Yesterday was Pi Day, and as a high school science teacher, this is a big deal. Not as big of a deal as it is for math teachers, but until the practical but not-yet-widely-accepted Tau catches on, it’s the best mathematical constant we can celebrate during the school year.
My wife Carol and I about to devour some “banarama” and “shady wake” pie at Muddy’s Grindhouse here in midtown Memphis! I also made sure to share some Pi puns with my students during the day and remind them what Pi means (it’s the ratio of circumference divided by diameter of ANY CIRCLE EVERRRR).
But that’s not why I’m writing this post. This post will use my second-favorite mathematical constant to bolster your economic future. If you readily look for applications of geometry in your everyday life, then you may already know what I’m about to say. If not, then this may be the most important statement you are reading at this very moment. Here it is:
You should always buy the biggest pizza.
For this post, I’ll be using prices from this menu from the Memphis Pizza Cafe on Broad Avenue. Here are the prices for the 10″, 13″, and 15″ “Hey Meat!” pizza:
At first glance, it seems like each inch of pizza diameter costs you about a dollar. It’s just under $10 for the 10″. But the deal seems to get worse as you add more inches. The 15″ costs $16.35, which is more than $1 per inch! It’s a WORSE deal than the smaller pizza!
Pizza prices are misleading though. Most pizza locations (unless they use the ambiguous sizes of small/medium/large) list pizza sizes by the diameter of the pizza. But of course, you aren’t eating a linear pizza, you are eating a circular pizza. The AREA, not the diameter, is what you care about. And it turns out that each additional inch of diameter nets you an increasing amount of area. For example, adding an inch to the diameter of the 10″ pizza increases the total area by a little, but adding an inch to the diameter of the 15″ pizza increases the total area by a lot!
The equation for area is:
A = π r², where r is the radius (i.e., half the diameter)
Here is my calculation for area of the 10″ diameter pizza:
A = π r²; r = 5″
A = (3.1415)(5″)²
A = 78.5 in²
The 78.5 in² (10″ diameter) pizza costs $9.90. Divide the cost by the area, and you get $0.126/in², or 12.6¢/in². Not bad, only 12.6 cents for every square inch of pizza!
I did the same calculation for the other two sizes, getting the following results:
10″ pizza: 12.6¢/in²
13″ pizza: 9.91¢/in²
15″ pizza: 9.25¢/in²
These numbers would be like the “unit price” you find at grocery stores, telling you the price per unit (such as ounce or gram) that you can compare to other brands/sizes. Look at that! The 15″ pizza costs you only 70% the price per square inch of the 10″ pizza!
So, unless you hate leftover pizza, it’s always the best deal to get the biggest pizza possible! Share that pizza with some other folks and bask in the glory of savings! Thank goodness for π and for geometry!