The red points at the border of the square below are all at a constant distance from the square's center.
That is, if the distance function is the *taxicab metric*, also known as *L1 norm* or *Manhattan distance*.
$$
d_1(p, q) = |p_1 - q_1| + |p_2 - q_2|
$$

So technically, this square is a circle.

If the radius is 1, then the circumference must be 8, the diameter 2, and thus \(\pi = 4\)! Edward J. Goodwin was right after all. ðŸ˜›