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Author: Francis Buekenhout
Publisher: Springer Science & Business Media
ISBN: 3642344534
Category : Mathematics
Languages : en
Pages : 597
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Book Description
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.
Author: Francis Buekenhout
Publisher: Springer Science & Business Media
ISBN: 3642344534
Category : Mathematics
Languages : en
Pages : 597
Get Book Here
Book Description
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.
Author: Luigi A. Rosati
Publisher: Springer
ISBN: 3540398015
Category : Mathematics
Languages : en
Pages : 287
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Book Description
Author:
Publisher:
ISBN: 9780387164663
Category :
Languages : en
Pages :
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Book Description
Author: Kenneth S. Brown
Publisher: Springer Science & Business Media
ISBN: 1461210194
Category : Mathematics
Languages : en
Pages : 221
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Book Description
For years I have heard about buildings and their applications to group theory. I finally decided to try to learn something about the subject by teaching a graduate course on it at Cornell University in Spring 1987. This book is based on the not es from that course. The course started from scratch and proceeded at a leisurely pace. The book therefore does not get very far. Indeed, the definition of the term "building" doesn't even appear until Chapter IV. My hope, however, is that the book gets far enough to enable the reader to tadle the literat ure on buildings, some of which can seem very forbidding. Most of the results in this book are due to J. Tits, who originated the the ory of buildings. The main exceptions are Chapter I (which presents some classical material), Chapter VI (which prcsents joint work of F. Bruhat and Tits), and Chapter VII (which surveys some applications, due to var ious people). It has been a pleasure studying Tits's work; I only hope my exposition does it justice.
Author: Centro internazionale matematico estivo. Session
Publisher:
ISBN: 9780387164397
Category : Automorphisms
Languages : en
Pages : 307
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Book Description
Author: Jeffrey Balmer
Publisher: Routledge
ISBN: 042901502X
Category : Architecture
Languages : en
Pages : 711
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Book Description
Becoming an architect is a daunting task. Beyond the acquisition of new skills and procedures, beginning designers face an entirely unfamiliar mode of knowledge: design thinking. In Diagramming the Big Idea, Jeffrey Balmer and Michael T. Swisher introduce the fundamentals of design thinking by illustrating how architects make and use diagrams to clarify their understanding of both specific architectural projects and universal principles of form and order. With accessible, step-by-step procedures that interweave diagrams, drawings and virtual models, the authors demonstrate how to compose clear and revealing diagrams. Design thinking defines a method for engaging the world through observation and analysis. Beyond problem solving, design is a search for possibilities. Mastering design thinking begins with learning the fundamentals of visual composition. It embraces the ability to synthesize deductive and imaginative reasoning, combining both shrewd scrutiny and fevered speculation. Design diagrams make visible the abstractions that order the built environment. Premised upon the Beaux-Arts notion of the architectural parti, Balmer and Swisher adopt the ‘Big Idea’ as a foil and as a suitcase to organize fundamentals of architectural composition. The goal of this book is to make explicit to students what they are learning, why they are learning it and how to internalize such lessons toward their lifelong development as designers.
Author: Robert Bork
Publisher: Routledge
ISBN: 1351888978
Category : History
Languages : en
Pages : 783
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Book Description
The flowering of Gothic architecture depended to a striking extent on the use of drawing as a tool of design. By drawing precise "blueprints" with simple tools such as the compass and straightedge, Gothic draftsmen were able to develop a linearized architecture of unprecedented complexity and sophistication. Examination of their surviving drawings can provide valuable and remarkably intimate information about the Gothic design process. Gothic drawings include compass pricks, uninked construction lines, and other telltale traces of the draftsman's geometrically based working method. The proportions of the drawings, moreover, are those actually intended by the designer, uncompromised by errors introduced in the construction process. All of these features make these drawings ideal subjects for the study of Gothic design practice, but their geometry has to date received little systematic attention. This book offers a new perspective on Gothic architectural creativity. It shows, in a series of rigorous geometrical case studies, how Gothic design evolved over time, in two senses: in the hours of the draftsman's labor, and across the centuries of the late Middle Ages. In each case study, a series of computer graphics show in unprecedented detail how a medieval designer could have developed his architectural concept step by step, using only basic geometrical operations. Taken together, these analyses demonstrate both remarkable methodological continuity across the Gothic era, and the progressive development of new and sophisticated permutations on venerable design themes. This rich tradition ultimately gave way in the Renaissance not because of any inherent problem with Gothic architecture, but because the visual language of Classicism appealed more directly to the pretensions of Humanist princes than the more abstract geometrical order of Gothic design, as the book's final chapter demonstrates.
Author: Francis Buekenhout
Publisher: North-Holland
ISBN:
Category : Mathematics
Languages : en
Pages : 1440
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Book Description
Hardbound. This Handbook deals with the foundations of incidence geometry, in relationship with division rings, rings, algebras, lattices, groups, topology, graphs, logic and its autonomous development from various viewpoints. Projective and affine geometry are covered in various ways. Major classes of rank 2 geometries such as generalized polygons and partial geometries are surveyed extensively.More than half of the book is devoted to buildings at various levels of generality, including a detailed and original introduction to the subject, a broad study of characterizations in terms of points and lines, applications to algebraic groups, extensions to topological geometry, a survey of results on diagram geometries and nearby generalizations such as matroids.
Author: Frank Hilton
Publisher:
ISBN: 9780582410787
Category : Structural drawing
Languages : en
Pages : 168
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Book Description
Author: Bernhard Mühlherr
Publisher: Princeton University Press
ISBN: 0691166919
Category : Mathematics
Languages : en
Pages : 352
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Book Description
Descent in Buildings begins with the resolution of a major open question about the local structure of Bruhat-Tits buildings. The authors then put their algebraic solution into a geometric context by developing a general fixed point theory for groups acting on buildings of arbitrary type, giving necessary and sufficient conditions for the residues fixed by a group to form a kind of subbuilding or "form" of the original building. At the center of this theory is the notion of a Tits index, a combinatorial version of the notion of an index in the relative theory of algebraic groups. These results are combined at the end to show that every exceptional Bruhat-Tits building arises as a form of a "residually pseudo-split" Bruhat-Tits building. The book concludes with a display of the Tits indices associated with each of these exceptional forms. This is the third and final volume of a trilogy that began with Richard Weiss' The Structure of Spherical Buildings and The Structure of Affine Buildings.
