This is how I first really understood the Pythagorean Theorem.
The outer circle looks just a little bit larger than the inner circle. But actually, its area is twice as large.
Just think about that.
Other ideas involved here:
- scaling properties of squared quantities
(gravitational force, skin, paint, loudness, brightness)
- circumcircle & incircle
This is also how I first really understood √2, now my favourite number.