Let's suppose two people want to share the pizza “**artistically**”: one slice each, taking turns.

If the pizza is divided by making three cuts across its diameter, at least one of which goes through the centre, the two will eat an equal amount of pizza (as shown in the picture to the left).

But what happens if the person cutting the pizza does not go through the centre?

If an **even number of cuts is made** (for example, 4) they will get the same amount of pizza. We know this thanks to a certain **Mr Upton** who in 1968 stated that “the sum of the areas of odd segments is equal to the sum of the areas of even segments.”

But what happens if we cut through the pizza 3, 7, 11, or 15 times, or 5, 9, 13, or 17 times?

Everything **gets complicated**: in the first scenario, the person who gets the slice with the centre of the pizza in it gets more, in the second, the person who gets the slice not containing the centre gets more.

The last two images show how our two scientists used sub segments to explain the solution, and someone has even come up with a **hypothesis** on the distribution of toppings.

But then we had an idea: couldn't the two people eat a **pizza each**?