The next unit I am teaching to my Geometry classes filled with sophomores and a few freshman is a unit on circles. What is one thing most of us think about when we think of circles? FOOD!

Pie… a pizza pie or a dessert pie… all involve pi! How fun.

Anyway, I want to tell you a funny mathematical story I heard that pertains to circles.

My mother works at a local restaurant that sells super great pizza, among other things. For context, my mother is a recently retired mathematics teacher (yeah, yeah, I know the apple doesn’t fall far from the tree.) At this restaurant they sometimes run out of 14 inch crusts and the joint also sells 10 in pizzas, so in that event they give the customer two 10 inch pizzas.

Mom says the owner is always belly-aching over losing money for the switch–“I keep getting ripped off!” But how much, if any, is he really getting ripped off? My mom thought it through, and… here are the numbers:

Area of a 14″ diameter pizza: π(7)^2 = 49π square inches

Area of two 10″ diameter pizzas: 2*π(5)^2 = 2*25π = 50π square inches

So we can see that the difference is only 50π – 49π = π… and remember that π is approximately 3.14, so the rip off is slim. Think about it this way… the extra pizza that the customer gets with 2 10″ diameter pizzas is a 2″ diameter pizza–so, like a bite or two difference.

So, this will make a great lesson reminding my geometry students of area. How important is mathematical literacy? But we must understand the owner’s thoughts–it is difficult to convince yourself visually that 2 10 inch diameter pizzas are of almost equal area to the 14 inch diameter pizza…

I plan to do a project this unit where students create a menu where they calculate the price of making a circular food and figure how to price it per whole and slice to address area and sector area of circles. Won’t this story be a great one to tell to launch the project? We will see.