Shapes, Space, and Symmetry

Shapes, Space, and Symmetry
Title Shapes, Space, and Symmetry PDF eBook
Author Alan Holden
Publisher Courier Corporation
Pages 218
Release 1991-01-01
Genre Mathematics
ISBN 9780486268514

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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, Shape and Space

Symmetry, Shape and Space
Title Symmetry, Shape and Space PDF eBook
Author L.Christine Kinsey
Publisher Springer Science & Business Media
Pages 524
Release 2006-05-09
Genre Mathematics
ISBN 9781930190092

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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.

The Shape of Space

The Shape of Space
Title The Shape of Space PDF eBook
Author Jeffrey R. Weeks
Publisher CRC Press
Pages 405
Release 2001-12-12
Genre Mathematics
ISBN 0203912667

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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.

Number, Shape, & Symmetry

Number, Shape, & Symmetry
Title Number, Shape, & Symmetry PDF eBook
Author Diane L. Herrmann
Publisher CRC Press
Pages 446
Release 2012-10-18
Genre Mathematics
ISBN 1466554649

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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.

The Universe in the Rearview Mirror

The Universe in the Rearview Mirror
Title The Universe in the Rearview Mirror PDF eBook
Author Dave Goldberg
Publisher Penguin
Pages 354
Release 2014-06-24
Genre Science
ISBN 0142181048

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“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.

The Symmetries of Things

The Symmetries of Things
Title The Symmetries of Things PDF eBook
Author John H. Conway
Publisher CRC Press
Pages 442
Release 2016-04-05
Genre Mathematics
ISBN 1439864896

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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 Shape of Inner Space

The Shape of Inner Space
Title The Shape of Inner Space PDF eBook
Author Shing-Tung Yau
Publisher Il Saggiatore
Pages 398
Release 2010-09-07
Genre Mathematics
ISBN 0465020232

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The leading mind behind the mathematics of string theory discusses how geometry explains the universe we see. Illustrations.