We study a variant of the ErdH os unit distance problem, concerning angles between successive triples of points chosen from a large finite point set. Specifically, given a large finite set of $n$ points $E$, and a sequence of angles $(alpha_1,ldots,alpha_k)$, we give upper and lower bounds on the maximum possible number of tuples of distinct points $(x_1,dots, x_{k+2})in E^{k+2}$ satisfying $angle (x_j,x_{j+1},x_{j+2})=alpha_j$ for every $1le j le k$ as well as pinned analogues.
تحميل البحث