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The Pi Day pizza problem

Today is March 14th meaning, for folks in the US, it’s “Pi Day” i.e. 3/14. The mathematical constant of pi (π) is used mostly for calculating measurements of circular and spherical objects e.g. radius, diameter, circumference, and surface area.

Since pizza is the probably the world’s most famous circular food, this gives us a fun opportunity to use Pi for some pizza math. 

Here’s a hypothetical math problem for you: your friend orders two medium pizza pies, and you order one large pizza pie. Who has more pizza? Let our little friend pi help you figure that one out…

The area of a circle is calculated by multiplying the radius of the circle by π (3.14) and squaring it — the formula looks like a=rπ2. Your friend ordered two medium pizzas which are, on average, 14” wide. That means each pie has a radius of 7” and a surface area of 153.94 in2, making a total of 307.88 in2. If you ordered a large, 18” pie, your pie has a radius of 9”, meaning a surface area of 254.47 in2.

So far, this all makes sense. Your friend obviously has more pizza. But who is getting the best return on their investment i.e. who is paying the least per square inch? 

Well, a large 18” pizza costs, on average, $16, and two medium 14” pizzas cost, on average, $26. If we divide the total surface area by the amount spent, you spent just over 6¢ per square inch, whereas your friend spent just over 8¢ per square inch. That’s a saving of two whole cents.

This might not look like much when broken down. When you consider, however, that to get the same amount of pizza as you, your friend would have to order 1.7 medium pies, totaling $22.10, while you paid just $16, you really start to see the savings. 

So if you’re looking for the best bite for your buck, go for the large pie. Happy Pi Day!

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