Document Type
Lecture
Publication Date
3-18-2015
Abstract
Suppose that d 2 and n are xed, and that 1 2 n specified angles. How many points do we need to place in Rd to realize all of these angles by triples of these points? A simple degrees of freedom argument shows that m points in R2 cannot realize more than 2m 4 general angles. We give a construction to show that this bound is sharp when m 5. n are In d dimensions the degrees of freedom argument gives an upper bound of dm d+1 2 1general angles. However, the above result does not generalize to this case; surprisingly, the bound of 2m 4 from two dimensions cannot be improved at all: there are sets of 2m 3 of angles that cannot be realized by m points in any dimension. Joint work with Bela Bollobas, Zoltan Furedi, Imre Leader, and Mark Walters.
Relational Format
presentation
Recommended Citation
Balister, Paul, "Subtending many angles with few points" (2015). Combinatorics Seminar. 39.
https://egrove.olemiss.edu/math_combinatorics/39
