Linear Algebra and Its Applications, Vol. 225 (1995), pp. 1-12.
Ömer Egecioglu
Parallelogram-Law Type Identities
Abstract.
Identities generalizing the well-known formula relating the lengths of the
sides and the diagonals of a parallelogram in the plane are given. These
generalizations all have the flavor of the parallelogram-law, and specialize
to formulas involving sums of roots of unity, trigonometric functions,
binomial coefficients, and permutations over the symmetric and the
alternating groups.
omer@cs.ucsb.edu