arXiv:2010.04670v1 [math.DS] 9 Oct 2020 Page 1 OCTAGONAL CONTINUED FRACTION AND DIAGONAL CHANGES MAURO ARTIGIANI Abstract. In this short note we show that the octagon Farey map introduced by Smillie and Ulcigrai in [8, 9] is an acceleration of the diagonal changes algorithm introduced by Delecroix and Ulcigrai in [2]. 1. Introduction The theory of continued fractions is a beautiful page of mathematics which connects number theory, (hyperbolic) geometry and dynamical systems. Given a number α ∈ R, its continued fraction
