**Pythagorean Theorem**

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**.

Kind of like the difference between medium and large soda cups, or how a tiny house still requires kind of a lot of timber, for how much air it encloses. If you buy a slightly wider pizza or cake it will serve proportionally more people; and if an inverse-square force (sound, radio power, light brightness) expands a little bit more it will lose a lot of its energy.

Ideas involved here:

- scaling properties of squared quantities

(gravitational force, skin, paint, loudness, brightness) - circumcircle & incircle
- âˆš2

This is also how I first really understood **âˆš2**, now my favourite number.