Fifth Property of the Euclidean Metric
From Wikimization
For a list of points in Euclidean vector space, distance-square between points and is defined
Euclidean distance must satisfy the requirements imposed by any metric space:
- (nonnegativity)
- (self-distance)
- (symmetry)
- (triangle inequality)
where is the Euclidean metric in .
Fifth property of the Euclidean metric
(Relative-angle inequality.)
Augmenting the four fundamental Euclidean metric properties in , for all , , and for distinct points , the inequalities
where is the angle between vectors at vertex must be satisfied at each point regardless of affine dimension.