Recall the Coordinate Plane $($i$.$e$.,$ Cartesian Plane$)$ we are all familiar with in which every point is associated with a unique ordered pair of real numbers. Define the Taxicab Distance between points P and Q int he coordinate plane to be PQ$=|$x$2-$x$1|+|$y$2-$y$1|,$ where $($x$1,$y$1)$ and $($x$2,$y$2)$ are the ordered pairs for points P and Q$,$ respectively. The Taxicab Circle centered at A and passing through B is defined to be $\{$P$|$AP$=$AB$\}.$ Recall, in Euclidean Geometry, the ratio of the circumference to the diameter of any circle is constant $($the number is defined to be this constant$).$ Construct three Taxicab circles. One with radius length $2,$ and one with radius length $3$ and one with radius length $5.$ Find the ratio of the circumference $($using Taxicab distance$)$ to the diameter of each of these circles. As is the case for circles in Euclidean Geometry, does the ratio of the circumference to the diameter of any taxicab circle appear to be constant $($make a conjecture$)?$ If so$,$ what is that constant $($i$.$e$.,$ what is the number analogous to in Taxicab Geometry$)?$