## Friday, June 29, 2007

### What Difference Does Two Inches Make? Pizza Mathematics, Part I

A few nights ago, a friend and I went out for pizza. We deliberated over whether to order a 10" or 12" (stuffed, not thin crust). We chose the larger size but didn't finish it. Knowing that my friend is a top engineer for one of the nation's premiere steel fabricators, I figured he'd enjoy the mental exercise of determining whether we made the right choice.

First, we recalled the formula we learned long ago for the area of a circle: π * r2 or "pi times the radius squared"

My friend took out his PDA, and we used 3.1416 for π. For our calculations, the value of π to ten-thousandths would be plenty, especially considering that pizza dimensions are imprecise enough to introduce a significant margin of error. This table shows how pizza diameter translates into area:

 Size (inches) Area (square inches) 10 78.5 12 113.1 14 153.9 16 201.1

We discovered that the 12" pizza we ordered had 34.6 more square inches of area than the 10" pizza. Since we ate 75% of the 12" pizza (84.8 square inches), the 10" pizza would not have been big enough, assuming we would notice the difference of six square inches. That's unlikely, but at least I got a second meal out of the leftovers!