Download or read book Symmetry Shape and Space written by L.Christine Kinsey and published by Springer Science & Business Media. This book was released on 2006-05-09 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book will appeal to at least three groups of readers: prospective high school teachers, liberal arts students, and parents whose children are studying high school or college math. It is modern in its selection of topics, and in the learning models used by the authors. The book covers some exciting but non-traditional topics from the subject area of geometry. It is also intended for undergraduates and tries to engage their interest in mathematics. Many innovative pedagogical modes are used throughout.
Download or read book Shapes Space and Symmetry written by Alan Holden and published by Courier Corporation. This book was released on 1991-01-01 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Number Shape Symmetry written by Diane L. Herrmann and published by CRC Press. This book was released on 2012-10-18 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: Through a careful treatment of number theory and geometry, Number, Shape, & Symmetry: An Introduction to Number Theory, Geometry, and Group Theory helps readers understand serious mathematical ideas and proofs. Classroom-tested, the book draws on the authors’ successful work with undergraduate students at the University of Chicago, seventh to tenth grade mathematically talented students in the University of Chicago’s Young Scholars Program, and elementary public school teachers in the Seminars for Endorsement in Science and Mathematics Education (SESAME). The first half of the book focuses on number theory, beginning with the rules of arithmetic (axioms for the integers). The authors then present all the basic ideas and applications of divisibility, primes, and modular arithmetic. They also introduce the abstract notion of a group and include numerous examples. The final topics on number theory consist of rational numbers, real numbers, and ideas about infinity. Moving on to geometry, the text covers polygons and polyhedra, including the construction of regular polygons and regular polyhedra. It studies tessellation by looking at patterns in the plane, especially those made by regular polygons or sets of regular polygons. The text also determines the symmetry groups of these figures and patterns, demonstrating how groups arise in both geometry and number theory. The book is suitable for pre-service or in-service training for elementary school teachers, general education mathematics or math for liberal arts undergraduate-level courses, and enrichment activities for high school students or math clubs.
Download or read book The Shape of Inner Space written by Shing-Tung Yau and published by Il Saggiatore. This book was released on 2010-09-07 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: The leading mind behind the mathematics of string theory discusses how geometry explains the universe we see. Illustrations.
Download or read book Symmetry A Very Short Introduction written by Ian Stewart and published by OUP Oxford. This book was released on 2013-05-30 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Digital Foundations written by xtine burrough and published by Peachpit Press. This book was released on 2008-12-11 with total page 563 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fuses design fundamentals and software training into one cohesive book! The only book to teach Bauhaus design principles alongside basic digital tools of Adobe's Creative Suite, including the recently released Adobe CS4 Addresses the growing trend of compressing design fundamentals and design software into the same course in universities and design trade schools. Lessons are timed to be used in 50-minute class sessions. Digital Foundations uses formal exercises of the Bauhaus to teach the Adobe Creative Suite. All students of digital design and production—whether learning in a classroom or on their own—need to understand the basic principles of design in order to implement them using current software. Far too often design is left out of books that teach software. Consequently, the design software training exercise is often a lost opportunity for visual learning. Digital Foundations reinvigorates software training by integrating Bauhaus design exercises into tutorials fusing design fundamentals and core Adobe Creative Suite methodologies. The result is a cohesive learning experience. Design topics and principles include: Composition; Symmetry and Asymmetry; Gestalt; Appropriation; The Bauhaus Basic Course Approach; Color Theory; The Grid; Scale, Hierarchy and Collage; Tonal Range; Elements of Motion. Digital Foundations is an AIGA Design Press book, published under Peachpit's New Riders imprint in partnership with AIGA, the professional association for design.
Download or read book The Shape of Space written by Jeffrey R. Weeks and published by CRC Press. This book was released on 2001-12-12 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: Maintaining the standard of excellence set by the previous edition, this textbook covers the basic geometry of two- and three-dimensional spaces Written by a master expositor, leading researcher in the field, and MacArthur Fellow, it includes experiments to determine the true shape of the universe and contains illustrated examples and engaging exercises that teach mind-expanding ideas in an intuitive and informal way. Bridging the gap from geometry to the latest work in observational cosmology, the book illustrates the connection between geometry and the behavior of the physical universe and explains how radiation remaining from the big bang may reveal the actual shape of the universe.
Download or read book The Symmetries of Things written by John H. Conway and published by CRC Press. This book was released on 2016-04-05 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Symmetry Causality Mind written by Michael Leyton and published by MIT Press. This book was released on 1992 with total page 644 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Groups and Symmetry A Guide to Discovering Mathematics written by David W. Farmer and published by American Mathematical Soc.. This book was released on 1996 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics is discovered by looking at examples, noticing patterns, making conjectures, and testing those conjectures. Once discovered, the final results get organized and put in textbooks. The details and the excitement of the discovery are lost. This book introduces the reader to the excitement of the original discovery. By means of a wide variety of tasks, readers are led to find interesting examples, notice patterns, devise rules to explain the patterns, and discover mathematics for themselves. The subject studied here is the mathematics behind the idea of symmetry, but the methods and ideas apply to all of mathematics. The only prerequisites are enthusiasm and a knowledge of basic high-school math. The book is only a guide. It will start you off in the right direction and bring you back if you stray too far. The excitement and the discovery are left to you.
Download or read book The Shape of a Life written by Shing-Tung Yau and published by Yale University Press. This book was released on 2019-02-19 with total page 449 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Fields medalist recounts his lifelong effort to uncover the geometric shape—the Calabi-Yau manifold—that may store the hidden dimensions of our universe. Harvard geometer Shing-Tung Yau has provided a mathematical foundation for string theory, offered new insights into black holes, and mathematically demonstrated the stability of our universe. In this autobiography, Yau reflects on his improbable journey to becoming one of the world’s most distinguished mathematicians. Beginning with an impoverished childhood in China and Hong Kong, Yau takes readers through his doctoral studies at Berkeley during the height of the Vietnam War protests, his Fields Medal–winning proof of the Calabi conjecture, his return to China, and his pioneering work in geometric analysis. This new branch of geometry, which Yau built up with his friends and colleagues, has paved the way for solutions to several important and previously intransigent problems. With complicated ideas explained for a broad audience, this book offers not only insights into the life of an eminent mathematician, but also an accessible way to understand advanced and highly abstract concepts in mathematics and theoretical physics. “The remarkable story of one of the world’s most accomplished mathematicians . . . Yau’s personal journey—from escaping China as a youngster, leading a gang outside Hong Kong, becoming captivated by mathematics, to making breakthroughs that thrust him on the world stage—inspires us all with humankind’s irrepressible spirit of discovery.” —Brian Greene, New York Times–bestselling author of The Elegant Universe “An unexpectedly intimate look into a highly accomplished man, his colleagues and friends, the development of a new field of geometric analysis, and a glimpse into a truly uncommon mind.” —The Boston Globe “Engaging, eminently readable. . . . For those with a taste for elegant and largely jargon-free explanations of mathematics, The Shape of a Life promises hours of rewarding reading.” —American Scientist
Download or read book Shape written by Jordan Ellenberg and published by Penguin. This book was released on 2021-05-25 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: An instant New York Times Bestseller! “Unreasonably entertaining . . . reveals how geometric thinking can allow for everything from fairer American elections to better pandemic planning.” —The New York Times From the New York Times-bestselling author of How Not to Be Wrong—himself a world-class geometer—a far-ranging exploration of the power of geometry, which turns out to help us think better about practically everything. How should a democracy choose its representatives? How can you stop a pandemic from sweeping the world? How do computers learn to play Go, and why is learning Go so much easier for them than learning to read a sentence? Can ancient Greek proportions predict the stock market? (Sorry, no.) What should your kids learn in school if they really want to learn to think? All these are questions about geometry. For real. If you're like most people, geometry is a sterile and dimly remembered exercise you gladly left behind in the dust of ninth grade, along with your braces and active romantic interest in pop singers. If you recall any of it, it's plodding through a series of miniscule steps only to prove some fact about triangles that was obvious to you in the first place. That's not geometry. Okay, it is geometry, but only a tiny part, which has as much to do with geometry in all its flush modern richness as conjugating a verb has to do with a great novel. Shape reveals the geometry underneath some of the most important scientific, political, and philosophical problems we face. Geometry asks: Where are things? Which things are near each other? How can you get from one thing to another thing? Those are important questions. The word "geometry"comes from the Greek for "measuring the world." If anything, that's an undersell. Geometry doesn't just measure the world—it explains it. Shape shows us how.
Download or read book The Universe in the Rearview Mirror written by Dave Goldberg and published by Penguin. This book was released on 2014-06-24 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: “A great read… Goldberg is an excellent guide.”—Mario Livio, bestselling author of The Golden Ratio Physicist Dave Goldberg speeds across space, time and everything in between showing that our elegant universe—from the Higgs boson to antimatter to the most massive group of galaxies—is shaped by hidden symmetries that have driven all our recent discoveries about the universe and all the ones to come. Why is the sky dark at night? If there is anti-matter, can there be anti-people? Why are past, present, and future our only options? Saluting the brilliant but unsung female mathematician Emmy Noether as well as other giants of physics, Goldberg answers these questions and more, exuberantly demonstrating that symmetry is the big idea—and the key to what lies ahead.
Download or read book Shape Perception in Human and Computer Vision written by Sven J. Dickinson and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 505 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive and authoritative text/reference presents a unique, multidisciplinary perspective on Shape Perception in Human and Computer Vision. Rather than focusing purely on the state of the art, the book provides viewpoints from world-class researchers reflecting broadly on the issues that have shaped the field. Drawing upon many years of experience, each contributor discusses the trends followed and the progress made, in addition to identifying the major challenges that still lie ahead. Topics and features: examines each topic from a range of viewpoints, rather than promoting a specific paradigm; discusses topics on contours, shape hierarchies, shape grammars, shape priors, and 3D shape inference; reviews issues relating to surfaces, invariants, parts, multiple views, learning, simplicity, shape constancy and shape illusions; addresses concepts from the historically separate disciplines of computer vision and human vision using the same “language” and methods.
Download or read book Symmetry written by Hermann Weyl and published by Princeton University Press. This book was released on 2015-07-06 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Timeless Reality written by Victor J. Stenger and published by Prometheus Books. This book was released on 2009-12-02 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: A professor of physics and astronomy studies a theory that time is reversible, and explains how physicists have generally been reluctant to accept the reversibility of time because of the implied causal paradoxes. Illustrations.
Download or read book Dynamic Symmetry written by Tavis Leaf Glover and published by Tavis Leaf Glover. This book was released on 2019-02-25 with total page 510 pages. Available in PDF, EPUB and Kindle. Book excerpt: Serious visual artists can now easily understand and apply the secret geometry that masters used to create remarkable art. Superior mathematical skills aren’t required because there are hundreds of excellent step-by-step diagrams to explain everything with simplicity. Learn how the ancient and modern masters used dynamic symmetry to promote unity, movement, rhythm, and strength. These qualities, along with many others, allowed their art to have visual clarity, impact, and stand the test of time. This is an essential book for painters, photographers, sculptors, and cinematographers that hold composition and design with a high priority. For far too long, artists have been stuck with the basic tools of artistic composition, like the rule of thirds and leading lines. Unfortunately, we’re incapable of reaching the master level if all we know are the basics. Powerful tools like dynamic symmetry and other composition techniques have been kept a secret from all of us. It’s time to learn of them, push past any plateau that stands in our way, and finally unlock our true potential!
