# Pi Visits Manhattan

@article{RudolphLilith2017PiVM, title={Pi Visits Manhattan}, author={M. Rudolph-Lilith}, journal={arXiv: History and Overview}, year={2017} }

Is it possible to draw a circle in Manhattan, using only its discrete network of streets and boulevards? In this study, we will explore the construction and properties of circular paths on an integer lattice, a discrete space where the distance between two points is not governed by the familiar Euclidean metric, but the Manhattan or taxicab distance, a metric linear in its coordinates. In order to achieve consistency with the continuous ideal, we need to abandon Euclid's very original… Expand

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On a Recursive Construction of Circular Paths and the Search for $$\pi $$π on the Integer Lattice $$\mathbb {Z}^2$$Z2

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A new algorithm for the construction of digital circles on the integer lattice Z2, which makes sole use of the signum function, which recovers the defining constantπ of a circle in R2, in a space endowed withℓ1-norm. Expand

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