Mathematics Goes to the Movies

by Burkard Polster and Marty Ross

Battlefield Earth (2000)

After being put through a learning machine by his alien captors our hero explains some mathematics to his FRIEND:s.

FRIEND:1: This is the masters’ language.
HERO: No, no, this is mathematics, the unifying language of the entire universe. Look, this symbol is called the triangle. If all its sides are equal, then these three angles must also be equal.

FRIEND:2: Equal to what?
HERO: To each other. It is the basic foundation of Euclidean geometry.
FRIEND:3: Seems pretty hard to understand.

Images: Parabola intersecting x-axis in two points. Right next to it the general solution to a quadratic equation. Right next to that a circle.

They seem to be deriving the formula for the derivative of the product of two functions
At the top an integral becomes visible
I= \int_0^\pi \cos ^2 x dx
In the following line evaluated by partial integration
f(x) = \sum_{n=0}^\infty 1/n! d?/dx^n(0)

e^x=\sum_{n=0}^infty x^n/n!
sin?=\sum_{n=0}^\infty (-1)^n etc.