Symmetry And Pattern In Projective Geometry
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Symmetry And Pattern In Projective Geometry
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Author : Eric Lord
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-14
Symmetry And Pattern In Projective Geometry written by Eric Lord and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-14 with Mathematics categories.
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.
Symmetry And Pattern In Projective Geometry
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Author : Abby Enger
language : en
Publisher:
Release Date : 2016-10-01
Symmetry And Pattern In Projective Geometry written by Abby Enger and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-01 with categories.
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.
Isomorphisms Symmetry And Computations In Algebraic Graph Theory
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Author : Gareth A. Jones
language : en
Publisher: Springer Nature
Release Date : 2020-01-10
Isomorphisms Symmetry And Computations In Algebraic Graph Theory written by Gareth A. Jones and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-10 with Mathematics categories.
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.
Projective Geometry
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Author : Albrecht Beutelspacher
language : en
Publisher: Cambridge University Press
Release Date : 1998-01-29
Projective Geometry written by Albrecht Beutelspacher and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-01-29 with Mathematics categories.
Projective geometry is not only a jewel of mathematics, but has also many applications in modern information and communication science. This book presents the foundations of classical projective and affine geometry as well as its important applications in coding theory and cryptography. It also could serve as a first acquaintance with diagram geometry. Written in clear and contemporary language with an entertaining style and around 200 exercises, examples and hints, this book is ideally suited to be used as a textbook for study in the classroom or on its own.
Advances In Structural And Syntactical Pattern Recognition
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Author : Petra Perner
language : en
Publisher: Springer Science & Business Media
Release Date : 1996-08-07
Advances In Structural And Syntactical Pattern Recognition written by Petra Perner and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-08-07 with Computers categories.
This book constitutes the refereed proceedings of the 6th International Workshop on Structural and Syntactical Pattern Recognition, SSPR '96, held in Leipzig, Germany in August 1996. The 36 revised full papers included together with three invited papers were carefully selected from a total of 52 submissions. The papers are organized in topical sections on grammars and languages; morphology and mathematical approaches to pattern recognition; semantic nets, relational models and graph-based methods; 2D and 3D shape recognition; document image analysis and recognition; and handwritten and printed character recognition.
Cognitive Governance And The Historical Distortion Of The Norm Of Modern Development A Theory Of Political Asymmetry
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Author : Rueda, Renny
language : en
Publisher: IGI Global
Release Date : 2023-11-27
Cognitive Governance And The Historical Distortion Of The Norm Of Modern Development A Theory Of Political Asymmetry written by Rueda, Renny and has been published by IGI Global this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-27 with Business & Economics categories.
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 asymmetry—an 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.
Perspectives On Projective Geometry
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Author : Jürgen Richter-Gebert
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-02-04
Perspectives On Projective Geometry written by Jürgen Richter-Gebert and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-02-04 with Mathematics categories.
Projective geometry is one of the most fundamental and at the same time most beautiful branches of geometry. It can be considered the common foundation of many other geometric disciplines like Euclidean geometry, hyperbolic and elliptic geometry or even relativistic space-time geometry. This book offers a comprehensive introduction to this fascinating field and its applications. In particular, it explains how metric concepts may be best understood in projective terms. One of the major themes that appears throughout this book is the beauty of the interplay between geometry, algebra and combinatorics. This book can especially be used as a guide that explains how geometric objects and operations may be most elegantly expressed in algebraic terms, making it a valuable resource for mathematicians, as well as for computer scientists and physicists. The book is based on the author’s experience in implementing geometric software and includes hundreds of high-quality illustrations.
Symmetry And Complexity The Spirit And Beauty Of Nonlinear Science
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Author : Klaus Mainzer
language : en
Publisher: World Scientific
Release Date : 2005-06-10
Symmetry And Complexity The Spirit And Beauty Of Nonlinear Science written by Klaus Mainzer and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-06-10 with Science categories.
Cosmic evolution leads from symmetry to complexity by symmetry breaking and phase transitions. The emergence of new order and structure in nature and society is explained by physical, chemical, biological, social and economic self-organization, according to the laws of nonlinear dynamics. All these dynamical systems are considered computational systems processing information and entropy. Are symmetry and complexity only useful models of science or are they universals of reality? Symmetry and Complexity discusses the fascinating insights gained from natural, social and computer sciences, philosophy and the arts. With many diagrams and pictures, this book illustrates the spirit and beauty of nonlinear science. In the complex world of globalization, it strongly argues for unity in diversity.
A Participatory Approach To Modern Geometry
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Author : Jay Kappraff
language : en
Publisher: World Scientific Publishing Company
Release Date : 2014-08-25
A Participatory Approach To Modern Geometry written by Jay Kappraff and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-25 with Mathematics categories.
This book aims to make the subject of geometry and its applications easy and comfortable to understand by students majoring in mathematics or the liberal arts, architecture and design. It can be used to teach students at different levels of computational ability and there is also sufficient novel material to interest students at a higher cognitive level. While the book goes deeply into the applications of geometry, it contains much introductory material which up to now may not have been known to the student. The constructive approach using compass and straightedge engages students, not just on an intellectual level, but also at a tactile level. This may be the only rigorous book offering geometry that attempts to engage students outside of the mathematics discipline.
Connections The Geometric Bridge Between Art Science 2nd Edition
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Author : Jay Kappraff
language : en
Publisher: World Scientific
Release Date : 2001-11-28
Connections The Geometric Bridge Between Art Science 2nd Edition written by Jay Kappraff and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-11-28 with Mathematics categories.
The first edition of Connections was chosen by the National Association of Publishers (USA) as the best book in “Mathematics, Chemistry, and Astronomy — Professional and Reference” in 1991. It has been a comprehensive reference in design science, bringing together in a single volume material from the areas of proportion in architecture and design, tilings and patterns, polyhedra, and symmetry. The book presents both theory and practice and has more than 750 illustrations. It is suitable for research in a variety of fields and as an aid to teaching a course in the mathematics of design. It has been influential in stimulating the burgeoning interest in the relationship between mathematics and design. In the second edition there are five new sections, supplementary, as well as a new preface describing the advances in design science since the publication of the first edition.