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Interpret this geometrically, as a statement about parallelograms.

  1. Oct 10, 2011 #1
    1. The problem statement, all variables and given/known data

    Prove that

    |x+y|2 + |x-y|2 = 2|x|2 + 2|y|2

    if x and y are elements of ℝk

    2. Relevant equations

    Ordinary stuff

    3. 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.

    screen-capture-1-34.png
     
  2. jcsd
  3. Oct 11, 2011 #2
    In a parallelogram the sum of squares of sides equals the sum of squares of its diagonals
     
  4. Oct 11, 2011 #3
    since [itex]\left|X+Y\right|[/itex] and [itex]\left|X-Y\right|[/itex] are diagonals of the parallelogram with [itex]\left|X\right|[/itex]and [itex]\left|Y\right|[/itex] as the sides , it states the property
    "In a parallelogram The sum of squares of diagonals equals the sum of squares of the sides"
     
    Last edited: Oct 12, 2011
  5. Oct 12, 2011 #4
    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
     
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