The nice thing about this proof, is that
it can be made into a puzzle. The same is true for the more well known
proof called as Perigal's
Apparently, Perigal even has this one carved on his tombstone!
I thought Perigal's proof might yield a too easy puzzle, so I used this
It turns out to be surprisingly hard. When I first got it from the
laser cutting shop, it took my several minutes to solve.
The idea came from a file on Wikimedia
[I have not seen the proof used in this anywhere else, so maybe the
author of the Wikimedia commons discovered it.]
->Actually, after further Googling,
I found that Al-Nayrizi
may have discovered it in 900 AD
I also found out that the tessellation of the plane I used is called a
Pythagorean tiling. This Wikipedia page
explains how both Perigal and Al-Nayrizi can be constructed from it.
You can buy this puzzle on Etsy