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Geometry And Symmetry
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Book Synopsis Geometry and Symmetry by : L. Christine Kinsey
Download or read book Geometry and Symmetry written by L. Christine Kinsey and published by John Wiley & Sons. This book was released on 2010-04-19 with total page 960 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new book helps students gain an appreciation of geometry and its importance in the history and development of mathematics. The material is presented in three parts. The first is devoted to Euclidean geometry. The second covers non-Euclidean geometry. The last part explores symmetry. Exercises and activities are interwoven with the text to enable them to explore geometry. The activities take advantage of geometric software so they'll gain a better understanding of its capabilities. Mathematics teachers will be able to use this material to create exciting and engaging projects in the classroom.
Book Synopsis Geometry and Symmetry by : Paul B. Yale
Download or read book Geometry and Symmetry written by Paul B. Yale and published by Courier Corporation. This book was released on 2014-05-05 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: DIVIntroduction to the geometry of euclidean, affine and projective spaces with special emphasis on the important groups of symmetries of these spaces. Many exercises, extensive bibliography. Advanced undergraduate level. /div
Book Synopsis Mirror Symmetry and Algebraic Geometry by : David A. Cox
Download or read book Mirror Symmetry and Algebraic Geometry written by David A. Cox and published by American Mathematical Soc.. This book was released on 1999 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematicians wanting to get into the field ... will find a very well written and encyclopaedic account of the mathematics which was needed in, and was developed from, what now might be termed classical mirror symmetry. --Bulletin of the LMS The book is highly recommended for everyone who wants to learn about the fascinating recent interplay between physics and mathematics. --Mathematical Reviews Mirror symmetry began when theoretical physicists made some astonishing predictions about rational curves on quintic hypersurfaces in four-dimensional projective space. Understanding the mathematics behind these predictions has been a substantial challenge. This book is a completely comprehensive monograph on mirror symmetry, covering the original observations by the physicists through the most recent progress made to date. Subjects discussed include toric varieties, Hodge theory, Kahler geometry, moduli of stable maps, Calabi-Yau manifolds, quantum cohomology, Gromov-Witten invariants, and the mirror theorem.
Book Synopsis Number, Shape, & Symmetry by : Diane L. Herrmann
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.
Book Synopsis Symmetry, Shape and Space by : L.Christine Kinsey
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.
Book Synopsis Symmetry and Pattern in Projective Geometry by : Eric Lord
Download or read book Symmetry and Pattern in Projective Geometry written by Eric Lord and published by Springer Science & Business Media. This book was released on 2012-12-14 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: Symmetry and Pattern in Projective Geometry is a self-contained study of projective geometry which compares and contrasts the analytic and axiomatic methods. The analytic approach is based on homogeneous coordinates, and brief introductions to Plücker coordinates and Grassmann coordinates are presented. This book looks carefully at linear, quadratic, cubic and quartic figures in two, three and higher dimensions. It deals at length with the extensions and consequences of basic theorems such as those of Pappus and Desargues. The emphasis throughout is on special configurations that have particularly interesting symmetry properties. The intricate and novel ideas of ‘Donald’ Coxeter, who is considered one of the great geometers of the twentieth century, are also discussed throughout the text. The book concludes with a useful analysis of finite geometries and a description of some of the remarkable configurations discovered by Coxeter. This book will be appreciated by mathematics students and those wishing to learn more about the subject of geometry. It makes accessible subjects and theorems which are often considered quite complicated and presents them in an easy-to-read and enjoyable manner.
Book Synopsis Geometric Symmetry in Patterns and Tilings by : C E Horne
Download or read book Geometric Symmetry in Patterns and Tilings written by C E Horne and published by Elsevier. This book was released on 2000-10-23 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book encompasses a wide range of mathematical concepts relating to regularly repeating surface decoration from basic principles of symmetry to more complex issues of graph theory, group theory and topology. It presents a comprehensive means of classifying and constructing patterns and tilings. The classification of designs is investigated and discussed forming a broad basis upon which designers may build their own ideas. A wide range of original illustrative material is included. In a complex area previously best understood by mathematicians and crystallographers, the author develops and applies mathematical thinking to the context of regularly repeating surface-pattern design in a manner accessible to artists and designers. Design construction is covered from first principles through to methods appropriate for adaptation to large-scale screen-printing production. The book extends mathematical thinking beyond symmetry group classification. New ideas are developed involving motif orientation and positioning, including reference to a crystal structure, leading on to the classification and construction of discrete patterns and isohedral tilings. Designed to broaden the scope of surface-pattern designers by increasing their knowledge in otherwise impenetrable theory of geometry this 'designer friendly' book serves as a manual for all types of surface design including textiles, wallpapers and wrapping paper. It is also of value to crystallographers, mathematicians and architects.
Book Synopsis Geometric Mechanics and Symmetry by : Darryl D. Holm
Download or read book Geometric Mechanics and Symmetry written by Darryl D. Holm and published by Oxford University Press. This book was released on 2009-07-30 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Classical mechanics, one of the oldest branches of science, has undergone a long evolution, developing hand in hand with many areas of mathematics, including calculus, differential geometry, and the theory of Lie groups and Lie algebras. The modern formulations of Lagrangian and Hamiltonian mechanics, in the coordinate-free language of differential geometry, are elegant and general. They provide a unifying framework for many seemingly disparate physical systems, such as n particle systems, rigid bodies, fluids and other continua, and electromagnetic and quantum systems. Geometric Mechanics and Symmetry is a friendly and fast-paced introduction to the geometric approach to classical mechanics, suitable for a one- or two- semester course for beginning graduate students or advanced undergraduates. It fills a gap between traditional classical mechanics texts and advanced modern mathematical treatments of the subject. After a summary of the necessary elements of calculus on smooth manifolds and basic Lie group theory, the main body of the text considers how symmetry reduction of Hamilton's principle allows one to derive and analyze the Euler-Poincaré equations for dynamics on Lie groups. Additional topics deal with rigid and pseudo-rigid bodies, the heavy top, shallow water waves, geophysical fluid dynamics and computational anatomy. The text ends with a discussion of the semidirect-product Euler-Poincaré reduction theorem for ideal fluid dynamics. A variety of examples and figures illustrate the material, while the many exercises, both solved and unsolved, make the book a valuable class text.
Book Synopsis Why Beauty Is Truth by : Ian Stewart
Download or read book Why Beauty Is Truth written by Ian Stewart and published by . This book was released on 2008-04-29 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: Physics.
Book Synopsis Shapes, Space, and Symmetry by : Alan Holden
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.
Book Synopsis Symmetry: A Very Short Introduction by : Ian Stewart
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 152 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.
Book Synopsis Transformation Geometry by : George E. Martin
Download or read book Transformation Geometry written by George E. Martin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: Transformation Geometry: An Introduction to Symmetry offers a modern approach to Euclidean Geometry. This study of the automorphism groups of the plane and space gives the classical concrete examples that serve as a meaningful preparation for the standard undergraduate course in abstract algebra. The detailed development of the isometries of the plane is based on only the most elementary geometry and is appropriate for graduate courses for secondary teachers.
Book Synopsis Homological Mirror Symmetry and Tropical Geometry by : Ricardo Castano-Bernard
Download or read book Homological Mirror Symmetry and Tropical Geometry written by Ricardo Castano-Bernard and published by Springer. This book was released on 2014-10-07 with total page 445 pages. Available in PDF, EPUB and Kindle. Book excerpt: The relationship between Tropical Geometry and Mirror Symmetry goes back to the work of Kontsevich and Y. Soibelman (2000), who applied methods of non-archimedean geometry (in particular, tropical curves) to Homological Mirror Symmetry. In combination with the subsequent work of Mikhalkin on the “tropical” approach to Gromov-Witten theory and the work of Gross and Siebert, Tropical Geometry has now become a powerful tool. Homological Mirror Symmetry is the area of mathematics concentrated around several categorical equivalences connecting symplectic and holomorphic (or algebraic) geometry. The central ideas first appeared in the work of Maxim Kontsevich (1993). Roughly speaking, the subject can be approached in two ways: either one uses Lagrangian torus fibrations of Calabi-Yau manifolds (the so-called Strominger-Yau-Zaslow picture, further developed by Kontsevich and Soibelman) or one uses Lefschetz fibrations of symplectic manifolds (suggested by Kontsevich and further developed by Seidel). Tropical Geometry studies piecewise-linear objects which appear as “degenerations” of the corresponding algebro-geometric objects.
Download or read book Symmetry written by David Wade and published by Bloomsbury Publishing USA. This book was released on 2006-10-17 with total page 68 pages. Available in PDF, EPUB and Kindle. Book excerpt: As much of interest to mathematicians as it is to artists, as relevant to physics as to architecture, symmetry underlies almost every aspect of nature and our experience of the world. Illustrated with old engravings and original work by the author, this book moves from church windows and mirror reflections to the deepest ideas of hidden symmetries in physics and geometry, music and the arts, left- and right-handedness.
Book Synopsis Introduction to Geometry of Manifolds with Symmetry by : V.V. Trofimov
Download or read book Introduction to Geometry of Manifolds with Symmetry written by V.V. Trofimov and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: One ofthe most important features of the development of physical and mathematical sciences in the beginning of the 20th century was the demolition of prevailing views of the three-dimensional Euclidean space as the only possible mathematical description of real physical space. Apriorization of geometrical notions and identification of physical 3 space with its mathematical modellR were characteristic for these views. The discovery of non-Euclidean geometries led mathematicians to the understanding that Euclidean geometry is nothing more than one of many logically admissible geometrical systems. Relativity theory amended our understanding of the problem of space by amalgamating space and time into an integral four-dimensional manifold. One of the most important problems, lying at the crossroad of natural sciences and philosophy is the problem of the structure of the world as a whole. There are a lot of possibilities for the topology offour dimensional space-time, and at first sight a lot of possibilities arise in cosmology. In principle, not only can the global topology of the universe be complicated, but also smaller scale topological structures can be very nontrivial. One can imagine two "usual" spaces connected with a "throat", making the topology of the union complicated.
Book Synopsis Continuous Symmetry by : William H. Barker
Download or read book Continuous Symmetry written by William H. Barker and published by American Mathematical Soc.. This book was released on 2007 with total page 570 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fundamental idea of geometry is that of symmetry. With that principle as the starting point, Barker and Howe begin an insightful and rewarding study of Euclidean geometry. The primary focus of the book is on transformations of the plane. The transformational point of view provides both a path for deeper understanding of traditional synthetic geometry and tools for providing proofs that spring from a consistent point of view. As a result, proofs become more comprehensible, as techniques can be used and reused in similar settings. The approach to the material is very concrete, with complete explanations of all the important ideas, including foundational background. The discussions of the nine-point circle and wallpaper groups are particular examples of how the strength of the transformational point of view and the care of the authors' exposition combine to give a remarkable presentation of topics in geometry. This text is for a one-semester undergraduate course on geometry. It is richly illustrated and contains hundreds of exercises.
Book Synopsis Tropical Geometry and Mirror Symmetry by : Mark Gross
Download or read book Tropical Geometry and Mirror Symmetry written by Mark Gross and published by American Mathematical Soc.. This book was released on 2011-01-20 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tropical geometry provides an explanation for the remarkable power of mirror symmetry to connect complex and symplectic geometry. The main theme of this book is the interplay between tropical geometry and mirror symmetry, culminating in a description of the recent work of Gross and Siebert using log geometry to understand how the tropical world relates the A- and B-models in mirror symmetry. The text starts with a detailed introduction to the notions of tropical curves and manifolds, and then gives a thorough description of both sides of mirror symmetry for projective space, bringing together material which so far can only be found scattered throughout the literature. Next follows an introduction to the log geometry of Fontaine-Illusie and Kato, as needed for Nishinou and Siebert's proof of Mikhalkin's tropical curve counting formulas. This latter proof is given in the fourth chapter. The fifth chapter considers the mirror, B-model side, giving recent results of the author showing how tropical geometry can be used to evaluate the oscillatory integrals appearing. The final chapter surveys reconstruction results of the author and Siebert for ``integral tropical manifolds.'' A complete version of the argument is given in two dimensions.
