Better Visual Proof of Pythagoras' Theorem

Most people know about Pythagoras' theorem from school, and it’s often taught with a visual proof using three squares around a triangle, most commonly with sides of length 3, 4, and 5:

But in my opinion, this is not overly helpful. To see the validity, you have to calculate three squares and hope for pleasant values. That's obviously not witchcraft, but why the extra steps when there is a proof out there where you can spot a²+b²=c² at first glance? There’s also the debate about whether a visual proof relying on calculations is truly a visual proof.

So here is a truly visual proof:

You have a triangle as before, with three identical copies, and place them into a square. If you arrange them like in the left picture, you can instantly see that the empty space consists of two squares: a² and b².

If you rearrange the same triangles, you can see that the empty square is one square with an area of c².

Since we didn’t change the "frame" and neither the area nor the number of triangles, the empty space is the same on both sides, ergo a²+b²=c².

You can show this for any right-angled triangle. If you want to use an outer frame, it has to have side lengths of aaa and bbb. Now, is this something that needs to be 3D printed? Not really, to be honest. Actually, it’s almost the opposite; if you don’t have a well-calibrated printer with sharp corners, it can be hard to fit the triangles. But I wanted to add what I believe to be a useful and truly visual proof for a long time, as with the contest, the old proof gets recycled again and again.

This proof here comes with three different triangles. The frame is upscaled a bit to allow easier placing:

It doesn’t matter if you print it out, show it on paper, or whatever, but when I first saw this version, I was really confused why people still use the outdated proof instead of this one—so here I am, spreading the word. ;)