Diagram Geometry

Related to Classical Groups and Buildings

Author: Francis Buekenhout,Arjeh M. Cohen

Publisher: Springer Science & Business Media

ISBN: 3642344534

Category: Mathematics

Page: 594

View: 3007

This book provides a self-contained introduction to diagram geometry. Tight connections with group theory are shown. It treats thin geometries (related to Coxeter groups) and thick buildings from a diagrammatic perspective. Projective and affine geometry are main examples. Polar geometry is motivated by polarities on diagram geometries and the complete classification of those polar geometries whose projective planes are Desarguesian is given. It differs from Tits' comprehensive treatment in that it uses Veldkamp's embeddings. The book intends to be a basic reference for those who study diagram geometry. Group theorists will find examples of the use of diagram geometry. Light on matroid theory is shed from the point of view of geometry with linear diagrams. Those interested in Coxeter groups and those interested in buildings will find brief but self-contained introductions into these topics from the diagrammatic perspective. Graph theorists will find many highly regular graphs. The text is written so graduate students will be able to follow the arguments without needing recourse to further literature. A strong point of the book is the density of examples.

Projective Geometry

From Foundations to Applications

Author: Albrecht Beutelspacher,Ute Rosenbaum

Publisher: Cambridge University Press

ISBN: 9780521483643

Category: Mathematics

Page: 258

View: 6022

A textbook on projective geometry that emphasises applications in modern information and communication science.

Generalized Voronoi Diagram: A Geometry-Based Approach to Computational Intelligence

Author: Marina L. Gavrilova

Publisher: Springer Science & Business Media

ISBN: 3540851259

Category: Mathematics

Page: 312

View: 3052

The year 2008 is a memorial year for Georgiy Vorono (1868-1908), with a number of events in the scientific community commemorating his tremendous contribution to the area of mathematics, especially number theory, through conferences and scientific gatherings in his honor. A notable event taking place in September 2008 a joint c- ference: the 5th Annual International Symposium on Voronoi Diagrams (ISVD) and the 4th International Conference on Analytic Number Theory and Spatial Tessel- tions held in Kyiv, Georgiy Vorono ’s native land. The main ideas expressed by G. Vorono ’s through his fundamental works have influenced and shaped the key dev- opments in computation geometry, image recognition, artificial intelligence, robotics, computational science, navigation and obstacle avoidance, geographical information systems, molecular modeling, astrology, physics, quantum computing, chemical en- neering, material sciences, terrain modeling, biometrics and other domains. This book is intended to provide the reader with in-depth overview and analysis of the fundamental methods and techniques developed following G. Voronoi ideas, in the context of the vast and increasingly growing area of computational intelligence. It represents the collection of state-of-the art research methods merging the bridges between two areas: geometric computing through Voronoi diagrams and intelligent computation techniques, pushing the limits of current knowledge in the area, impr- ing on previous solutions, merging sciences together, and inventing new ways of approaching difficult applied problems.

Patterns of Eternity

Sacred Geometry and the Starcut Diagram

Author: Malcolm Stewart

Publisher: N.A

ISBN: 9780863157127

Category: Body, Mind & Spirit

Page: 279

View: 2737

Malcolm Stewart has discovered a remarkable geometrical device. The 'starcut diagram', as he has called it, is at first glance a simple way of dividing the area of a square. After extensive research, however, he found that it has extraordinary mathematical properties, suggesting that it may be no less than the source of the number system used when ancient humanity first built cities.He shows that the starcut diagram underlies many significant patterns and proportions across the world: in China, the shaman's dance; in Egypt, the Great Pyramid; in Europe, a Raphael fresco; in Asia, the Vedic Fire Altar, and many others. This book is an intellectual adventure, written for a general reader without specialist knowledge. Illustrated with around 180 photographs, drawings and diagrams, it tells the story of many fresh discoveries, bringing sacred geometry to life in an original and inspiring way.

Geometry Leveled Problems: Venn Diagram and Shape Properties

Venn Diagram and Shape Properties

Author: Linda Dacey, Ed.D.

Publisher: Teacher Created Materials

ISBN: 1480786705

Category:

Page: 4

View: 4564

Differentiate problem solving in your classroom using effective, research-based strategies. This lesson focuses on solving problems related to venn diagrams and shape properties. The problem-solving mini-lesson guides teachers in how to teach differentiated lessons. The student activity sheet features a problem tiered at three levels.

On the Computational Geometry of Pocket Machining

Author: Martin Held

Publisher: Springer Science & Business Media

ISBN: 9783540541035

Category: Computers

Page: 178

View: 927

This monograph presents a thorough geometrical investigation of practical and theoretical problems arising from NC pocket machining. Practical topics include selection of tool sizes and determination of optimal tool paths. A rigorous theoretical framework based on Voronoi diagrams is given.

Sacred Geometry

Deciphering the Code

Author: Stephen Skinner

Publisher: Sterling Publishing Company, Inc.

ISBN: 9781402765827

Category: Mathematics

Page: 160

View: 8586

A fascinating and inspirational look at the vital link between the hidden geometrical order of the universe, geometry in nature, and the geometry of the man-made world. The Da Vinci Code has awakened the public to the powerful and very ancient idea that religious truths and mathematical principles are intimately intertwined. Sacred Geometry offers an accessible way of understanding how that connection is revealed in nature and the arts. Over the centuries, temple builders have relied on magic numbers to shape sacred spaces, astronomers have used geometry to calculate holy seasons, and philosophers have observed the harmony of the universe in the numerical properties of music. By showing how the discoveries of mathematics are manifested over and over again in biology and physics, and how they have inspired the greatest works of art, this illuminating study reveals the universal principles that link us to the infinite.

Computational Geometry

Algorithms and Applications

Author: Mark de Berg

Publisher: Springer Science & Business Media

ISBN: 3540779736

Category: Computers

Page: 386

View: 1737

This introduction to computational geometry focuses on algorithms. Motivation is provided from the application areas as all techniques are related to particular applications in robotics, graphics, CAD/CAM, and geographic information systems. Modern insights in computational geometry are used to provide solutions that are both efficient and easy to understand and implement.

Surveys in Combinatorics

Invited Papers for the Ninth British Combinatorial Conference 1983

Author: E. Keith Lloyd

Publisher: Cambridge University Press

ISBN: 0521275520

Category: Mathematics

Page: 256

View: 8851

This volume contains the invited papers from the 1983 British Combinatorial Conference. Several distinguished mathematicians were invited to give a lecture and write a paper for the conference volume. The papers cover a broad range of combinatorial topics, including enumeration, finite geometries, graph theory and permanents.

Discrete and Computational Geometry

Author: Satyan L. Devadoss,Joseph O'Rourke

Publisher: Princeton University Press

ISBN: 9781400838981

Category: Mathematics

Page: 280

View: 4645

Discrete geometry is a relatively new development in pure mathematics, while computational geometry is an emerging area in applications-driven computer science. Their intermingling has yielded exciting advances in recent years, yet what has been lacking until now is an undergraduate textbook that bridges the gap between the two. Discrete and Computational Geometry offers a comprehensive yet accessible introduction to this cutting-edge frontier of mathematics and computer science. This book covers traditional topics such as convex hulls, triangulations, and Voronoi diagrams, as well as more recent subjects like pseudotriangulations, curve reconstruction, and locked chains. It also touches on more advanced material, including Dehn invariants, associahedra, quasigeodesics, Morse theory, and the recent resolution of the Poincaré conjecture. Connections to real-world applications are made throughout, and algorithms are presented independently of any programming language. This richly illustrated textbook also features numerous exercises and unsolved problems. The essential introduction to discrete and computational geometry Covers traditional topics as well as new and advanced material Features numerous full-color illustrations, exercises, and unsolved problems Suitable for sophomores in mathematics, computer science, engineering, or physics Rigorous but accessible An online solutions manual is available (for teachers only). To obtain access, please e-mail: [email protected]

The Art of City Sketching

A Field Manual

Author: Michael Abrams

Publisher: Routledge

ISBN: 1136665382

Category: Architecture

Page: 312

View: 3819

The Art of City Sketching: A Field Manual guides you through the laborious and sometimes complex process of sketching what you see in the built environment so that you can learn to draw what you imagine. Illustrated with hundreds of drawings by students and professionals of cityscapes around Europe and the United States, the book helps you develop your conceptual drawing skills so that you can communicate graphically to represent the built environment. Short exercises, projects, drawing tips, step-by-step demonstrations, and composition do's and don'ts make it easy for you to get out into the city and experiment in your own work. Author Michael Abrams uses his experience as a field sketching instructor, to show you that by drawing, you can discover, analyze, and comprehend the built environment.

Diagrammatic Representation and Inference

Second International Conference, Diagrams 2002 Callaway Gardens, GA, USA, April 18-20, 2002 Proceedings

Author: Mary Hegarty,Bernd Meyer,N. Hari Narayanan

Publisher: Springer Science & Business Media

ISBN: 3540435611

Category: Computers

Page: 362

View: 3535

This book constitutes the refereed proceedings of the Second International Conference Diagrams 2002, held in Callaway Gardens, Georgia, USA, in April 2002. The 21 revised full papers and 19 posters presented were carefully reviewed and selected from 77 submissions. The papers are organized in topical sections on understanding and communicating with diagrams, diagrams in mathematics, computational aspects of diagrammatic representation and reasoning, logic and diagrams, diagrams in human-computer interaction, tracing the process of diagrammatic reasoning, visualizing information with diagrams, diagrams and software engineering, and cognitive aspects.

Effective Computational Geometry for Curves and Surfaces

Author: Jean-Daniel Boissonnat,Monique Teillaud

Publisher: Springer Science & Business Media

ISBN: 3540332596

Category: Mathematics

Page: 344

View: 5386

This book covers combinatorial data structures and algorithms, algebraic issues in geometric computing, approximation of curves and surfaces, and computational topology. Each chapter fully details and provides a tutorial introduction to important concepts and results. The focus is on methods which are both well founded mathematically and efficient in practice. Coverage includes references to open source software and discussion of potential applications of the presented techniques.

Computational Geometry and Its Applications

CG '88 International Workshop on Computational Geometry Würzburg, FRG, March 24-25, 1988. Proceedings

Author: Hartmut Noltemeier

Publisher: Springer Science & Business Media

ISBN: 9783540503354

Category: Computers

Page: 252

View: 5227

The International Workshop CG '88 on "Computational Geometry" was held at the University of Würzburg, FRG, March 24-25, 1988. As the interest in the fascinating field of Computational Geometry and its Applications has grown very quickly in recent years the organizers felt the need to have a workshop, where a suitable number of invited participants could concentrate their efforts in this field to cover a broad spectrum of topics and to communicate in a stimulating atmosphere. This workshop was attended by some fifty invited scientists. The scientific program consisted of 22 contributions, of which 18 papers with one additional paper (M. Reichling) are contained in the present volume. The contributions covered important areas not only of fundamental aspects of Computational Geometry but a lot of interesting and most promising applications: Algorithmic Aspects of Geometry, Arrangements, Nearest-Neighbor-Problems and Abstract Voronoi-Diagrams, Data Structures for Geometric Objects, Geo-Relational Algebra, Geometric Modeling, Clustering and Visualizing Geometric Objects, Finite Element Methods, Triangulating in Parallel, Animation and Ray Tracing, Robotics: Motion Planning, Collision Avoidance, Visibility, Smooth Surfaces, Basic Models of Geometric Computations, Automatizing Geometric Proofs and Constructions.

Computational Geometry on Surfaces

Performing Computational Geometry on the Cylinder, the Sphere, the Torus, and the Cone

Author: Clara Grima,Alberto Marquez

Publisher: Springer Science & Business Media

ISBN: 9401598096

Category: Computers

Page: 192

View: 9994

In the last thirty years Computational Geometry has emerged as a new discipline from the field of design and analysis of algorithms. That dis cipline studies geometric problems from a computational point of view, and it has attracted enormous research interest. But that interest is mostly concerned with Euclidean Geometry (mainly the plane or Eu clidean 3-dimensional space). Of course, there are some important rea sons for this occurrence since the first applieations and the bases of all developments are in the plane or in 3-dimensional space. But, we can find also some exceptions, and so Voronoi diagrams on the sphere, cylin der, the cone, and the torus have been considered previously, and there are manY works on triangulations on the sphere and other surfaces. The exceptions mentioned in the last paragraph have appeared to try to answer some quest ions which arise in the growing list of areas in which the results of Computational Geometry are applicable, since, in practiee, many situations in those areas lead to problems of Com putational Geometry on surfaces (probably the sphere and the cylinder are the most common examples). We can mention here some specific areas in which these situations happen as engineering, computer aided design, manufacturing, geographie information systems, operations re search, roboties, computer graphics, solid modeling, etc.

Algorithmic Geometry

Author: Jean-Daniel Boissonnat,Mariette Yvinec

Publisher: Cambridge University Press

ISBN: 9780521565295

Category: Computers

Page: 519

View: 9652

The design and analysis of geometric algorithms have seen remarkable growth in recent years, due to their application in, for example, computer vision, graphics, medical imaging and CAD. The goals of this book are twofold: first to provide a coherent and systematic treatment of the foundations; secondly to present algorithmic solutions that are amenable to rigorous analysis and are efficient in practical situations. When possible, the algorithms are presented in their most general d-dimensional setting. Specific developments are given for the 2- or 3-dimensional cases when this results in significant improvements. The presentation is confined to Euclidean affine geometry, though the authors indicate whenever the treatment can be extended to curves and surfaces. The prerequisites for using the book are few, which will make it ideal for teaching advanced undergraduate or beginning graduate courses in computational geometry.

Foundations of Incidence Geometry

Projective and Polar Spaces

Author: Johannes Ueberberg

Publisher: Springer Science & Business Media

ISBN: 3642209726

Category: Mathematics

Page: 248

View: 7573

Incidence geometry is a central part of modern mathematics that has an impressive tradition. The main topics of incidence geometry are projective and affine geometry and, in more recent times, the theory of buildings and polar spaces. Embedded into the modern view of diagram geometry, projective and affine geometry including the fundamental theorems, polar geometry including the Theorem of Buekenhout-Shult and the classification of quadratic sets are presented in this volume. Incidence geometry is developed along the lines of the fascinating work of Jacques Tits and Francis Buekenhout. The book is a clear and comprehensible introduction into a wonderful piece of mathematics. More than 200 figures make even complicated proofs accessible to the reader.