Posted December 15, 2011 By Presh Talwalkar. Read about me , or email me .

Rushmore is a rather quirky but interesting movie that came out in 1998.

One of the scenes I particularly enjoyed is about the main character doing a mathematical proof. During class, Max Fischer asks the teacher about a math problem written on the board.

The teacher explains the problem is a joke: it is too hard for anyone to solve, which gets Max even more curious about the problem.

Here’s the clip after the jump.

.

.

"All will be well if you use your mind for your decisions, and mind only your decisions." Since 2007, I have devoted my life to sharing the joy of game theory and mathematics. MindYourDecisions now has over 1,000 free articles with no ads thanks to community support! Help out and get early access to posts with a pledge on Patreon. .

.



Video: Hardest Geometry Problem in the World

Rough transcript of the clip

Teacher: Good, except when the value of the x-coordinate is equal to or less than value of the y-coordinate. Yes, Isaac? Isaac: What about that problem? Teacher: That, oh don’t worry about that problem. Isaac: Why? Teacher: I just put that up as a joke. That’s probably the hardest geometry equation in the world. Isaac: How much extra credit is it worth? Teacher: Well, considering I’ve never seen anyone get it right, including my mentor at MIT…I guess if anyone here could solve that problem, I’d see to it that none of you would ever have to open another math book again for the rest of your lives. Max, are you going to try it? Max: I’m sorry, did someone say my name? Max solves the problem on the board Teacher: You got it. Class cheers for Max Fischer. Max then awakes and we learn this is all a DAYDREAM

The problem that Max solved

If you watch closely, you can see the problem that Max was working on. It is not the hardest geometry in the world, nor it is even that hard of a problem at all. That was just part of Max’s fantasy that he solved an unsolved problem and became revered by his classmates.

The geometry problem may not be easy for a high school student, but it is a relatively easy one in the grand scheme of math. The problem is to derive the area of an ellipse using calculus.

I will give the movie credit because the proof is correct and includes all the necessary steps.

So I’ll conclude this post with a proof of the problem presented in the movie. Here it is: