Steinhaus triangles

Abstract

In this thesis, we study Steinhaus's problem. We begin with the definitions of Steinhaus triangle and balanced binary sequence, and we study sequences with different properties. We then show three different proofs of the existence of balanced binary sequences of any length n ≡ 0 or 3 (mod 4). In the last chapter, we present Molluzzo s problem, a generalization of Steinhaus s problem. We study arithmetic progressions and antisymmetric sequences and their associated generalized triangles. On the one hand, we show the existence of balanced sequences in Z/3 k Z of any valid length. On the other hand, we see different cases in which Molluzzo s problem is answered negatively.