The Decomposition of Figures Into Smaller Parts

By: Vladimir Grigor'evich Boltyanskii, Izrail' Tsudikovich Gokhberg

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Paperback | 15 April 1980 | Edition Number 1

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80 Pages

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2.3 x 1.54 x 0.06

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In contrast to the vast literature on Euclidean geometry as a whole, little has been published on the relatively recent developments in the field of combinatorial geometry. Boltyanskii and Gohberg's book investigates this area, which has undergone particularly rapid growth in the last thirty years. By restricting themselves to two dimensions, the authors make the book uniquely accessible to interested high school students while maintaining a high level of rigor. They discuss a variety of problems on figures of constant width, convex figures, coverings, and illumination. The book offers a thorough exposition of the problem of cutting figures into smaller pieces. The central theorem gives the minimum number of pieces into which a figure can be divided so that all the pieces are of smaller diameter than the original figure. This theorem, which serves as a basis for the rest of the material, is proved for both the Euclidean plane and Minkowski's plane.

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Non-Fiction Mathematics Combinatorics & Graph Theory Geometry Miscellaneous Items

Preface
Division of Figures into Pieces of Smaller Diameter
The Diameter of a Figure
Formulation of the Problem
Borsuk's Theorem
Convex Figures
Figures of Constant Width
Embedding in a Figure of Constant Width
For Which Figures isa(F) = 3?
Division of Figures in the Minkowski Plane
A Graphic Example
The Minkowski Plane
Borsuk's Problem in Minkowski Planes
The Covering of Convex Figures by Reduced Copies
Formulation of the Problem
Another Formulation of the Problem
Solution of the Covering Problem
Proof of Theorem 2.2
The Problem of Illumination
Formulation of the Problem
Solution of the Problem of Illumination
The Equivalence of the Last Two Problems
Division and Illumination of Unbounded Convex
Figures
Remarks
Table of Contents provided by Publisher. All Rights Reserved.

The Decomposition of Figures Into Smaller Parts

At a Glance

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