Interpret this geometrically, as a statement about parallelograms.

[Jamin2112]

Homework Statement

Prove that

|x+y|² + |x-y|² = 2|x|² + 2|y|²

if x and y are elements of ℝ^k

Homework Equations

Ordinary stuff

The Attempt at a Solution

Got the first part, but I don't understand the parallelogram thing yet. The little sketch I drew didn't help.

 

[vrmuth]

In a parallelogram the sum of squares of sides equals the sum of squares of its diagonals

 

[vrmuth]

Prove that

|x+y|² + |x-y|² = 2|x|² + 2|y|²

if x and y are elements of ℝ^k

since \left|X+Y\right| and \left|X-Y\right| are diagonals of the parallelogram with \left|X\right|and \left|Y\right| as the sides , it states the property
"In a parallelogram The sum of squares of diagonals equals the sum of squares of the sides"

 

[Jamin2112]

since \left|X+Y\right| and \left|X-Y\right| are diagonals of the parallelogram with \left|X\right|and \left|Y\right| as the sides , it states the property
"In a parallelogram The sum of squares of diagonals equals the sum of squares of the sides"

Drew the picture again. Now I understand it. Indeed: On a parallelogram, the sum of squares of diagonals equals the sum of squares of the sides