How are Math and Pizza related: The Pizza Theorem

How are Math and Pizza related: The Pizza Theorem

The Pizza Theorem is one of the most favourite theorems in maths. It is named after a traditional pizza slicing technique and states the equality of two areas when a person divides a flat disk from a particular point. It was originally proposed by Upton as a challenge problem. Michael Goldberg published the solution of this problem.

Example:

Tessa and Karen are good friends and they decided to have study session together. Both of them are determined to make it into Maths Olympiad Final, hence they decided to study together. They ordered pizza and Karen volunteered to cut the Pizza into slices. Tessa gave her the following instructions to cut the pizza:

• Cut it into 8 pieces so it can be divide equally among the two of them.
• Make 4 slices in the centre.
• The cut of the pizza will be in Horizontal and vertical (+) Lines first.
• And then two more cuts at 45 degree angles (x). Like this.

• Karen enters the kitchen but gets back with the pizza cut in the following way.

• Do you think that both of them will get the equal share of the pizza?

Yes, they will. This is the manifestation of the pizza theorem. According to it, if the disk is divided into 8, 12, 16.....sections by making cuts at equal angles from a particular point, then the sum of the areas of alternate pieces will be equal.

So as long as both of them take the alternate pieces, they can have their fare share of pizza and Karen can beam with proud due the amount of mathematical knowledge she contains.

So, now whenever you go out to have a pizza, keep this pizza theorem in mind and ask the pizza person to not to cut the pizza for you. Instead, ask a knife from him and let your inner mathematician play some magic on the pizza.