# Which gives you more Pizza, 1 Large or 2 Medium?

It’s Friday night. My friends and I gather for game night and plan to order pizzas. The same debate comes up. Should it be two medium pizzas or one large?

Mathematics consists of proving the most obvious thing in the least obvious way.

George Polya, Hungarian Mathematician

People often make the mistake of ordering two medium pizzas instead of one large and spend more money than they should. Not because they have extra money, no. I am talking about regular people ordering regular pizza on a typical Friday night. They would take all measures to save money—from applying discount coupons to ordering more than needed for reaching the minimum cart value for that additional discount.

The same people, however, falter when it comes to basic math.

The logic is simple. Though I have recently heard of square pizzas, the pizzas we mostly order are circular. We know that the area of a circle is π r², r being the radius of the circle, and π (≈3.14) being a constant. The size mentioned of the pizza is its diameter, i.e. double the radius.

Now, let’s do some math!

Area of two small 8 inch pizzas (with r=4 inches) = 2 X π r² = 2 X π 4² = 32π inch²

Area of one large 12 inch pizza (with r=6 inches)= π r² = π 6² = 36π inch²

**More area = More pizza to EAT!**

Also, the cost of two 8 inch pizzas is almost always more than one 12 inch pizza.

So we end up spending more on less food! The reason why pizza restaurants give you irresistible offers like:

How do Pizza companies sell their menu? They always advertise for 2 pizzas.

The advertisements ensure that our inherent thought for more pizza is 2 regular (read small) ones.

I don't blame the pizza companies entirely. Like all businesses, they are trying to make more money. However, with simple math, we can get the best value for money.

Ordering 2 different pizzas make sense if we specifically want different toppings. However, if all we want is more pizza to eat, it’s always better to order a larger pizza to get more in our pie!