proof of generalization of the parallelogram law

Let g(x,y)=x+y2-x2 and m(x,y)=x,y+y,x. Then


Hence, taking x1=x4=x,x2=y,x3=z we have:

i=13xi+xi+12-i=13xi2 = i=13g(xi,xi+1)
= i=13xi2+i=13m(xi,xi+1)
= i=13xi2.
Title proof of generalizationPlanetmathPlanetmath of the parallelogram lawMathworldPlanetmath
Canonical name ProofOfGeneralizationOfTheParallelogramLaw
Date of creation 2013-03-22 16:08:58
Last modified on 2013-03-22 16:08:58
Owner Mathprof (13753)
Last modified by Mathprof (13753)
Numerical id 7
Author Mathprof (13753)
Entry type Proof
Classification msc 46C05