My favorite* online math puzzle contest — Monday Math Madness — has decided to use a problem that I submitted for a previous contest.
CHECK IT OUT HERE!
*It’s really the only one that I know. But that shouldn’t be taken disparagingly; the problems are just hard enough that you have to make one really rewarding conceptual leap, and just easy enough that with enough perseverance you know you can conquer it.
I was watching the TV show MONK this weekend, and the latest episode featured a double rainbow.
I got excited, because last year one of my calculus students did a mini-project on rainbows and I learned what caused double rainbows. One thing I learned while helping this student is that when you have a double rainbow, the colors of the “top” rainbow are reversed.
When I noticed that the colors on this rainbow weren’t reversed, I was like… “hmmm… this is a crucial clue to the mystery.” Turns out, however, that it was just a rainbow badly superimposed by someone who doesn’t know about rainbows.
A double rainbow actually looks like this (notice the reversed colors):
If you care to learn about the mathematics behind rainbows, I suggest reading this very accessible paper.
One thing I didn’t know about rainbows is that they are actually circular; from the ground, we are just privy to part of them. But from air, we could see the whole thing!
Pretty cool, huh.
Continuous Everywhere but Differentiable Nowhere 