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Michael Rudolph
THEORETICAL PHYSICS • DISCRETE MATHEMATICS
On a recursive construction of circular paths and the
search for π on the integer lattice Z2


M. Rudolph-Lilith

arXiv:1602.06239 [cs.GR], 2016

Abstract

Digital circles not only play an important role in various technological settings, but also provide a lively playground for more fundamental number-theoretical questions. In this paper, we present a new recursive algorithm for the construction of digital circles on the integer lattice Z2, which makes sole use of the signum function. By briefly elaborating on the nature of discretization of circular paths, we then find that this algorithm recovers, in a space endowed with 1-norm, the defining constant π of a circle in R2.