Convex Polyhedra
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Convex Polyhedra
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Author : A.D. Alexandrov
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-02-10
Convex Polyhedra written by A.D. Alexandrov 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 2005-02-10 with Mathematics categories.
This classic geometry text explores the theory of 3-dimensional convex polyhedra in a unique fashion, with exceptional detail. Vital and clearly written, the book includes the basics of convex polyhedra and collects the most general existence theorems for convex polyhedra that are proved by a new and unified method. This edition includes a comprehensive bibliography by V.A. Zalgaller, and related papers as supplements to the original text.
Reshaping Convex Polyhedra
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Author : Joseph O'Rourke
language : en
Publisher: Springer Nature
Release Date : 2024-02-28
Reshaping Convex Polyhedra written by Joseph O'Rourke and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-02-28 with Mathematics categories.
^ the="" study="" of="" convex="" polyhedra="" in="" ordinary="" space="" is="" a="" central="" piece="" classical="" and="" modern="" geometry="" that="" has="" had="" significant="" impact="" on="" many="" areas="" mathematics="" also="" computer="" science.="" present="" book="" project="" by="" joseph="" o’rourke="" costin="" vîlcu="" brings="" together="" two="" important="" strands="" subject="" —="" combinatorics="" polyhedra,="" intrinsic="" underlying="" surface.="" this="" leads="" to="" remarkable="" interplay="" concepts="" come="" life="" wide="" range="" very="" attractive="" topics="" concerning="" polyhedra.="" gets="" message="" across="" thetheory="" although="" with="" roots,="" still="" much="" alive="" today="" continues="" be="" inspiration="" basis="" lot="" current="" research="" activity.="" work="" presented="" manuscript="" interesting="" applications="" discrete="" computational="" geometry,="" as="" well="" other="" mathematics.="" treated="" detail="" include="" unfolding="" onto="" surfaces,="" continuous="" flattening="" convexity="" theory="" minimal="" length="" enclosing="" polygons.="" along="" way,="" open="" problems="" suitable="" for="" graduate="" students="" are="" raised,="" both="" a The focus of this monograph is converting—reshaping—one 3D convex polyhedron to another via an operation the authors call “tailoring.” A convex polyhedron is a gem-like shape composed of flat facets, the focus of study since Plato and Euclid. The tailoring operation snips off a corner (a “vertex”) of a polyhedron and sutures closed the hole. This is akin to Johannes Kepler’s “vertex truncation,” but differs in that the hole left by a truncated vertex is filled with new surface, whereas tailoring zips the hole closed. A powerful “gluing” theorem of A.D. Alexandrov from 1950 guarantees that, after closing the hole, the result is a new convex polyhedron. Given two convex polyhedra P, and Q inside P, repeated tailoringallows P to be reshaped to Q. Rescaling any Q to fit inside P, the result is universal: any P can be reshaped to any Q. This is one of the main theorems in Part I, with unexpected theoretical consequences. Part II carries out a systematic study of “vertex-merging,” a technique that can be viewed as a type of inverse operation to tailoring. Here the start is P which is gradually enlarged as much as possible, by inserting new surface along slits. In a sense, repeated vertex-merging reshapes P to be closer to planarity. One endpoint of such a process leads to P being cut up and “pasted” inside a cylinder. Then rolling the cylinder on a plane achieves an unfolding of P. The underlying subtext is a question posed by Geoffrey Shephard in 1975 and already implied by drawings by Albrecht Dürer in the 15th century: whether every convex polyhedron can be unfolded to a planar “net.” Toward this end, the authors initiate an exploration of convexity on convex polyhedra, a topic rarely studiedin the literature but with considerable promise for future development. This monograph uncovers new research directions and reveals connections among several, apparently distant, topics in geometry: Alexandrov’s Gluing Theorem, shortest paths and cut loci, Cauchy’s Arm Lemma, domes, quasigeodesics, convexity, and algorithms throughout. The interplay between these topics and the way the main ideas develop throughout the book could make the “journey” worthwhile for students and researchers in geometry, even if not directly interested in specific topics. Parts of the material will be of interest and accessible even to undergraduates. Although the proof difficulty varies from simple to quite intricate, with some proofs spanning several chapters, many examples and 125 figures help ease the exposition and illustrate the concepts. ^>
Discrete Convex Analysis
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Author : Kazuo Murota
language : en
Publisher: SIAM
Release Date : 2003-01-01
Discrete Convex Analysis written by Kazuo Murota and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-01-01 with Mathematics categories.
Discrete Convex Analysis is a novel paradigm for discrete optimization that combines the ideas in continuous optimization (convex analysis) and combinatorial optimization (matroid/submodular function theory) to establish a unified theoretical framework for nonlinear discrete optimization. The study of this theory is expanding with the development of efficient algorithms and applications to a number of diverse disciplines like matrix theory, operations research, and economics. This self-contained book is designed to provide a novel insight into optimization on discrete structures and should reveal unexpected links among different disciplines. It is the first and only English-language monograph on the theory and applications of discrete convex analysis. Discrete Convex Analysis provides the information that professionals in optimization will need to "catch up" with this new theoretical development. It also presents an unexpected connection between matroid theory and mathematical economics and expounds a deeper connection between matrices and matroids than most standard textbooks.
Encyclopaedia Of Mathematics Set
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Author : Michiel Hazewinkel
language : en
Publisher: Springer Science & Business Media
Release Date : 1994-02-28
Encyclopaedia Of Mathematics Set written by Michiel Hazewinkel 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 1994-02-28 with Mathematics categories.
The Encyclopaedia of Mathematics is the most up-to-date, authoritative and comprehensive English-language work of reference in mathematics which exists today. With over 7,000 articles from `A-integral' to `Zygmund Class of Functions', supplemented with a wealth of complementary information, and an index volume providing thorough cross-referencing of entries of related interest, the Encyclopaedia of Mathematics offers an immediate source of reference to mathematical definitions, concepts, explanations, surveys, examples, terminology and methods. The depth and breadth of content and the straightforward, careful presentation of the information, with the emphasis on accessibility, makes the Encyclopaedia of Mathematics an immensely useful tool for all mathematicians and other scientists who use, or are confronted by, mathematics in their work. The Enclyclopaedia of Mathematics provides, without doubt, a reference source of mathematical knowledge which is unsurpassed in value and usefulness. It can be highly recommended for use in libraries of universities, research institutes, colleges and even schools.
Algorithms And Data Structures
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Author : Selim G. Akl
language : en
Publisher: Springer Science & Business Media
Release Date : 1995-08-02
Algorithms And Data Structures written by Selim G. Akl 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 1995-08-02 with Computers categories.
This volume constitutes the proceedings of the Fourth International Workshop on Algorithms and Data Structures, WADS '95, held in Kingston, Canada in August 1995. The book presents 40 full refereed papers selected from a total of 121 submissions together with invited papers by Preparata and Bilardi, Sharir, Toussaint, and Vitanyi and Li. The book addresses various aspects of algorithms, data structures, computational geometry, scheduling, computational graph theory, and searching.
Polyhedra
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Author : Peter R. Cromwell
language : en
Publisher: Cambridge University Press
Release Date : 1997
Polyhedra written by Peter R. Cromwell 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 1997 with Mathematics categories.
Polyhedra have cropped up in many different guises throughout recorded history. In modern times, polyhedra and their symmetries have been cast in a new light by combinatorics an d group theory. This book comprehensively documents the many and varied ways that polyhedra have come to the fore throughout the development of mathematics. The author strikes a balance between covering the historical development of the theory surrounding polyhedra, and presenting a rigorous treatment of the mathematics involved. It is attractively illustrated with dozens of diagrams to illustrate ideas that might otherwise prove difficult to grasp. Historians of mathematics, as well as those more interested in the mathematics itself, will find this unique book fascinating.
Static Analysis
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Author : Jens Palsberg
language : en
Publisher: Springer
Release Date : 2009-08-03
Static Analysis written by Jens Palsberg and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-08-03 with Computers categories.
This book constitutes the refereed proceedings of the 16th International Symposium on Static Analysis, SAS 2009, held in Los Angeles, CA, USA in August 2009 - co-located with LICS 2009, the 24th IEEE Symposium on Logic in Computer Science. The 21 revised full papers presented together with two invited lectures were carefully reviewed and selected from 52 submissions. The papers address all aspects of static analysis including abstract domains, abstract interpretation, abstract testing, compiler optimizations, control flow analysis, data flow analysis, model checking, program specialization, security analysis, theoretical analysis frameworks, type based analysis, and verification systems.
Understanding And Using Linear Programming
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Author : Jiri Matousek
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-07-04
Understanding And Using Linear Programming written by Jiri Matousek 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 2007-07-04 with Mathematics categories.
The book is an introductory textbook mainly for students of computer science and mathematics. Our guiding phrase is "what every theoretical computer scientist should know about linear programming". A major focus is on applications of linear programming, both in practice and in theory. The book is concise, but at the same time, the main results are covered with complete proofs and in sufficient detail, ready for presentation in class. The book does not require more prerequisites than basic linear algebra, which is summarized in an appendix. One of its main goals is to help the reader to see linear programming "behind the scenes".
Graphics Gems Iv
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Author : Paul S. Heckbert
language : en
Publisher: Morgan Kaufmann
Release Date : 1994
Graphics Gems Iv written by Paul S. Heckbert and has been published by Morgan Kaufmann this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Computers categories.
Accompanying disk contains ... "all of the code from all four volumes."--Page 4 of cover.
Fundamentals Of Mathematics
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Author : Heinrich Behnke
language : en
Publisher: MIT Press
Release Date : 1974
Fundamentals Of Mathematics written by Heinrich Behnke and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with Mathematics categories.
Volume II of a unique survey of the whole field of pure mathematics.