Introduction Assumptions Distance Euclidian or Not? Conic Sections Applications Beyond Taxicabs Resources Contact References	Beyond Taxicab Geometry Taxicab geometry opens the door to a wide array of new mathematics, a group known as non-Euclidian geometry, where Euclid's assumptions do not hold. There is the interesting question of perpendicular bisectors in taxicab form.In both geometries the perpendicular bisector of a line segment is defined the same: The set of all points that are equidistant from the endpoints of the line segment. In the Euclidean plane the perpendicular bisector looks like: Here the perpendicular bisector of segment AB is defined as the set of all points where the AC = BC. In the taxicab plane the perpendicular bisector looks like: Here the perpendicular bisector is defined as the set of all points where taxicab distance AC = taxicab distance CB.