Several methods to perform exact computations on real numbers have been proposed in the literature. In some of these methods real numbers are represented by infinite (lazy) strings of digits. It is a well known fact that, when this approach is taken, the standard digit notation cannot be used. New forms of digit notations are necessary. The usual solution to this representation problem consists...

Given a finite set of real numbers A, the generalised golden ratio is the unique real number G(A) > 1 for which we only have trivial unique expansions in smaller bases, and have non-trivial unique expansions in larger bases. We show that G(A) varies continuously with the alphabet A (of fixed size). What is more, we demonstrate that as we vary a single parameter m within A, the generalised golde...

UNLABELLED This study aimed to investigate the association of facial proportion and its relation to the golden ratio with the evaluation of facial appearance among Malaysian population. This was a cross-sectional study with 286 randomly selected from Universiti Sains Malaysia (USM) Health Campus students (150 females and 136 males; 100 Malaysian Chinese, 100 Malaysian Malay and 86 Malaysian Ind...