On some metric and combinatorial geometric problems
✍ Scribed by P. Erdös
- Publisher
- Elsevier Science
- Year
- 1986
- Tongue
- English
- Weight
- 515 KB
- Volume
- 60
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
✦ Synopsis
Let x1, , x, be n distinct points in the plane. Denote by D(x,, ,x,) the minimum number of distinct distances determined by x1, , x,. Put f(n) = min D(x,,
📜 SIMILAR VOLUMES
The structure of rational functions of two real variables which take few distinct values on large (finite) Cartesian products is described. As an application, a problem of G. Purdy is solved on finite subsets of the plane which determine few distinct distances.
We consider the space of functions with bounded (k+1) th derivatives in a general domain in R n . Is every such function extendible to a function of the same class defined on the whole R n ? H. Whitney showed that the equivalence of the intrinsic ( =geodesic) metric in this domain to the Euclidean o