The Pizza Dispute: Explained

Written by Isha Chakraborty

Bio

Do you know what happens when a team of math geeks come together to have a debate over warm slices of pepperoni pizzas?

-It becomes a session of finding math in food.

Well that’s exactly what happened at the Cuemath HQ today. Upon ordering a pizza that apparently came in a square box, we decided to wrack our brains with the most challenging math question we could come up with – by looking at a pizza.

As hunger struck our minds, a eureka moment was born and the small task of slicing the pizza, was twisted into a math problem. The team member tasked to slice the pizza was asked to:

Slice it into 8 pieces, so that two people get 4 slices each.

Our friend cut the pizza like this:

Needless to say, he sliced the pizza following all the instructions we asked him to follow.

Are you as confused and wowed as we were?

Let me explain:

The way he cut the entire pizza, is actually a derivation of the Pizza Theorem.

What is the Pizza Theorem?

The Pizza theorem basically states that when a circle is divided taking an internal point (P) and  four cuts are made at biscecting right angles to each other.

The 4 parts, coloured yellow will have the same total area as the four parts, coloured blue.

Then if two people take up alternative pieces of the pizza sliced in this way, they would end up having equal amounts of pizza.

You can see how it worked in the image below:

In this figure, ‘A’ and ‘a’ have equal areas

So the next time someone asks you to cut a pizza normally, leave them confused with this math trick.