[lagadu]

Easiest way of visualising the pythagorean theorem is to think about it the way it was initially written: think about areas formed by tree squares.

This image[0] from wikipedia shows it all: the area of square a plus the area of square b equals the area of square c. It's just really convenient that we can use that to calculate triangle sides without resorting to trigonometry.

[0] https://upload.wikimedia.org/wikipedia/commons/thumb/d/d2/Py...

[caseymarquis]

I find that that's a terrible way of visualising the theorum, as it offers no indication of why the theorem is true. I much prefer the below picture: https://www.mathalino.com/sites/default/files/images/01-pyth...

It could be improved by putting -(ab/2) inside the triangles, but I'm on mobile, so making something is out of the question.