On a Recursive Construction of Circular Paths and the Search for π on the Integer Lattice Z2

Michael Rudolph (1, 2)

1 UNIC - Unité de Neurosciences Information et Complexité [Gif sur Yvette]
2 NeuroPSI - Institut des Neurosciences Paris-Saclay

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 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 ℓ1-norm, the defining constant π of a circle in R2.

Domaines: Neurobiologie; Psychologie et comportements; Sciences cognitives

Michael Rudolph. On a Recursive Construction of Circular Paths and the Search for π on the Integer Lattice Z2. Discrete and Computational Geometry, 2017, 59 (3), pp.643-662. ⟨10.1007/s00454-017-9930-7⟩. ⟨hal-02425731⟩