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# Pi Mu Epsilon Seminar – David Cruz-Uribe

## October 21, 2015 @ 12:00 am - 1:00 pm

Free“The bread and butter of first semester calculus are optimization problems.

In this talk we will start with a classic example: given a rectangular sheet of

metal/paper/cardboard, cut equal size squares from each corner so that the

sides can be folded up to make an open top box. Given the dimensions of

the original rectangle, how big should these squares be in order t maximize

the volume of the box?

We will solve this problem, and then consider the following extension:

suppose the rectangle has integer dimensions. Is it possible to get a box

such that its dimensions are rational? The solution of this problem leads us

to number theory and the solution of a Diophantine equation. We will also

talk about a generalization of this calculus problem that leads to another

Diophantine equation. Along the way we will talk about various moments

in the history of mathematics and questions related to teaching calculus.”