2 papers
math.NT2025
The Gauss circle problem for Penrose tilings
Alan Haynes, Christopher Lutsko
Let denote the closed Euclidean ball of radius in the plane. In this paper we prove that, if is the set of vertices of any unit length rhombic Penrose tiling then, fo…
math.NT2023
Totally real cubic numbers are well approximable
Alan Haynes
In this paper we prove that all irrational numbers from totally real cubic number fields are well approximable by rationals (i.e. the partial quotients in the continued fraction ex…