Unrolling these circles fills a triangle with base 2 π r and height r (where r is the radius of the filled disk). Such a triangle has area π r². This does not serve as a complete proof for why this is the area of a circle, but can give you some intuition for why it should be. [code]
You should always order the bigger
pizza. While an 8“ pizza is roughly
50 square inches, a 16” pizza is 200
square inches, which is 4 times
bigger but most pizza places charge
by radius and don’t consider the
overall area of the pizza. An NPR study
found that one 20” pizza is actually
bigger than two 14” pizzas, but is
also, on average, $9.00 cheaper. Source
Benjamin Franklin - Magic Circle, “Experiments and Observations on Electricity”, 1750.
Each radius of this Magic Circle (including the center entry) sums to 360, as does each annulus. Franklin has also highlighted 20 “excentric” annuli, each of which, together with the central 12, sums to 360.