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The Decomposition of Figures into Smaller Parts

Popular Lectures in Mathematics

Paperback Published: 1st January 1980
ISBN: 9780226063577
Number Of Pages: 84

Paperback

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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.

 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.

ISBN: 9780226063577
ISBN-10: 0226063577
Series: Popular Lectures in Mathematics
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 84
Published: 1st January 1980
Publisher: The University of Chicago Press
Country of Publication: US
Dimensions (cm): 27.5 x 15.0  x 0.64
Weight (kg): 0.14

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