Download or read book Reshaping Convex Polyhedra written by Joseph O’Rourke and published by Springer Nature. This book was released on with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Convex Polyhedra written by A.D. Alexandrov and published by Springer Science & Business Media. This book was released on 2005-02-10 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Shaping Space written by Marjorie Senechal and published by . This book was released on 1988 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Convex Polyhedra written by Aleksandr Danilovich Aleksandrov and published by . This book was released on 2010 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt: Convex Polyhedra is one of the classics in geometry. There simply is no other book with so many of the aspects of the theory of 3-dimensional convex polyhedra in a comparable way, and in anywhere near its detail and completeness. It is the definitive source of the classical field of convex polyhedra and contains the available answers to the question of the data uniquely determining a convex polyhedron. This question concerns all data pertinent to the poly hedron, e.g. the lengths of edges, areas of faces, etc. This viatal and clearly written 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. It is a wonderful source of ideas for students. The English edition includes numerous comments as well as added material and a comprehensive bibliography by V.A. Zalgaller to bring the work up to date. Moreover, related papers by L.A. Shor and Yu. A. Volkov have been added as supplements to this book.
Download or read book Convex Polyhedra with Regularity Conditions and Hilbert s Third Problem written by A. R. Rajwade and published by Springer. This book was released on 2001-01-01 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Convex Polyhedra with Regular Faces written by Viktor A. Zalgaller and published by Springer. This book was released on 1969 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Convex Polyhedra with Regular Faces written by Viktor A. Zalgaller and published by Springer. This book was released on 2014-09-12 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On Shortest Paths Amidst Convex Polyhedra Classic Reprint written by Micha Sharir and published by . This book was released on 2015-08-04 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from On Shortest Paths Amidst Convex Polyhedra Let K be a 3-D convex polyhedron having n vertices. A sequence of edges of K is called a shortest-path sequence if there exist two points X, Y on the surface S of K such that is the sequence of edges crossed by the shortest path from X to Y along S. We show that the number of shortest-path sequences for K is polynomial inn, and as a consequence prove that the shortest path between two points in 3-space which must avoid the interiors of a fixed number of disjoint convex polyhedral obstacles, can be calculated in time polynomial in the total number of vertices of these obstacles (but exponential in the number of obstacles). 1. Introduction In this paper we study several problems related to the problem of calculating the Euclidean shortest path between two points in 3-dimensional space, which must avoid the interiors of a collection of polyhedral obstacles having altogether n vertices. This general problem seems to be intractable, and the only known algorithms for it require exponential time ([SS], [RS]), although no lower bounds are known as yet for this problem. On the other extreme hand we have the problem of finding the shortest path between two points in 3-space which must avoid the interior of a single convex polyhedral obstacle. In this case the problem is solvable in time 0(n log n) ([SS], [Mo]). Interpolating between these two extreme cases, one might consider the problem in which the polyhedral obstacles consist of a fixed number k of disjoint convex polyhedra (having altogether n vertices), and attempt to calibrate the complexity of this problem as a function of k and n. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works."
Download or read book Polyhedra written by Anthony Pugh and published by Univ of California Press. This book was released on 2023-11-10 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book ADJACENCY ON CONVEX POLYHEDRA written by Katta G. Murty and published by . This book was released on 1970 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt: Some results on the adjacency properties of extreme points of a convex polyhedron are discussed. (Author).
Download or read book Integral Convex Polyhedra and an Approach to Integralization written by Murray Edelberg and published by . This book was released on 1970 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many combinatorial optimization problems may be formulated as integer linear programming problems, that is, problems of the form: given a convex polyhedron P contained in the non-negative orthant of n-dimensional space, find an integer point in P which maximizes (or minimizes) a given linear objective function. Well known linear programming methods would suffice to solve such a problem if: (1) P is an integral convex polyhedron, or (2) P is transformed into the integral convex polyhedron that is the convex hull of the set of integer points in P, a process which is called integralization. This thesis provides some theoretical results concerning integral convex polyhedra and the process of integralization. Necessary and sufficient conditions for a convex polyhedron P to have the integral property are derived in terms of the system of linear inequalities defining P.A number-theoretic method for integralizing two-dimensional convex polyhedra is developed which makes use of a generalization of the division theorem for integers. The method is applicable to a restricted class of higher dimensional polyhedra as well. (Author).
Download or read book The Convex Polyhedra with Regular Vertices written by Charles Pasquini and published by . This book was released on 1980 with total page 72 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Polyhedra written by Peter R. Cromwell and published by Cambridge University Press. This book was released on 1997 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book A Lipschitzian Characterization of Convex Polyhedra written by David W. Walkup and published by . This book was released on 1968 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Hausdorff distance between parallel cross-sections of a closed convex polyhedron (whether bounded or not) possesses a Lipschitzian property. Moreover, this property characterizes convex polyhedra among the class of closed convex sets. (Author).
Download or read book On the Minkowski Constant Kantenkruemmung for Special Convex Polyhedra written by William James Perry and published by . This book was released on 1950 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Convex Polyhedra with Regular Faces Translated from Russian written by Viktor A. Zalgaller and published by . This book was released on 1969 with total page 95 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Isoperimetric Inequality for Convex Polyhedra written by George Edward Crane and published by . This book was released on 1949 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt:
