Search Results for "the-symmetries-of-things"

The Symmetries of Things

The Symmetries of Things

  • Author: John H. Conway,Heidi Burgiel,Chaim Goodman-Strauss
  • Publisher: A K Peters, Ltd.
  • ISBN: 1568812205
  • Category: Mathematics
  • Page: 426
  • View: 9582
DOWNLOAD NOW »
Start with a single shape. Repeat it in some way—translation, reflection over a line, rotation around a point—and you have created symmetry. Symmetry is a fundamental phenomenon in art, science, and nature that has been captured, described, and analyzed using mathematical concepts for a long time. Inspired by the geometric intuition of Bill Thurston and empowered by his own analytical skills, John Conway, with his coauthors, has developed a comprehensive mathematical theory of symmetry that allows the description and classification of symmetries in numerous geometric environments. This richly and compellingly illustrated book addresses the phenomenological, analytical, and mathematical aspects of symmetry on three levels that build on one another and will speak to interested lay people, artists, working mathematicians, and researchers.

The Symmetries of Things

The Symmetries of Things

  • Author: John H. Conway,Heidi Burgiel,Chaim Goodman-Strauss
  • Publisher: CRC Press
  • ISBN: 1439864896
  • Category: Mathematics
  • Page: 448
  • View: 353
DOWNLOAD NOW »
Start with a single shape. Repeat it in some way—translation, reflection over a line, rotation around a point—and you have created symmetry. Symmetry is a fundamental phenomenon in art, science, and nature that has been captured, described, and analyzed using mathematical concepts for a long time. Inspired by the geometric intuition of Bill Thurston and empowered by his own analytical skills, John Conway, with his coauthors, has developed a comprehensive mathematical theory of symmetry that allows the description and classification of symmetries in numerous geometric environments. This richly and compellingly illustrated book addresses the phenomenological, analytical, and mathematical aspects of symmetry on three levels that build on one another and will speak to interested lay people, artists, working mathematicians, and researchers.

Über Zahlen und Spiele

Über Zahlen und Spiele

  • Author: John H. Conway
  • Publisher: Springer-Verlag
  • ISBN: 3322889971
  • Category: Mathematics
  • Page: 205
  • View: 8418
DOWNLOAD NOW »

Symmetrie

Symmetrie

  • Author: H. Weyl
  • Publisher: Springer-Verlag
  • ISBN: 3034868766
  • Category: Juvenile Nonfiction
  • Page: 157
  • View: 9348
DOWNLOAD NOW »

Symmetry

Symmetry

  • Author: Hermann Weyl
  • Publisher: Princeton University Press
  • ISBN: 1400874343
  • Category: Science
  • Page: 176
  • View: 6964
DOWNLOAD NOW »
Symmetry is a classic study of symmetry in mathematics, the sciences, nature, and art from one of the twentieth century's greatest mathematicians. Hermann Weyl explores the concept of symmetry beginning with the idea that it represents a harmony of proportions, and gradually departs to examine its more abstract varieties and manifestations—as bilateral, translatory, rotational, ornamental, and crystallographic. Weyl investigates the general abstract mathematical idea underlying all these special forms, using a wealth of illustrations as support. Symmetry is a work of seminal relevance that explores the great variety of applications and importance of symmetry.

Unvergängliche Geometrie

Unvergängliche Geometrie

  • Author: H.S. Coxeter
  • Publisher: Springer-Verlag
  • ISBN: 3034851510
  • Category: Juvenile Nonfiction
  • Page: 558
  • View: 4219
DOWNLOAD NOW »

Die Macht der Symmetrie

Die Macht der Symmetrie

Warum Schönheit Wahrheit ist

  • Author: Ian Stewart
  • Publisher: Springer Spektrum
  • ISBN: 9783642364358
  • Category: Science
  • Page: 304
  • View: 9689
DOWNLOAD NOW »
m dichten Morgennebel des 30. Mai 1832 stehen sich zwei junge franzö- sche Männer gegenüber, die Pistolen in der Hand. Sie duellieren sich wegen einer Frau. Es fällt ein Schuss, und einer der Männer liegt schwer verletzt am IBoden. Am nächsten Tag stirbt er an den Folgen seiner inneren Verletzungen. Kein Stein markiert das Grab des 20-Jährigen, und beinahe wäre eine der wi- tigsten Ideen in der Geschichte der Mathematik und der Naturwissenschaften mit ihm beerdigt worden. Der Name des Überlebenden bleibt unbekannt; der tragisch Getötete hieß Évariste Galois. In politischer Hinsicht war er ein Rebell, doch seine Leidenschaft war die Mathematik, auch wenn seine gesammelten Werke kaum sechzig Seiten umfassen. Galois hinterließ ein Erbe, das die Mathematik revolutionierte. Er e- wickelte eine Sprache zur Beschreibung von Symmetrien und ihrer Bedeutung in mathematischen Strukturen. Diese Sprache nennt man heute „Gruppentheorie“, und in allen Bereichen der reinen und angewandten Mathematik dient sie zur Charakterisierung von Mustern und Formen. Symmetrien spielen auch eine zentrale Rolle in den Gre- gebieten der Physik: der Quantenwelt im Kleinen und der Welt der Relativitä- theorie im Großen. Sie könnten sogar der Schlüssel zur lange gesuchten „Theorie von Allem“ sein, einer mathematischen Vereinigung dieser beiden Zweige der modernen Physik. Und alles begann mit einer einfachen Frage zur Lösung mat- matischer Gleichungen: Wie ?ndet man eine „unbekannte“ Zahl aus wenigen, allgemeinen mathematischen Vorgaben? Symmetrie ist keine Zahl und auch keine Form.

Symmetries of Islamic Geometrical Patterns

Symmetries of Islamic Geometrical Patterns

  • Author: S. J. Abas,Amer Shaker Salman
  • Publisher: World Scientific
  • ISBN: 9789810217044
  • Category: Mathematics
  • Page: 396
  • View: 1831
DOWNLOAD NOW »
... a major contribution to the world of science and of particular value to the documention of the culture of Islam. N Gedal ... a masterly account of the way in which art and science are combined into aesthetic beauty by the Islamic geometric designs and motifs which decorate much of the Eastern World. M Evans ... This book will allow readers to travel through time and space, from ancient ornaments to the most modern computer graphics patterns. C. Pickover Ever since the discovery of the existence of seventeen space groups in two dimensions by Fedorov in 1891, it has been speculated that all seventeen could be found in Islamic art. But it is in this book that this remarkable fact is for the first time detailed and analysed, with beautiful illustrations. Rarely is there such a thought-provoking blend of esthetics and geometry with abstraction. C N Yang Geometrical form. Here, mathematics combines with art and exhibits clearly its aesthetic appeal Islamic patterns provide a marvellous illustration of symmetry and Drs. Abas and Salman perform a useful service by taking this as their theme and blending it with ideas on computer graphics. Foreword by Michael Atiyah Abas and Salman have assembled a fascinating collection that combines art, history, culture, science, mathematics and philosophy. Their examples range from a 12th-century minaret in Uzbekistan via the Alhambra in Granada to modern computer graphics of Koranic calligraphy on dodecahedrons and tori. They conclude by speculating on the prospect of creating Islamic patterns in virtual reality, where 'a seeker after unity in science and art would be able to submerge himself or herself in exquisite Alhambras of the mind'.Judging by the evidence presented here, it would be an unforgettable experience. New Scien

Albert Einstein Memorial Lectures

Albert Einstein Memorial Lectures

  • Author: Jacob D. Bekenstein,Raphael Mechoulam
  • Publisher: World Scientific
  • ISBN: 9814329428
  • Category: Science
  • Page: 204
  • View: 3448
DOWNLOAD NOW »
This volume consists of a selection of Albert Einstein Memorial Lectures covering a broad spectrum of subjects in physics, chemistry, life science, mathematics, historiography and social issues. The lectures were presented by eminent scientists and scholars, including Nobel laureates. Established in 1980 by the Israel Academy of Sciences and Humanities, this distinguished annual memorial lecture series was inaugurated following an international symposium held in Jerusalem in March 1979 to commemorate the centenary of Albert Einstein's birth. Considering that Einstein's interests, activities and influence were not restricted to theoretical physics but spanned broad fields affecting society and the welfare of humankind, it was felt that these memorial lectures should be addressed to scientists, scholars and erudite laypersons rather than to physicists alone.

Liebe und Mathematik

Liebe und Mathematik

Im Herzen einer verborgenen Wirklichkeit

  • Author: Edward Frenkel
  • Publisher: Springer-Verlag
  • ISBN: 3662434210
  • Category: Mathematics
  • Page: 317
  • View: 5977
DOWNLOAD NOW »

Why Is There Philosophy of Mathematics At All?

Why Is There Philosophy of Mathematics At All?

  • Author: Ian Hacking
  • Publisher: Cambridge University Press
  • ISBN: 1107050170
  • Category: Mathematics
  • Page: 308
  • View: 4540
DOWNLOAD NOW »
Hacking explores how mathematics became possible for the human race, and how it ensured our status as the dominant species.

The symmetry of natural laws

The symmetry of natural laws

  • Author: Laurie M. Brown
  • Publisher: N.A
  • ISBN: N.A
  • Category: Science
  • Page: 21
  • View: 4385
DOWNLOAD NOW »

The Epistemology of Keith Lehrer

The Epistemology of Keith Lehrer

  • Author: Erik Olsson
  • Publisher: Springer Science & Business Media
  • ISBN: 9401000131
  • Category: Philosophy
  • Page: 356
  • View: 6953
DOWNLOAD NOW »
This book is an extensive, self-contained, up-to-date study of Lehrer's epistemological work. Covering all major aspects, it contains original contributions by some of the most distinguished specialists in the field, outgoing from the latest, significantly revised version of Lehrer's theory. All basic ideas are explained in an introductory chapter. Lehrer's extensive replies in a final chapter give unique access to his current epistemological thinking.

The Greek and Roman Critics

The Greek and Roman Critics

  • Author: G. M. A. Grube
  • Publisher: Hackett Publishing
  • ISBN: 9780872203105
  • Category: Literary Criticism
  • Page: 372
  • View: 3221
DOWNLOAD NOW »
A reprint of the University of Toronto edition of 1965.

Symmetry: A Very Short Introduction

Symmetry: A Very Short Introduction

  • Author: Ian Stewart
  • Publisher: OUP Oxford
  • ISBN: 019165275X
  • Category: Mathematics
  • Page: 152
  • View: 2488
DOWNLOAD NOW »
In the 1800s mathematicians introduced a formal theory of symmetry: group theory. Now a branch of abstract algebra, this subject first arose in the theory of equations. Symmetry is an immensely important concept in mathematics and throughout the sciences, and its applications range across the entire subject. Symmetry governs the structure of crystals, innumerable types of pattern formation, how systems change their state as parameters vary; and fundamental physics is governed by symmetries in the laws of nature. It is highly visual, with applications that include animal markings, locomotion, evolutionary biology, elastic buckling, waves, the shape of the Earth, and the form of galaxies. In this Very Short Introduction, Ian Stewart demonstrates its deep implications, and shows how it plays a major role in the current search to unify relativity and quantum theory. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.

Reflection: Principles and Practices for Healthcare Professionals 2nd Edition

Reflection: Principles and Practices for Healthcare Professionals 2nd Edition

  • Author: Tony Ghaye,Sue Lillyman
  • Publisher: Andrews UK Limited
  • ISBN: 1856424510
  • Category: Medical
  • Page: 203
  • View: 3155
DOWNLOAD NOW »
In this newly updated edition of the bestselling Reflections: Principles and Practice for Healthcare Professionals, the authors reinforce the need to invest in the development of reflective practice, not only for practitioners, but also for healthcare students. The book discusses the need for skilful facilitation, high quality mentoring and the necessity for good support networks. The book describes the 12 principles of reflection and the many ways it can be facilitated. It attempts to support, with evidence, the claims that reflection can be a catalyst for enhancing clinical competence, safe and accountable practice, professional self-confidence, self-regulation and the collective improvement of more considered and appropriate healthcare. Each principle is illustrated with examples from practice and clearly positioned within the professional literature. New chapters on appreciative reflection and the value of reflection for continuing professional development are included making this an essential guide for all healthcare professionals.

Enhancing Mathematics Understanding through Visualization: The Role of Dynamical Software

Enhancing Mathematics Understanding through Visualization: The Role of Dynamical Software

The Role of Dynamical Software

  • Author: Habre, Samer
  • Publisher: IGI Global
  • ISBN: 1466640510
  • Category: Education
  • Page: 298
  • View: 3556
DOWNLOAD NOW »
Mathematics is, by its very nature, an abstract discipline. However, many students learn best by thinking in terms of tangible constructs. Enhancing Mathematics Understanding through Visualization: The Role of Dynamical Software brings these conflicting viewpoints together by offering visual representations as a method of mathematics instruction. The book explores the role of technology in providing access to multiple representations of concepts, using software applications to create a rich environment in which a student’s understanding of mathematical concepts can flourish. Both students and instructors of mathematics at the university level will use this book to implement various novel techniques for the delivery of mathematical concepts in their classrooms. This book is part of the Research Essential collection.

From Summetria to Symmetry: The Making of a Revolutionary Scientific Concept

From Summetria to Symmetry: The Making of a Revolutionary Scientific Concept

  • Author: Giora Hon,Bernard R. Goldstein
  • Publisher: Springer Science & Business Media
  • ISBN: 140208448X
  • Category: Science
  • Page: 336
  • View: 7389
DOWNLOAD NOW »
Many literary critics seem to think that an hypothesis about obscure and remote questions of history can be refuted by a simple demand for the production of more evidence than in fact exists. The demand is as easy to make as it is impossible to satisfy. But the true test of an hypothesis, if it cannot be shown to con?ict with known truths, is the number of facts that it correlates and explains. Francis M. Cornford [1914] 1934, 220. It was in the autumn of 1997 that the research project leading to this publication began. One of us [GH], while a visiting fellow at the Center for Philosophy of Science (University of Pittsburgh), gave a talk entitled, “Proportions and Identity: The Aesthetic Aspect of Symmetry”. The presentation focused on a confusion s- rounding the concept of symmetry: it exhibits unity, yet it is often claimed to reveal a form of beauty, namely, harmony, which requires a variety of elements. In the audience was the co-author of this book [BRG] who responded with enthusiasm, seeking to extend the discussion of this issue to historical sources in earlier periods. A preliminary search of the literature persuaded us that the history of symmetry was rich in possibilities for new insights into the making of concepts. John Roche’s brief essay (1987), in which he sketched the broad outlines of the history of this concept, was particularly helpful, and led us to conclude that the subject was worthy of monographic treatment.

Introductory Tiling Theory for Computer Graphics

Introductory Tiling Theory for Computer Graphics

  • Author: Craig Kaplan
  • Publisher: Morgan & Claypool Publishers
  • ISBN: 160845018X
  • Category: Computers
  • Page: 113
  • View: 5220
DOWNLOAD NOW »
Tiling theory is an elegant branch of mathematics that has applications in several areas of computer science. The most immediate application area is graphics, where tiling theory has been used in the contexts of texture generation, sampling theory, remeshing, and of course the generation of decorative patterns. The combination of a solid theoretical base (complete with tantalizing open problems), practical algorithmic techniques, and exciting applications make tiling theory a worthwhile area of study for practitioners and students in computer science. This synthesis lecture introduces the mathematical and algorithmic foundations of tiling theory to a computer graphics audience. The goal is primarily to introduce concepts and terminology, clear up common misconceptions, and state and apply important results. The book also describes some of the algorithms and data structures that allow several aspects of tiling theory to be used in practice. Table of Contents: Introduction / Tiling Basics / Symmetry / Tilings by Polygons / Isohedral Tilings / Nonperiodic and Aperiodic Tilings / Survey

Crystallography and the World of Symmetry

Crystallography and the World of Symmetry

  • Author: Sanat K. Chatterjee
  • Publisher: Springer Science & Business Media
  • ISBN: 354069899X
  • Category: Science
  • Page: 152
  • View: 3817
DOWNLOAD NOW »
Symmetry exists in realms from crystals to patterns, in external shapes of living or non-living objects, as well as in the fundamental particles and the physical laws that govern them. In fact, the search for this symmetry is the driving force for the discovery of many fundamental particles and the formulation of many physical laws. While one can not imagine a world which is absolutely symmetrical nor can one a world which is absolutely asymmetrical. These two aspects of nature are intermingled with each other inseparably. This is the basis of the existence of aperiodicity manifested in the liquid crystals and also quasi-crystals also discussed in “Crystallography and the World of Symmetry”.