Saturday, February 17, 2018

Cool Integral

From KarlMagnus Petersson‏ on Twitter:

In the same way, you can show (I think) that

which is also cool, but not as cool, since "3" is not as cool as "e."

Note: 1/3 < 1/e. This makes sense, since for 0 < x <1, sqrt(x) < cuberoot(x) < fourthroot(x), etc.

Note II: Speaking of e, one of my best friends, a colleague in graduate school (we had the same advisor, and have gotten even closer since), once wrote a paper that contained the number e^e, which I think is about the coolest thing ever published in physics. I wrote about it here for Physics World.

1 comment:

Harold said...

I'm not sure about the 3 not being as cool as e. My fumble fingers frequently hit "e" when I'm trying to type "3", so my left hand apparently thinks they're the same thing.:-)