I saw this math quiz question today on the theydidthemath subreddit. Pi is obviously slightly bigger than 3.14, but I didn't know whether a higher power is more important than a higher base.
Turns out the answer is "sometimes" - depending on whether the number in question is larger or smaller than Euler's number. Explanation at the link is way over my head. Posted for those who enjoy such things.
I’ve come across the similar question e^pi versus pi^e. This requires knowledge of both constants to several digits, and you can do it without a calculator, but the surprising answer is that both are very close and you need to go to second order. But I’m so long out of practice with math, I can’t remember how I did it 30 years ago.
ReplyDeleteThe most amazing equation in math is that e to the power of (i times pi) plus one is zero. It ties together 5 of the most important mathematical constants into one equation.