The Decomposition of Figures Into Smaller Parts
80 pages

© 1980
 Contents
Table of Contents
Contents
Preface
1. Division of Figures into Pieces of Smaller Diameter
1.1. The Diameter of a Figure
1.2. Formulation of the Problem
1.3. Borsuk's Theorem
1.4. Convex Figures
1.5. Figures of Constant Width
1.6. Embedding in a Figure of Constant Width
1.7. For Which Figures is a(F) = 3?
2. Division of Figures in the Minkowski Plane
2.1. A Graphic Example
2.2. The Minkowski Plane
2.3. Borsuk's Problem in Minkowski Planes
3. The Covering of Convex Figures by Reduced Copies
3.1. Formulation of the Problem
3.2. Another Formulation of the Problem
3.3. Solution of the Covering Problem
3.4. Proof of Theorem 2.2
4. The Problem of Illumination
4.1. Formulation of the Problem
4.2. Solution of the Problem of Illumination
4.3. The Equivalence of the Last Two Problems
4.4. Division and Illumination of Unbounded Convex Figures
Remarks
1. Division of Figures into Pieces of Smaller Diameter
1.1. The Diameter of a Figure
1.2. Formulation of the Problem
1.3. Borsuk's Theorem
1.4. Convex Figures
1.5. Figures of Constant Width
1.6. Embedding in a Figure of Constant Width
1.7. For Which Figures is a(F) = 3?
2. Division of Figures in the Minkowski Plane
2.1. A Graphic Example
2.2. The Minkowski Plane
2.3. Borsuk's Problem in Minkowski Planes
3. The Covering of Convex Figures by Reduced Copies
3.1. Formulation of the Problem
3.2. Another Formulation of the Problem
3.3. Solution of the Covering Problem
3.4. Proof of Theorem 2.2
4. The Problem of Illumination
4.1. Formulation of the Problem
4.2. Solution of the Problem of Illumination
4.3. The Equivalence of the Last Two Problems
4.4. Division and Illumination of Unbounded Convex Figures
Remarks
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