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Symmetry And Pattern In Projective Geometry
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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 Symmetry and Pattern in Projective Geometry by : Abby Enger
Download or read book Symmetry and Pattern in Projective Geometry written by Abby Enger and published by . This book was released on 2016-10-01 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: We are all familiar with Euclidean geometry and with the fact that it describes our three dimensional world so well. In Euclidean geometry, the sides of objects have lengths, intersecting lines determine angles between them, and two lines are said to be parallel if they lie in the same plane and never meet. Moreover, these properties do not change when the Euclidean transformations (translation and rotation) are applied. Since Euclidean geometry describes our world so well, it is at first tempting to think that it is the only type of geometry. However, when we consider the imaging process of a camera, it becomes clear that Euclidean geometry is insufficient: Lengths and angles are no longer preserved, and parallel lines may intersect. Euclidean geometry is actually a subset of what is known as projective geometry. Projective geometry exists in any number of dimensions, just like Euclidean geometry. Projective geometry has its origins in the early Italian Renaissance, particularly in the architectural drawings of Filippo Brunelleschi (1377-1446) and Leon Battista Alberti (1404-72), who invented the method of perspective drawing. Projective geometry deals with the relationships between geometric figures and the images, or mappings that result from projecting them onto another surface. Common examples of projections are the shadows cast by opaque objects and motion pictures displayed on a screen.First of all, projective geometry is a jewel of mathematics, one of the outstanding achievements of the nineteenth century, a century of remarkable mathematical achievements such as non-Euclidean geometry, abstract algebra, and the foundations of calculus. Projective geometry is as much a part of a general education in mathematics as differential equations and Galois theory. Moreover, projective geometry is a prerequisite for algebraic geometry, one of today's most vigorous and exciting branches of mathematics. Secondly, for more than fifty years projective geometry has been propelled in a new direction by its combinatorial connections. The challenge of describing a classical geometric structure by its parameters - properties that at first glance might seem superficial - provided much of the impetus for finite geometry, another of today's flourishing branches of mathematics.
Book Synopsis Spiral Symmetry by : Istvan Hargittai
Download or read book Spiral Symmetry written by Istvan Hargittai and published by World Scientific. This book was released on 1992-03-24 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the tiny twisted biological molecules to the gargantuan curling arms of many galaxies, the physical world contains a startling repetition of spiral patterns. Today, researchers have a keen interest in identifying, measuring, and defining these patterns in scientific terms. Spirals play an important role in the growth processes of many biological forms and organisms. Also, through time, humans have imitated spiral motifs in their art forms, and invented new and unusual spirals which have no counterparts in the natural world. Therefore, one goal of this multiauthored book is to stress the conspicuous role that spirals play in science, and to show the reader how to create such spirals using a computer. Another goal is to show how simple mathematical formulas can reveal magnificent shapes and images. This interdisciplinary book revolves around a common theme, spiral symmetry, and is intended for scientists, humanists, and interested laypeople.
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 Woodhead Publishing. This book was released on 2000-10-23 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers a wide range of mathematical concepts as they are applied to regularly repeating surface decoration for textiles and other decorated materials such as wallpapers and wrappings. Starting with basic principles of symmetry it moves on to cover more complex issues of graph theory, group theory and topology. All these concepts are extensively illustrated with over 1000 original illustrations. A complex area, previously best understood by mathematicians and crystallographers, is made accessible here to artists and designers.
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 Isomorphisms, Symmetry and Computations in Algebraic Graph Theory by : Gareth A. Jones
Download or read book Isomorphisms, Symmetry and Computations in Algebraic Graph Theory written by Gareth A. Jones and published by Springer Nature. This book was released on 2020-01-10 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of a selection of peer-reviewed contributions to the Workshop on Algebraic Graph Theory that took place in Pilsen, Czech Republic in October 2016. Primarily intended for early career researchers, it presents eight self-contained articles on a selection of topics within algebraic combinatorics, ranging from association schemes to symmetries of graphs and isomorphism testing. Algebraic combinatorics is a compelling mathematical discipline based on the powerful interplay of algebraic and combinatorial methods. Algebraic interpretation of combinatorial structures (such as symmetry or regularity) has often led to enlightening discoveries and powerful results, while discrete and combinatorial structures have given rise to new algebraic structures that have found valuable applications. In addition to these original research contributions, the reader will find a survey linking numerous threads in algebraic combinatorics, and an extensive tutorial showcasing the universality of algebraic methods in the study of combinatorial structures.
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 An Introduction to Projective Geometry and Its Applications by : Arnold Emch
Download or read book An Introduction to Projective Geometry and Its Applications written by Arnold Emch and published by . This book was released on 1905 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Symmetry in Chaos by : Michael Field
Download or read book Symmetry in Chaos written by Michael Field and published by SIAM. This book was released on 2009-01-01 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: Symmetry suggests order and regularity whilst chaos suggests disorder and randomness. 'Symmetry in Chaos' is an exploration of how combining seemingly contradictory principles can lead to the construction of striking and beautiful images. This book is an engaging look at the interplay of art and mathematics.
Book Synopsis Cognitive Governance and the Historical Distortion of the Norm of Modern Development: A Theory of Political Asymmetry by : Rueda, Renny
Download or read book Cognitive Governance and the Historical Distortion of the Norm of Modern Development: A Theory of Political Asymmetry written by Rueda, Renny and published by IGI Global. This book was released on 2023-11-27 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the world of academic scholarship, there exists a pressing problem that has long confounded researchers and scholars alike. The issue at hand is the glaring gap in our understanding of political asymmetryan elusive concept that holds the key to deciphering how institutions evolve and influence normative constructs within contemporary governance structures. Despite its undeniable relevance, political asymmetry has remained a neglected subject in social science discourse. This omission hampers our capacity to explore the intricate interplay between cultural diversity, normative representations, and political dynamics. As such, a critical void persists in comprehending the complex mechanisms that underpin governance practices in our ever-evolving global landscape. Cognitive Governance and the Historical Distortion of the Norm of Modern Development: A Theory of Political Asymmetry offers an illuminating solution to this enduring problem. This pioneering work presents a comprehensive and meticulously crafted exploration of the concept of political asymmetry, providing both a theoretical taxonomy and an empirical roadmap for scholars eager to delve into uncharted territory. By bridging this knowledge gap, the book equips researchers with the tools needed to redefine how political asymmetry is not only understood but also applied in rigorous social science research. It marks a transformative shift in our approach to political science, enabling us to navigate the labyrinth of contemporary governance structures with newfound clarity.
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 College Geometry with GeoGebra by : Barbara E. Reynolds
Download or read book College Geometry with GeoGebra written by Barbara E. Reynolds and published by John Wiley & Sons. This book was released on 2021-01-20 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: From two authors who embrace technology in the classroom and value the role of collaborative learning comes College Geometry Using GeoGebra, a book that is ideal for geometry courses for both mathematics and math education majors. The book's discovery-based approach guides students to explore geometric worlds through computer-based activities, enabling students to make observations, develop conjectures, and write mathematical proofs. This unique textbook helps students understand the underlying concepts of geometry while learning to use GeoGebra software—constructing various geometric figures and investigating their properties, relationships, and interactions. The text allows students to gradually build upon their knowledge as they move from fundamental concepts of circle and triangle geometry to more advanced topics such as isometries and matrices, symmetry in the plane, and hyperbolic and projective geometry. Emphasizing active collaborative learning, the text contains numerous fully-integrated computer lab activities that visualize difficult geometric concepts and facilitate both small-group and whole-class discussions. Each chapter begins with engaging activities that draw students into the subject matter, followed by detailed discussions that solidify the student conjectures made in the activities and exercises that test comprehension of the material. Written to support students and instructors in active-learning classrooms that incorporate computer technology, College Geometry with GeoGebra is an ideal resource for geometry courses for both mathematics and math education majors.
Download or read book Symmetry written by Kristopher Tapp and published by Springer Nature. This book was released on 2021-08-28 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is perfect for a math course for non-math majors, with the goal of encouraging effective analytical thinking and exposing students to elegant mathematical ideas. It includes many topics commonly found in sampler courses, like Platonic solids, Euler’s formula, irrational numbers, countable sets, permutations, and a proof of the Pythagorean Theorem. All of these topics serve a single compelling goal: understanding the mathematical patterns underlying the symmetry that we observe in the physical world around us. The exposition is engaging, precise and rigorous. The theorems are visually motivated with intuitive proofs appropriate for the intended audience. Students from all majors will enjoy the many beautiful topics herein, and will come to better appreciate the powerful cumulative nature of mathematics as these topics are woven together into a single fascinating story about the ways in which objects can be symmetric.
Book Synopsis Geometric Symmetry by : E. H. Lockwood
Download or read book Geometric Symmetry written by E. H. Lockwood and published by CUP Archive. This book was released on 1978-12-07 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: Symmetry is of interest in two ways, artistic and mathematical. It underlies much scientific thought, playing an important role in chemistry and atomic physics, and a dominant one in crystallography. It is important in architectural and engineering design and particularly in the decorative arts. This book provides a comprehensive account of symmetry in a form acceptable to readers without much detailed mathematical knowledge or experience who nevertheless want to understand the basic principles of the subject. It will be useful in school and other libraries and as preliminary reading for students of crystallography. The treatment is geometrical, which should appeal to art students and to readers whose mathematical interests are that way inclined.
Book Synopsis Strong Rigidity of Locally Symmetric Spaces by : G. Daniel Mostow
Download or read book Strong Rigidity of Locally Symmetric Spaces written by G. Daniel Mostow and published by Princeton University Press. This book was released on 1973-12-21 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: Locally symmetric spaces are generalizations of spaces of constant curvature. In this book the author presents the proof of a remarkable phenomenon, which he calls "strong rigidity": this is a stronger form of the deformation rigidity that has been investigated by Selberg, Calabi-Vesentini, Weil, Borel, and Raghunathan. The proof combines the theory of semi-simple Lie groups, discrete subgroups, the geometry of E. Cartan's symmetric Riemannian spaces, elements of ergodic theory, and the fundamental theorem of projective geometry as applied to Tit's geometries. In his proof the author introduces two new notions having independent interest: one is "pseudo-isometries"; the other is a notion of a quasi-conformal mapping over the division algebra K (K equals real, complex, quaternion, or Cayley numbers). The author attempts to make the account accessible to readers with diverse backgrounds, and the book contains capsule descriptions of the various theories that enter the proof.
Book Synopsis Creating Symmetry by : Frank A. Farris
Download or read book Creating Symmetry written by Frank A. Farris and published by Princeton University Press. This book was released on 2015-06-02 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: A step-by-step illustrated introduction to the astounding mathematics of symmetry This lavishly illustrated book provides a hands-on, step-by-step introduction to the intriguing mathematics of symmetry. Instead of breaking up patterns into blocks—a sort of potato-stamp method—Frank Farris offers a completely new waveform approach that enables you to create an endless variety of rosettes, friezes, and wallpaper patterns: dazzling art images where the beauty of nature meets the precision of mathematics. Featuring more than 100 stunning color illustrations and requiring only a modest background in math, Creating Symmetry begins by addressing the enigma of a simple curve, whose curious symmetry seems unexplained by its formula. Farris describes how complex numbers unlock the mystery, and how they lead to the next steps on an engaging path to constructing waveforms. He explains how to devise waveforms for each of the 17 possible wallpaper types, and then guides you through a host of other fascinating topics in symmetry, such as color-reversing patterns, three-color patterns, polyhedral symmetry, and hyperbolic symmetry. Along the way, Farris demonstrates how to marry waveforms with photographic images to construct beautiful symmetry patterns as he gradually familiarizes you with more advanced mathematics, including group theory, functional analysis, and partial differential equations. As you progress through the book, you'll learn how to create breathtaking art images of your own. Fun, accessible, and challenging, Creating Symmetry features numerous examples and exercises throughout, as well as engaging discussions of the history behind the mathematics presented in the book.
