We study the following two problems: (1) Given n ≥ 2 and α, how large Hausdorff dimension can a compact set A ⊂ R have if A does not contain three points that form an angle α? (2) Given α and δ, how large Hausdorff dimension can a compact subset A of a Euclidean space have if A does not contain three points that form an angle in the δ-neighborhood of… (More)