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
  • √2

This is also how I first really understood √2, now my favourite number.

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s