Monday, February 2, 2015

Pizza Geometry

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.

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