This semester, Professor Hobby’s students in Elements of Geometry will be studying taxicab geometry. This is like normal geometry, except that the distance between two points is just the sum of the horizontal and vertical distances between them. (Since a taxicab would only be able to travel in those two directions, and could usually not go straight from one point to another.)
A taxicab circle and a standard circle
The figure in red is a normal circle, all points on it are 4 units from the center when measured using the “standard metric”. The figure in blue is a taxicab circle, all the points on it are 4 units from the center using the taxicab metric.