TITLE: Visual explanation of the following statement:
QUESTION [18 upvotes]: Can somebody fill me in on a visual explanation for the following:
If there exist integers $x, y$ such that $x^2 + y^2 = c$, then there also exist integers $w, z$ such that $w^2 + z^2 = 2c$
I know why it is true (ex. take $w = x-y, z = x+y$), but I would think there is a visual explanation hiding somewhere because of squared terms (we can make squares!!)

REPLY [7 votes]: I have devised what I believe to be a simpler construction of Anant's squares argument and have thus shared it here: