The Hurwitz continued fraction expansion as applied to real numbers (Q2406616)

Summary: In [Acta Math. 11, 187--200 (1888; JFM 20.0201.01)], \textit{A. Hurwitz} defined a continued fraction algorithm for complex numbers which is better behaved in many respects than a more ``natural'' extension of the classical continued fraction algorithm to the complex plane would be. Although the Hurwitz complex continued fraction algorithm is not ``reducible'' to another complex continued fraction algorithm, over the reals the story is different. In this note we make clear the relation between the restriction of Hurwitz's algorithm to the real numbers and the classical continued fraction algorithm. As an application we reprove the main result of \textit{M. Choudhuri} and \textit{S. G. Dani} [Math. Res. Lett. 22, No. 4, 1023--1045 (2015; Zbl 1328.11037)].