For 10 points, name this quantity, the separation between two points in space.
Minkowski's taxicab geometry created a version of this quantity named for Manhattan. In the calculus of variations, the smallest value of this quantity for distinct objects is the geodesic. A graph-theoretic notion of this quantity counts the number of edges in a shortest path between two graphs. A metric space is a set in which this notion can be quantified, and on those spaces, this notion must satisfy non-negativity, symmetry, and the (*)  triangle inequality. In Euclidean geometry, this quantity for points  x and  y  can be represented as the norm of  x  minus  y , which can otherwise be written as the square root of the sum of squared differences between each component of two vectors  a  and  b . For 10 points, name this quantity, the separation between two points in space.
Minkowski's taxicab geometry created a version of this quantity named for Manhattan.
distance  [or  displacement ; or  length ; prompt on  norm  until "graph-theoretic" is read; accept metric  until read] 