THE PIZZA THEOREM
It’s time for a snack, and you and your pal are all set to share a pizza, with each of you getting half. When the pizza arrives, however, you find that the slices are not all the same size.
The pizza slicer had made four cuts with equal angles, all crossing at one point, to end up with eight slices. But the crossing point is not at the pizza’s center, so some slices are larger than others.
Mathematicians have shown there’s an easy solution to sharing the pizza evenly. They call it the Pizza Theorem. If you and your pal take alternate slices, you each automatically end up with an equal amount. It doesn’t matter where the crossing point is or which wedge you start with.
The strategy of going around the pizza and taking alternate slices also gives each person exactly the same amount of edge crust. Nice, if you love stuffed-crust pizza.
The Pizza Theorem doesn’t work for a pizza cut into just four slices, but it does work for eight, 12, 16, 20, or any larger multiple of four. In all these cases, the sums of the areas of alternate slices are equal.
What if three of you want equal shares of a pizza? This time, you would need a pizza cut into 12 slices, with each person receiving four. For five people, you would need a pizza cut into 20 slices.
And there’s more. Suppose you have a pizza with, say, three toppings spread unevenly across the surface. As long as each topping covers a circular area and the crossing point of the cuts lies inside all three splotches of topping, the Pizza Theorem ensures that everyone sharing the pizza gets the same amount of the three toppings.
There’s nothing like math to help make sharing easier. Good thing too, because your pal gets pretty grouchy when you take more than your portion of the pie.
