So y = r^3/3. And if you determine the rate of change in this curve correctly, I think you'll be pleasantly surprised.
I enjoyed the discussion of math in The Simpsons using examples from Futurama. Maybe in the future you can discuss the philosophy of The Simpsons using examples from Futurama.
Since we're talking about the show itself, and not the members of the family, shouldn't the title be "The Simpsons and Its Mathematical Secrets"?
This bugged me then, and it bugs me now after years of math courses. You usually don't commute the 'infinitesimal' dr with 'normal' symbols like r; it's more like a placeholder or even a mnemonic device. I know, I know, I'm missing the point, etc.
Of course, maybe that prep school was so advanced that they were using Robinson's non-standard analysis, and Bart was actually making a stand for constructivism and against the Axiom of Choice required to complete the hyperreals.
Did it all the time in physics and engineering... That's how one solves a diffy q.
I hope you'll be doing a feature on my new book, catchily-titled:
The Simpsons and its clever writing that has nothing to do with mathematics and more to do with the writers' general intelligence and their understanding that there might be some people watching cartoons that aren't idiots.
"Indeed no other series in the history of primetime television has included so many mathematical references."
That's a pretty bold statement. While The Simpsons has the advantage of having been on the air forever, I think The Big Bang Theory includes far more mathematics per episode than The Simpsons ever does.
Anecdotal evidence. 
What? It's a perfectly cromulent strategy.
The door is that way. The one labeled "SHAME."
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