Category:
  • Page: 257
  • View: 4905
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This book provides a systematic introduction to various geometries, including Euclidean, affine, projective, spherical, and hyperbolic geometries. Also included is a chapter on infinite-dimensional generalizations of Euclidean and affine geometries. A uniform approach to different geometries, based on Klein's Erlangen Program is suggested, and similarities of various phenomena in all geometries are traced. An important notion of duality of geometric objects is highlighted throughout the book. The authors also include a detailed presentation of the theory of conics and quadrics, including the theory of conics for non-Euclidean geometries. The book contains many beautiful geometric facts and has plenty of problems, most of them with solutions, which nicely supplement the main text. With more than 150 figures illustrating the arguments, the book can be recommended as a textbook for undergraduate and graduate-level courses in geometry.

The First Six Books of the Elements of Euclid

The First Six Books of the Elements of Euclid

In which Coloured Diagrams and Symbols are Used Instead of Letters for the Greater Ease of Learners

  • Author: Oliver Byrne
  • Publisher: N.A
  • ISBN: N.A
  • Category: Elements
  • Page: 268
  • View: 2201
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Noncommutative Geometry

Noncommutative Geometry

Lectures given at the C.I.M.E. Summer School held in Martina Franca, Italy, September 3-9, 2000

  • Author: Alain Connes,Joachim Cuntz,Erik G. Guentner,Nigel Higson,Jerome Kaminker,John E. Roberts
  • Publisher: Springer Science & Business Media
  • ISBN: 9783540203575
  • Category: Mathematics
  • Page: 356
  • View: 7192
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Noncommutative Geometry is one of the most deep and vital research subjects of present-day Mathematics. Its development, mainly due to Alain Connes, is providing an increasing number of applications and deeper insights for instance in Foliations, K-Theory, Index Theory, Number Theory but also in Quantum Physics of elementary particles. The purpose of the Summer School in Martina Franca was to offer a fresh invitation to the subject and closely related topics; the contributions in this volume include the four main lectures, cover advanced developments and are delivered by prominent specialists.

Perspectives on Projective 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
  • View: 1734
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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.

The Seduction of Curves

The Seduction of Curves

The Lines of Beauty That Connect Mathematics, Art, and the Nude

  • Author: Allan McRobie
  • Publisher: Princeton University Press
  • ISBN: 0691175330
  • Category: Art
  • Page: 168
  • View: 5398
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In this large-format book, lavishly illustrated in color throughout, Allan McRobie takes the reader on an alluring exploration of the beautiful curves that shape our world--from our bodies to Salvador Dalí's paintings and the space-time fabric of the universe itself. The book focuses on seven curves--the fold, cusp, swallowtail, and butterfly, plus the hyperbolic, elliptical, and parabolic "umbilics"--and describes the surprising origins of their taxonomy in the catastrophe theory of mathematician René Thom.

Proofs from THE BOOK

Proofs from THE BOOK

  • Author: Martin Aigner,Günter M. Ziegler
  • Publisher: Springer
  • ISBN: 3662572656
  • Category: Mathematics
  • Page: 326
  • View: 6838
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This revised and enlarged sixth edition of Proofs from THE BOOK features an entirely new chapter on Van der Waerden’s permanent conjecture, as well as additional, highly original and delightful proofs in other chapters. From the citation on the occasion of the 2018 "Steele Prize for Mathematical Exposition" “... It is almost impossible to write a mathematics book that can be read and enjoyed by people of all levels and backgrounds, yet Aigner and Ziegler accomplish this feat of exposition with virtuoso style. [...] This book does an invaluable service to mathematics, by illustrating for non-mathematicians what it is that mathematicians mean when they speak about beauty.” From the Reviews "... Inside PFTB (Proofs from The Book) is indeed a glimpse of mathematical heaven, where clever insights and beautiful ideas combine in astonishing and glorious ways. There is vast wealth within its pages, one gem after another. ... Aigner and Ziegler... write: "... all we offer is the examples that we have selected, hoping that our readers will share our enthusiasm about brilliant ideas, clever insights and wonderful observations." I do. ... " Notices of the AMS, August 1999 "... This book is a pleasure to hold and to look at: ample margins, nice photos, instructive pictures and beautiful drawings ... It is a pleasure to read as well: the style is clear and entertaining, the level is close to elementary, the necessary background is given separately and the proofs are brilliant. ..." LMS Newsletter, January 1999 "Martin Aigner and Günter Ziegler succeeded admirably in putting together a broad collection of theorems and their proofs that would undoubtedly be in the Book of Erdös. The theorems are so fundamental, their proofs so elegant and the remaining open questions so intriguing that every mathematician, regardless of speciality, can benefit from reading this book. ... " SIGACT News, December 2011

The Algorithmic Beauty of Plants

The Algorithmic Beauty of Plants

  • Author: Przemyslaw Prusinkiewicz,Aristid Lindenmayer
  • Publisher: Springer Science & Business Media
  • ISBN: 1461384761
  • Category: Computers
  • Page: 228
  • View: 7105
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Now available in an affordable softcover edition, this classic in Springer's acclaimed Virtual Laboratory series is the first comprehensive account of the computer simulation of plant development. 150 illustrations, one third of them in colour, vividly demonstrate the spectacular results of the algorithms used to model plant shapes and developmental processes. The latest in computer-generated images allow us to look at plants growing, self-replicating, responding to external factors and even mutating, without becoming entangled in the underlying mathematical formulae involved. The authors place particular emphasis on Lindenmayer systems - a notion conceived by one of the authors, Aristid Lindenmayer, and internationally recognised for its exceptional elegance in modelling biological phenomena. Nonetheless, the two authors take great care to present a survey of alternative methods for plant modelling.

Geometry Snacks

Geometry Snacks

  • Author: Ed Southall
  • Publisher: Tarquin
  • ISBN: 1911093711
  • Category: Mathematics
  • Page: 94
  • View: 5528
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Geometry Snacks is a mathematical puzzle book filled with geometrical figures and questions designed to challenge, confuse and ultimately enlighten enthusiasts of all ages.

The Divine Proportion

The Divine Proportion

  • Author: H. E. Huntley
  • Publisher: Courier Corporation
  • ISBN: 0486131874
  • Category: Mathematics
  • Page: 208
  • View: 3920
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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.

Multiple View Geometry in Computer Vision

Multiple View Geometry in Computer Vision

  • Author: Richard Hartley,Andrew Zisserman
  • Publisher: Cambridge University Press
  • ISBN: 1139449141
  • Category: Computers
  • Page: N.A
  • View: 5269
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A basic problem in computer vision is to understand the structure of a real world scene given several images of it. Techniques for solving this problem are taken from projective geometry and photogrammetry. Here, the authors cover the geometric principles and their algebraic representation in terms of camera projection matrices, the fundamental matrix and the trifocal tensor. The theory and methods of computation of these entities are discussed with real examples, as is their use in the reconstruction of scenes from multiple images. The new edition features an extended introduction covering the key ideas in the book (which itself has been updated with additional examples and appendices) and significant new results which have appeared since the first edition. Comprehensive background material is provided, so readers familiar with linear algebra and basic numerical methods can understand the projective geometry and estimation algorithms presented, and implement the algorithms directly from the book.