Erdos Distance Problem

Includes index

Includes bibliography (p. 143-146) and references

1. The [square root of n] theory
2. The [n to the 2/3 power] theory
3. The Cauchy-Schwarz inequality
4. Graph theory and incidences
5. The [n to the 4/5 power] theory
6. The [n to the 6/7 power] theory
7. Beyond [n to the 6/7 power]
8. Information theory
9. Dot products
10. Vector spaces over finite fields
11. Distances in vector spaces over finite fields

The Erdos problem asks, What is the smallest possible number of distinct distances between points of a large finite subset of the Euclidean space in dimensions two and higher? The main goal of this book is to introduce the reader to the techniques, ideas, and consequences related to the Erdos problem. The authors introduce these concepts in a concrete and elementary way that allows a wide audience—from motivated high school students interested in mathematics to graduate students specializing in combinatorics and geometry—to absorb the content and appreciate its far-reaching implications. In the process, the reader is familiarized with a wide range of techniques from several areas of mathematics and can appreciate the power of the resulting symbiosis.