Diagram Geometry
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Diagram Geometry
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Author : Francis Buekenhout
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-01-26
Diagram Geometry written by Francis Buekenhout 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 2013-01-26 with Mathematics categories.
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.
Topics In Diagram Geometry
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Author : Antonio Pasini
language : en
Publisher:
Release Date : 2003
Topics In Diagram Geometry written by Antonio Pasini and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
Diagram Geometries
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Author : Antonio Pasini
language : en
Publisher: Oxford University Press on Demand
Release Date : 1994
Diagram Geometries written by Antonio Pasini and has been published by Oxford University Press on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Literary Criticism categories.
Diagram geometry provides a range of techniques that enable an interaction between group theory and geometry. These techniques allow the mathematician to get information on a multi-dimensional geometric object from some knowledge of its bi-dimensional properties. This book introduces thesetechniques and provides a survey of the development of the subject of diagram geometry.The first three chapters are descriptive; a number of examples are presented, basic concepts are explained, and the reader is introduced to the language of diagram geometries.The theory is developed in the next three chapters and in chapter 7 a number of characterizations are proved. This is continued in later chapters following a survey of more advanced concepts and techniques.
Buildings And The Geometry Of Diagrams
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Author : Luigi A. Rosati
language : en
Publisher: Springer
Release Date : 2006-11-14
Buildings And The Geometry Of Diagrams written by Luigi A. Rosati and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
The Diagram
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Author : Adam Tetlow
language : en
Publisher: Wooden Books North America Edi
Release Date : 2023-09-15
The Diagram written by Adam Tetlow and has been published by Wooden Books North America Edi this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-15 with Art categories.
How do you divide a line into three? Or five? Or seven? Is there a simple way to marry harmony and geometry? What is the secret diagram alluded to by writers of antiquity? In this groundbreaking book, philosopher Adam Tetlow reveals the long lost Helicon, the master diagram of the ancient arts and crafts.Watch in astonishment as this magical geometric figure produces simple fractions, musical harmonies, Pythagorean triangles, perspective and more. WOODEN BOOKS US EDITIONS. Small books, BIG ideas. Tiny but packed with information. "Stunning" NEW YORK TIMES. "Fascinating" FINANCIAL TIMES. "Beautiful" LONDON REVIEW OF BOOKS. "Rich and Artful" THE LANCET. "Genuinely mind-expanding" FORTEAN TIMES. "Excellent" NEW SCIENTIST.
Diagram Groups
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Author : Victor Guba
language : en
Publisher: American Mathematical Soc.
Release Date : 1997
Diagram Groups written by Victor Guba and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.
Diagram groups are groups consisting of spherical diagrams (pictures) over monoid presentations. They can be also defined as fundamental groups of the Squier complexes associated with monoid presentations. The authors show that the class of diagram groups contains some well-known groups, such as the R. Thompson group F. This class is closed under free products, finite direct products, and some other group-theoretical operations. The authors develop combinatorics on diagrams similar to the combinatorics on words. This helps in finding some structure and algorithmic properties of diagram groups. Some of these properties are new even for R. Thompson's group F. In particular, the authors describe the centralizers of elements in F, prove that it has solvable conjugacy problems, etc.
Generalized Voronoi Diagram A Geometry Based Approach To Computational Intelligence
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Author : Marina L. Gavrilova
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-10-13
Generalized Voronoi Diagram A Geometry Based Approach To Computational Intelligence written by Marina L. Gavrilova 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 2008-10-13 with Mathematics categories.
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.
The Philosophical Status Of Diagrams
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Author : Mark Greaves
language : en
Publisher: Stanford Univ Center for the Study
Release Date : 2002
The Philosophical Status Of Diagrams written by Mark Greaves and has been published by Stanford Univ Center for the Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Language Arts & Disciplines categories.
The use of diagrams in logic and geometry has encountered resistance in recent years. For a proof to be valid in geometry, it must not rely on the graphical properties of a diagram. In logic, the teaching of proofs depends on sentenial representations, ideas formed as natural language sentences such as "If A is true and B is true...." No serious formal proof system is based on diagrams. This book explores the reasons why structured graphics have been largely ignored in contemporary formal theories of axiomatic systems. In particular, it elucidates the systematic forces in the intellectual history of mathematics which have driven the adoption of sentential representational styles over diagrammatic ones. In this book, the effects of historical forces on the evolution of diagrammatically-based systems of inference in logic and geometry are traced from antiquity to the early twentieth-century work of David Hilbert. From this exploration emerges an understanding that the present negative attitudes towards the use of diagrams in logic and geometry owe more to implicit appeals to their history and philosophical background than to any technical incompatibility with modern theories of logical systems.
Euclid And His Twentieth Century Rivals
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Author : Nathaniel Miller
language : en
Publisher: Center for the Study of Language and Information Publica Tion
Release Date : 2007
Euclid And His Twentieth Century Rivals written by Nathaniel Miller and has been published by Center for the Study of Language and Information Publica Tion this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
Twentieth-century developments in logic and mathematics have led many people to view Euclid's proofs as inherently informal, especially due to the use of diagrams in proofs. In Euclid and His Twentieth-Century Rivals, Nathaniel Miller discusses the history of diagrams in Euclidean Geometry, develops a formal system for working with them, and concludes that they can indeed be used rigorously. Miller also introduces a diagrammatic computer proof system, based on this formal system. This volume will be of interest to mathematicians, computer scientists, and anyone interested in the use of diagrams in geometry.
The Power Of Form Applied To Geometric Tracing
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Author : Robert William Billings
language : en
Publisher:
Release Date : 1851
The Power Of Form Applied To Geometric Tracing written by Robert William Billings and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1851 with Design categories.