Los Angeles Math Circle

4/8 -- LAMC Beginners: Taxicab Geometry, or When a circle is a square (Olga Radko)

The distance between two points is the length of the shortest line connecting them. Normally, such a path is a straight line. But in a city consisting of a square grid of streets shortest paths between two points are no longer straight lines (as every cab driver knows). We will explore the geometry of this unusual distance and play several related games.