The grid revisted

✍ Scribed by Paul Erdős; Zoltán Füredi; János Pach; Imre Z. Ruzsa

• Book ID: 103056917
• Publisher: Elsevier Science
• Year: 1993
• Tongue: English
• Weight: 482 KB
• Volume: 111
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(93)90155-m

✦ Synopsis

We construct a set of n points (i) on the unit sphere S dm 1 (d>4) so that they determine o(n) distinct distances and (ii) in the plane, in general position, so that they determine o(n'+') distinct distances for any E > 0. We also prove that if P is a set of n points in a disk of radius n such that the minimum distance between them is 1, and lPj/ n-cc, then the set of angles determined by these points is everywhere dense in [0,2x].