**Laser-cut
Pythagoras’ theorem
puzzle**

Gerard
Westendorp

The puzzle
is based on the fact that you can tessellate the plane using two
arbitrary
squares a^{2} and b^{2} and from this construct a third
set of tessellating squares
c^{2}, as shown below.

This implies a^{2} + b^{2}=
c^{2}, obviously the area of the plane is independent of how
you dissect it.

(This might be a cool idea for your kitchen floor...)

This implies a

(This might be a cool idea for your kitchen floor...)

The puzzle has an a^{2}
square translated so it aligns with a triangle.

To show
that this construction works for all {a,b,c}, I made the animation
below.

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
proof.

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 one.

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 commons, here:

[I have not seen the proof used in this anywhere else, so maybe the author of the Wikimedia commons discovered it.]

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 one.

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 commons, here:

[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.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.