Planet Money wrote about the economics of pizza size, but I feel like they left out the actual math. It's not complicated, but basically since `area = π*radius`^{2} = (π/4)*diameter^{2} , the area changes with the square of the diameter. So for an 8-inch pizza, the area is 50 square inches, while the area of a 12-inch pizza is 113 square inches. A 50% increase in diameter equates to a 125% increase in area. That's the power of exponents.
Simplifying the formula, you can write that the change in area is related to the change in diameter as follows: `Δa = ((π/4)*d`_{2}^{2} - (π/4)*d_{1}^{2})/((π/4)*d_{1}^{2}) = (d_{2}^{2}/d_{1}^{2}) - 1 Helpful for the next time you want to get a wedgie in a pizza place. #math |