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ISBN: 9780511843297 9780521879101 Year: 2022 Publisher: Cambridge Cambridge University Press
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ISBN: 1009234226 0511843291 Year: 2022 Publisher: Cambridge : Cambridge University Press,
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This introduction to the theory of rigid structures explains how to analyze the performance of built and natural structures under loads, paying special attention to the role of geometry. The book unifies the engineering and mathematical literatures by exploring different notions of rigidity - local, global, and universal - and how they are interrelated. Important results are stated formally, but also clarified with a wide range of revealing examples. An important generalization is to tensegrities, where fixed distances are replaced with 'cables' not allowed to increase in length and 'struts' not allowed to decrease in length. A special feature is the analysis of symmetric tensegrities, where the symmetry of the structure is used to simplify matters and allows the theory of group representations to be applied. Written for researchers and graduate students in structural engineering and mathematics, this work is also of interest to computer scientists and physicists.
Structural analysis (Engineering) --- Engineering mathematics. --- Rigidity (Geometry)
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ISBN: 1493907816 1493907808 1322132933 Year: 2014 Publisher: New York, NY : Springer New York : Imprint: Springer,
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This book contains recent contributions to the fields of rigidity and symmetry with two primary focuses: to present the mathematically rigorous treatment of rigidity of structures, and to explore the interaction of geometry, algebra, and combinatorics. Overall, the book shows how researchers from diverse backgrounds explore connections among the various discrete structures with symmetry as the unifying theme. Contributions present recent trends and advances in discrete geometry, particularly in the theory of polytopes. The rapid development of abstract polytope theory has resulted in a rich theory featuring an attractive interplay of methods and tools from discrete geometry, group theory, classical geometry, hyperbolic geometry and topology. The volume will also be a valuable source as an introduction to the ideas of both combinatorial and geometric rigidity theory and its applications, incorporating the surprising impact of symmetry. It will appeal to students at both the advanced undergraduate and graduate levels, as well as postdocs, structural engineers, and chemists.
Rigidity (Geometry) --- Mathematics. --- Graph theory. --- Graph theory --- Graphs, Theory of --- Theory of graphs --- Combinatorial analysis --- Topology --- Math --- Science --- Extremal problems --- Geometric rigidity --- Rigidity theorem --- Discrete geometry --- Combinatorics. --- Discrete groups. --- Topology. --- Graph Theory. --- Polytopes. --- Convex and Discrete Geometry. --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Geometry --- Polyhedra --- Set theory --- Algebras, Linear --- Groups, Discrete --- Infinite groups --- Combinatorics --- Algebra --- Mathematical analysis --- Discrete mathematics --- Convex geometry . --- Discrete geometry. --- Combinatorial geometry --- Hyperspace
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ISBN: 9781493907816 Year: 2014 Publisher: New York, NY Springer
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This book contains recent contributions to the fields of rigidity and symmetry with two primary focuses: to present the mathematically rigorous treatment of rigidity of structures, and to explore the interaction of geometry, algebra, and combinatorics. Overall, the book shows how researchers from diverse backgrounds explore connections among the various discrete structures with symmetry as the unifying theme. Contributions present recent trends and advances in discrete geometry, particularly in the theory of polytopes. The rapid development of abstract polytope theory has resulted in a rich theory featuring an attractive interplay of methods and tools from discrete geometry, group theory, classical geometry, hyperbolic geometry and topology. The volume will also be a valuable source as an introduction to the ideas of both combinatorial and geometric rigidity theory and its applications, incorporating the surprising impact of symmetry. It will appeal to students at both the advanced undergraduate and graduate levels, as well as postdocs, structural engineers, and chemists.
Statistical science --- Topology --- Geometry --- Discrete mathematics --- Mathematical statistics --- Mathematics --- Geology. Earth sciences --- grafieken --- discrete wiskunde --- statistiek --- wiskunde --- geometrie --- topologie
ISBN: 0933997000 0933997132 0933997116 Year: 1985 Publisher: Chicago Cinebooks
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