The standard
coordinate system. N-dimensional points are represented as ordered n-
tuples, with each element representing a distance along one of n
orthogonal axes.
For example, the 2 dimensional cartesian system (the cartesian plane) represents points as (x, y), where x is the distance along the x
axis, and y is the distance along the y axis. The distance between 2 points in a cartesian coordinate system is sqrt ((a1 - b1)^2 + (a2 - b2)^2 + ... + (an - bn)^2) (if you can fly -- it's sum (abs(a_i-b_i)) if you have to
take a cab), where a is one point and b is the other. ak is the kth
element of a.