A few applications of negative-type inequalities (Q1340125)

The authors study isometric embeddings of a finite metric space into Euclidean space, applying the negative-type inequalities for square Euclidean distance. At first they give a generalization of the parallelogram theorem. Then they present a short proof of Rankin's theorem on the maximum number of dispersed points on a sphere and also a short proof of the known result concerning the impossibility of \((\alpha,\beta)\)-embeddings for complete bipartite graphs \(K_{n,n}\) of large order.