On a recursive construction of circular paths and the search for π on the integer lattice Z^2
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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 Z^2, 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 ℓ^1-norm, the defining constant π of a circle in R^2.
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