Introduction to Combinatorial Methods in Geometry

<p>This book offers an introduction to some combinatorial (also set-theoretical) approaches and methods in geometry of the Euclidean space <b>R</b><i>m</i>. The topics discussed in the manuscript are due to the field of combinatorial and convex geometry.</p><p>The author’s primary intention is to discuss those themes of Euclidean geometry which might be of interest to a sufficiently wide audience of potential readers. Accordingly the material is explained in a simple and elementary form completely accessible to the college and university students. At the same time the author reveals profound interactions between various facts and statements from different areas of mathematics: the theory of convex sets finite and infinite combinatorics graph theory measure theory classical number theory etc.</p><p>All chapters (and also the five Appendices) end with a number of exercises. These provide the reader with some additional information about topics considered in the main text of this book. Naturally the exercises vary in their difficulty. Among them there are almost trivial standard nontrivial rather difficult and difficult. As a rule more difficult exercises are marked by asterisks and are provided with necessary hints.</p><p>The material presented is based on the lecture course given by the author. The choice of material serves to demonstrate the unity of mathematics and variety of unexpected interrelations between distinct mathematical branches.</p>