The Language of Symmetry

The Language of Symmetry PDF

Author: Benedict Rattigan

Publisher: CRC Press

Published: 2023-05-16

Total Pages: 138

ISBN-13: 1000840107

DOWNLOAD EBOOK →

The Language of Symmetry is a re-assessment of the structure and reach of symmetry, by an interdisciplinary group of specialists from the arts, humanities, and sciences at Oxford University. It explores, amongst other topics: order and chaos in the formation of planetary systems entropy and symmetry in physics group theory, fractals, and self-similarity symmetrical structures in western classical music how biological systems harness disorder to create order This book aims to open up the scope of interdisciplinary work in the study of symmetry and is intended for scholars of any background - whether it be science, arts, or philosophy.

The Symmetries of Things

The Symmetries of Things PDF

Author: John H. Conway

Publisher: CRC Press

Published: 2016-04-05

Total Pages: 442

ISBN-13: 1439864896

DOWNLOAD EBOOK →

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 Equation That Couldn't Be Solved

The Equation That Couldn't Be Solved PDF

Author: Mario Livio

Publisher: Simon and Schuster

Published: 2005-09-19

Total Pages: 367

ISBN-13: 0743274628

DOWNLOAD EBOOK →

The author of The Golden Ratio tells the “lively and fascinating” story of two nineteenth-century mathematicians whose work revealed the laws of symmetry (Nature). What do Bach’s compositions, Rubik’s Cube, the way we choose our mates, and the physics of subatomic particles have in common? All are governed by the laws of symmetry, which elegantly unify scientific and artistic principles. Yet the mathematical language of symmetry—known as group theory—did not emerge from the study of symmetry at all, but from an equation that couldn’t be solved. For three centuries, the quintic equation resisted efforts by mathematicians to find a solution. Working independently, two great prodigies ultimately proved that it couldn’t be solved by a simple formula. These geniuses, a Norwegian named Niels Henrik Abel and a romantic Frenchman named Évariste Galois, both died tragically young. Their incredible labor, however, produced the origins of group theory. The first extensive, popular account of the mathematics of symmetry and order, The Equation That Couldn’t Be Solved is told not through abstract formulas but in a dramatic account of the lives and work of some of the greatest mathematicians in history.

Symmetry Theory in Molecular Physics with Mathematica

Symmetry Theory in Molecular Physics with Mathematica PDF

Author: William McClain

Publisher: Springer Science & Business Media

Published: 2010-03-12

Total Pages: 672

ISBN-13: 0387734708

DOWNLOAD EBOOK →

Prof. McClain has, quite simply, produced a new kind of tutorial book. It is written using the logic engine Mathematica, which permits concrete exploration and development of every concept involved in Symmetry Theory. It is aimed at students of chemistry and molecular physics who need to know mathematical group theory and its applications, either for their own research or for understanding the language and concepts of their field. The book begins with the most elementary symmetry concepts, then presents mathematical group theory, and finally the projection operators that flow from the Great Orthogonality are automated and applied to chemical and spectroscopic problems.

Beautiful Symmetry

Beautiful Symmetry PDF

Author: Alex Berke

Publisher: MIT Press

Published: 2020-02-18

Total Pages: 165

ISBN-13: 026253892X

DOWNLOAD EBOOK →

A coloring book that invites readers to explore symmetry and the beauty of math visually. Beautiful Symmetry is a coloring book about math, inviting us to engage with mathematical concepts visually through coloring challenges and visual puzzles. We can explore symmetry and the beauty of mathematics playfully, coloring through ideas usually reserved for advanced courses. The book is for children and adults, for math nerds and math avoiders, for educators, students, and coloring enthusiasts. Through illustration, language that is visual, and words that are jargon-free, the book introduces group theory as the mathematical foundation for discussions of symmetry, covering symmetry groups that include the cyclic groups, frieze groups, and wallpaper groups. The illustrations are drawn by algorithms, following the symmetry rules for each given group. The coloring challenges can be completed and fully realized only on the page; solutions are provided. Online, in a complementary digital edition, the illustrations come to life with animated interactions that show the symmetries that generated them. Traditional math curricula focus on arithmetic and the manipulation of numbers, and may make some learners feel that math is not for them. By offering a more visual and tactile approach, this book shows how math can be for everyone. Combining the playful and the pedagogical, Beautiful Symmetry offers both relaxing entertainment for recreational colorers and a resource for math-curious readers, students, and educators.

Symmetry, Causality, Mind

Symmetry, Causality, Mind PDF

Author: Michael Leyton

Publisher: MIT Press

Published: 1992

Total Pages: 644

ISBN-13: 9780262621311

DOWNLOAD EBOOK →

In this investigation of the psychological relationship between shape and time, Leyton argues compellingly that shape is used by the mind to recover the past and as such it forms a basis for memory. Michael Leyton's arguments about the nature of perception and cognition are fascinating, exciting, and sure to be controversial. In this investigation of the psychological relationship between shape and time, Leyton argues compellingly that shape is used by the mind to recover the past and as such it forms a basis for memory. He elaborates a system of rules by which the conversion to memory takes place and presents a number of detailed case studies--in perception, linguistics, art, and even political subjugation--that support these rules. Leyton observes that the mind assigns to any shape a causal history explaining how the shape was formed. We cannot help but perceive a deformed can as a dented can. Moreover, by reducing the study of shape to the study of symmetry, he shows that symmetry is crucial to our everyday cognitive processing. Symmetry is the means by which shape is converted into memory. Perception is usually regarded as the recovery of the spatial layout of the environment. Leyton, however, shows that perception is fundamentally the extraction of time from shape. In doing so, he is able to reduce the several areas of computational vision purely to symmetry principles. Examining grammar in linguistics, he argues that a sentence is psychologically represented as a piece of causal history, an archeological relic disinterred by the listener so that the sentence reveals the past. Again through a detailed analysis of art he shows that what the viewer takes to be the experience of a painting is in fact the extraction of time from the shapes of the painting. Finally he highlights crucial aspects of the mind's attempt to recover time in examples of political subjugation.

Symmetry

Symmetry PDF

Author: R. McWeeny

Publisher: Elsevier

Published: 2013-09-03

Total Pages: 263

ISBN-13: 1483226247

DOWNLOAD EBOOK →

Symmetry: An Introduction to Group Theory and its Application is an eight-chapter text that covers the fundamental bases, the development of the theoretical and experimental aspects of the group theory. Chapter 1 deals with the elementary concepts and definitions, while Chapter 2 provides the necessary theory of vector spaces. Chapters 3 and 4 are devoted to an opportunity of actually working with groups and representations until the ideas already introduced are fully assimilated. Chapter 5 looks into the more formal theory of irreducible representations, while Chapter 6 is concerned largely with quadratic forms, illustrated by applications to crystal properties and to molecular vibrations. Chapter 7 surveys the symmetry properties of functions, with special emphasis on the eigenvalue equation in quantum mechanics. Chapter 8 covers more advanced applications, including the detailed analysis of tensor properties and tensor operators. This book is of great value to mathematicians, and math teachers and students.

Learning from Language

Learning from Language PDF

Author: Walter H. Beale

Publisher: University of Pittsburgh Pre

Published: 2010-06-15

Total Pages: 209

ISBN-13: 082297360X

DOWNLOAD EBOOK →

In Learning from Language, Walter H. Beale seeks to bring together the disciplines of linguistics, rhetoric, and literary studies through the concept of symmetry (how words mirror thought, society, and our vision of the world).Citing thinkers from antiquity to the present, Beale provides an in-depth study of linguistic theory, development, and practice. He views the historic division between the schools of symmetry and asymmetry (a belief that language developed as a structure independent of human experience), as built into the character of language itself, and as an impediment to literary humanism (the combined study of language, rhetoric, and literature to improve the competence and character of the individual). In his analysis, Beale outlines and critiques traditional claims of symmetry, then offers new avenues of approach to the subject. In doing so, he examines how important issues of human culture and consciousness have parallels in processes of language; how linguistic patterns relate to pervasive human problems; how language is an active participant in the expression, performance, and construction of reality; the concepts of designating versus naming; figurative language as a process of reenvisioning reality; and the linking of style to virtue by the ancients. Beale concludes that both asymmetrical and symmetrical elements exist in language, each with their own relevance, and that they are complementary, rather than opposing philosophies. The basic intuitions of symmetry that relate language to life are powerful and important to all of English studies. Combined with a love for the workings, sounds, and structures of language, Beale says, an understanding of symmetry can help guide the pursuit of literary humanism.

Shapes, Space, and Symmetry

Shapes, Space, and Symmetry PDF

Author: Alan Holden

Publisher: Courier Corporation

Published: 1991-01-01

Total Pages: 218

ISBN-13: 9780486268514

DOWNLOAD EBOOK →

Explains structure of nine regular solids and many semiregular solids and demonstrates how they can be used to explain mathematics. Instructions for cardboard models. Over 300 illustrations. 1971 edition.

Symmetry Comes of Age

Symmetry Comes of Age PDF

Author: Dorothy Koster Washburn

Publisher: University of Washington Press

Published: 2004

Total Pages: 396

ISBN-13: 9780295983660

DOWNLOAD EBOOK →

The two volumes together offer readers a new window into the communicative importance of design."--Jacket.