The aim of this book is to present some ideas, methods and topics in elementary combinatorial geometry. Even if most of the book can be understood without any mathematical background, so it is accessible for 12-14 years old children too, we recommend it to high school students and college students as an introduction to a few topics in combinatorial (or convex) geometry (counting problems, pigeonhole principle, Helly's theorem, Sperner lemma). Our approach is basically an elementary one, but it is useful to know some combinatorial techniques and some basic notions. These notions appear in the subject index, so they can be identified easily.
The main purpose was not to create an exhaustive collection, but to offer a quick and short overview, to present a few properties which have surprising applications also in higher mathematics (the Sperner lemma) and to show some interesting ways of generalizations. So this book wants to be a kind of bridge between elementary problems and university courses.
Cuprins
1. Counting
1.1 Counting points
1.2 Counting lines
1.3 Counting regions
1.4 Counting configurations
1.5 Counting paths
1.6 Solutions
1.6.1 Counting points
1.6.2 Counting lines
1.6.3 Counting regions
1.6.4 Counting configurations
1.6.5 Counting paths
2. The pigeonhole principle
2.2 Solutions
3. Helly type theorems
3.2 Solutions
4. The Sperner lemma
4.2 Solutions
5. Miscellaneous problems
5.2 Solutions
Author index
Subject index
