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How to Slice an Elliptical Pizza?

Updated: Aug 2

#calculus #mathematics

One day, a famous pizzeria in Chicago is booked by mathematicians for a special day (PI DAY) celebration. As being a Mathematics major, the store owner decides to serve elliptical pizzas to his guests on this day. In this regard, he makes sure that the pizzas served have the shape of an ellipse expressed mathematically as (we assume x and y have arbitrary units)

He bakes the pizzas and serves them uncut. He leaves it to his special guests to figure out how to slice each pizza so that everybody will have a fair share, noting that each pizza will be shared by 8 people. In few minutes, they all figure out how to slice the elliptical pizzas so that each slice would have the same size. Can you also figure it out? If so, can you also find a general solution for any pizza served in an elliptical shape and expressed mathematically as

where a and b are any positive real numbers.


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