Driving to Pizza House: A Mathematical Tale

Last year we started taking Jana out to dinner to celebrate Epiphany. This year Jana wanted to go to the Clyde Pizza House. Clyde is about 12 miles away from Abilene, but we think the Clyde Pizza House has some of the best pizza we've ever had. Plus, on weekends they often have local bands playing live, old school (very old school) country music.

Anyway, last week on the drive out to Clyde Jana and I had the following conversation. It's a story for all you math teachers out there:

Me: "Do you want to call ahead and get the pizza ordered?" (We often do this so we don't have to wait long for the pizza when we get there.)

Jana: "I'm not sure. The boys are eating a lot more so we need to order more pizza. I want to look at the sizes to see what we should order."

"You know what we should do? We should find out the area of the large pizza we get and then order an additional half of that. Because a large and a half would work, right?"

"Yes, that's about the amount we need."

"So all we need to do is find the area of the large pizza and then find the areas of the smaller pizzas to see which one comes closest to half the area of the large."

"Okay."

"So what's the formula to find the area of a circle?"

"I don't know."

"Me neither. Look it up on your iPad."

(Jana looks and reports back) "It's A = πr²

"r is the radius, half the diameter, right?"

"Right."

"So let's call and get the diameters of the pizzas they have."

(Jana calls Pizza House and reports back) "They have a 16'', the one we get, plus a 14'', 12" and 9"."

"Okay. Let's find the area for the 16''. That would be A = 3 (let's round to make this easy) x 8². What does that equal?"

"192."

"Okay, so a large is close to 200 square inches of pizza. So all we need to do is to find a smaller size that is about half that size, something close to 100 inches."

"Well, the next size is 14". That would give us A = 3 x 7². That's...147."

"Too much."

"Too much."

"Try the next size, the 12"."

"For the 12" we have A = 3 x 6²."

"That's 108."

"That's close to 100, just what we need."

"Right. Call it in."

(Jana dials) "Yes, we'd like to order one 16" pizza and one 12" pizza..."

And you know what? It was the perfect amount.