Introduction Assumptions Distance Euclidian or Not? Conic Sections Applications Beyond Taxicabs Resources Contact References	Taxicab (Manhattan) Distance Taxicab geometry is a non-Euclidean geometry that is accessible in a concrete form and is only one axiom away from being Euclidean in its basic structure. The points are the same, the lines are the same, and angles are measured the same way. Only the distance function is different. In Euclidean geometry distance between two points P(x1,y1) and Q(x2, y2) are defined by: The minimum distance between two points is a straight line in Euclidean geometry.. In taxicab geometry there may be many paths, all equally minimal, that join two points. Taxicab distance between two points P and Q is the length of a shortest path from P to Q composed of line segments parallel and perpendicular to the x-axis. We use the formula: This is known as the taxicab metric. Look at the distance between points L(3,2) and M(4,6): it becomes |3-4| + |6-2| = 1 + 4 = 5.