Alexander Kharazishvili

Introduction to Combinatorial Methods in Geometry (eBook, ePUB)

• Format: ePub

Produktbeschreibung

This book offers an introduction to some combinatorial (also, set-theoretical) approaches and methods in geometry of the Euclidean space Rm. The topics discussed in the manuscript are due to the field of combinatorial and convex geometry.

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Produktdetails

• Verlag: Taylor & Francis
• Seitenzahl: 360
• Erscheinungstermin: 7. Mai 2024
• Englisch
• ISBN-13: 9781040014288
• Artikelnr.: 70188816

Autorenporträt

Alexander Kharazishvili is Head of the Department of Discrete Mathematics at I. Vekua Institute of Applied Mathematics.

Inhaltsangabe

1. The index of an isometric embedding. 2. Maximal ot-subsets of the Euclidean plane. 3. The cardinalities of at-sets in a real Hilbert space. 4. Isosceles triangles and it-sets in Euclidean space. 5. Some geometric consequences of Ramsey's combinatorial theorem. 6. Convexly independent subsets of infinite sets of points. 7. Homogeneous coverings of the Euclidean plane. 8. Three-colorings of the Euclidean plane and associated triangles of a prescribed type. 9. Chromatic numbers of graphs associated with point systems in Euclidean space. 10. The Szemeredi-Trotter theorem. 11. Minkowski's theorem, number theory, and nonmeasurable sets. 12. Tarski's plank problem. 13. Borsuk's conjecture. 14. Piecewise affine approximations of continuous functions of several variables and Caratheodory-Gale polyhedral. 15. Dissecting a square into triangles of equal areas. 16. Geometric realizations of finite and infinite families of sets. 17. A geometric form of the Axiom of Choice.