Title: Pi Visits Manhattan,
Abstract: 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 definition of the circle in favour of a parametric
construction. Somewhat unexpectedly, we find that the Euclidean circle's
defining constant $\pi$ can be recovered in such a discrete setting.