First, let me say at the outset that despite strong temptation, I will refrain from using any pi/pie puns in this post. In fact, nobody says “pizza pie” anymore anyway.
For a long time, I've realized that a large (e.g., 16”) pizza is
actually qualitatively better than a small (e.g., 12”) inch
one. However, I had failed to demonstrate this with mathematical
rigor. I shall now correct this oversight.
The important point is that regardless of the pizza diameter, the crust
is always about an inch wide. That means that a 12” pizza really has a
covered area that's 10” in diameter, while a 16” pizza has a 14” covered area.
Some simple geometry based on the old formula, A = πr2, shows us
that a small pizza has a total area of 113 in2, but a covered area of
only 79.5 in2. In other words, it's about 30% plain crust.
A large pizza, on the other hand, has a total area of 201 in2, but a
covered area of 154 in2. That means the uncovered crust is only 23%
of the total.
Quod erat demonstrandum1
1Unless you don't eat the crust, in which case none of this matters.