Download PDF by A.D. Alexandrov, N.S. Dairbekov, S.S. Kutateladze, A.B.: Convex Polyhedra

By A.D. Alexandrov, N.S. Dairbekov, S.S. Kutateladze, A.B. Sossinsky

ISBN-10: 3540231587

ISBN-13: 9783540231585

Convex Polyhedra belongs to the classics in geometry. There easily isn't any different booklet that offers with some of the points of the idea of three-dimensional convex polyhedra in a similar means, and in anyplace close to its aspect and completeness. it's a definitive resource of the classical box of convex polyhedra and comprises the to be had solutions to the query of the information which can uniquely verify a convex polyhedron. this question issues all information pertinent to a polyhedron, e.g. the lengths of edges, components of faces, etc.

This very important and obviously written publication contains the fundamentals of convex polyhedra and collects the main common life theorems for convex polyhedra which are proved through a brand new and unified approach. it's a awesome resource of rules for college kids.

The English variation comprises a variety of reviews in addition to extra fabric and a complete bibliography through V.A. Zalgaller to deliver the paintings brand new. additionally, comparable papers via L.A.Shor and Yu.A.Volkov were additional as vitamins to this e-book.

Show description

Read or Download Convex Polyhedra PDF

Similar graph theory books

Graph Theory and Applications: With Exercises and Problems by Jean-Claude Fournier PDF

Content material: bankruptcy 1 easy suggestions (pages 21–43): bankruptcy 2 timber (pages 45–69): bankruptcy three colorations (pages 71–82): bankruptcy four Directed Graphs (pages 83–96): bankruptcy five seek Algorithms (pages 97–118): bankruptcy 6 optimum Paths (pages 119–147): bankruptcy 7 Matchings (pages 149–172): bankruptcy eight Flows (pages 173–195): bankruptcy nine Euler excursions (pages 197–213): bankruptcy 10 Hamilton Cycles (pages 26–236): bankruptcy eleven Planar Representations (pages 237–245): bankruptcy 12 issues of reviews (pages 247–259): bankruptcy A Expression of Algorithms (pages 261–265): bankruptcy B Bases of Complexity concept (pages 267–276):

New PDF release: Theory and Application of Graphs

Within the spectrum of arithmetic, graph thought which stories a mathe­ matical constitution on a collection of parts with a binary relation, as a well-known self-discipline, is a relative newcomer. In contemporary 3 many years the interesting and speedily starting to be region of the topic abounds with new mathematical devel­ opments and demanding purposes to real-world difficulties.

Additional resources for Convex Polyhedra

Example text

3 The spherical image of an unbounded polyhedron. A closed convex polyhedron has support planes of all possible directions. Hence, its spherical image covers the entire sphere and has area 4π. An unbounded convex polyhedron always contains a half-line. Therefore, given a support plane Q to the polyhedron, we can find a support plane of this half-line which is parallel to Q, by shifting Q inside the polyhedron until Q begins to touch the half-line. Consequently, the spherical image of our unbounded polyhedron lies inside the spherical image of the half-line.

Whenever we talk about some limit angle, these cases are not excluded in advance. If an unbounded polygon undergoes the infinite similarity contraction to some point O, then in the limit it transforms obviously into its limit angle (Fig. 21). Therefore, under an infinite similarity contraction of an unbounded polyhedron P with respect to a point, its unbounded faces transform into their limit angles and the polyhedron itself transforms into its limit angle. Consequently, the limit angle may also be defined as the result of an infinite similarity contraction of the polyhedron.

Prove the following generalization of Theorems 5 and 6: The convex hull of a finite collection of points Ai and half-lines aj starting at some of the points inward the interior of the same half-space is a convex solid polyhedron. Its limit angle is the convex hull of the collection of the half-lines aj starting at a single point. Its vertices are among the points Ai . Further, one of the points is a vertex if and only if it does not belong to the convex hull of the collection of the other points and the half-lines aj .

Download PDF sample

Convex Polyhedra by A.D. Alexandrov, N.S. Dairbekov, S.S. Kutateladze, A.B. Sossinsky


by Thomas
4.0

Rated 4.43 of 5 – based on 9 votes