Here’s a cute problem I heard from Moor Xu:

Let . has exactly three critical points. Find the parabola that passes through these critical points.

I’ve been doing a daily problem of the day for my physics camp students. Questions and answers are posted here the day after we give them to the students. I haven’t been copying them over to this blog because many are repeats, and none are original. They might still be entertaining if you’re in to that sort of thing.

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This entry was posted on July 28, 2011 at 3:19 am and is filed under problems and solutions. You can follow any responses to this entry through the RSS 2.0 feed.
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July 28, 2011 at 7:49 am

This is pretty cool. Any sane person would probably take the derivative and get .

Then I was thinking, okay, I definitely can’t solve that. But oh, I can consider in the polynomial ring with one variable modulo the ideal generated by , and pick a quadratic in the equivalence class.

Namely, if is a critical point, it would satisfy , and so any multiple of that would be satisfied. In particular, . Using that to simplify gives , and thus should work.

I don’t know if I did the calculations right, but I think the idea should be.

July 30, 2011 at 2:13 pm

What is physics camp?

September 17, 2011 at 8:40 am

http://epgy.stanford.edu/summer/