4

The other day I ran across a very nice video from Numberphile in YouTube, which proves that the following formula is approximate to $e$ by $18457734525360901453873570$ digits, which is pretty amazing.

\begin{align*} \left(1+9^{-4^{7\cdot 6}}\right)^{3^{2^{85}}} \approx e \end{align*}

I got excited about this, and thought about writing an article for my school magazine. Does anyone know any good references (articles, books, videos) that have interesting facts and curiosities concerning pandigital numbers and formulas?

Maybe something like the topic addressed in this this question is interesting as well, computing algorithms to find pandigital formulas...

Thanks in advance,

Miguel

migueldva
  • 404
  • 6
    I really don't know what is so amazing here (this seems to be funny only to pre-school children). Simply, $\lim_{n\to\infty}\left(1+\frac1n\right)^n=e$ and what this expression does is just using the digits in such way to make the $n$ as big as possible. –  Nov 24 '17 at 02:57
  • 9
    @ThePirateBay something doesn't have to be complicated or extravagant to be beautiful. As you claim, this may be only funny or nice to "pre-school children", but I'm glad I'm still amazed by simple things, which is something I believe gets us interested into math in the first place . Anyway, you have your right to your obnoxious comment. – migueldva Nov 24 '17 at 03:07
  • I'm very sorry if you find my comment obnoxious. –  Nov 24 '17 at 03:09
  • @ThePirateBay By the way where should i evaluate the limit for a $2\cdot 10^{25}$ precision?. Excel?, Matlab?, Mathematica? – Brethlosze Nov 24 '17 at 05:41
  • @hyprfrcb. Neither of them. Use C++. Write a BigInt library and evaluate the number. –  Nov 24 '17 at 09:57
  • 2
    Possible duplicate of pandigital rational approximations to the golden ratio and the base of the natural logarithm – Raskolnikov Nov 26 '17 at 18:18
  • 2
    @ThePirateBay Way to double-down with the fake apology. – Viktor Vaughn Nov 26 '17 at 20:33
  • I suspect that finding pandigital representations is similar to the problem solved by the inverse symbolic calculator. However, I don't know how that thing works. (Magic?) – Milo Brandt Nov 26 '17 at 20:36
  • 1
    @Quasicoherent. "Way to double-down with the fake apology." - I'm just trying to be nice. It doesn't mean that I find this question interesting, I just apologized if I was too aggresive. That's all. –  Nov 26 '17 at 21:59
  • 4
    @ThePirateBay You didn't apologize for anything. You said that you were sorry that they found your comment obnoxious. If you wanted to give a real apology, you could apologize for leaving an obnoxious comment and using belittling language ("only to pre-school children"), as is expressly forbidden in the guidelines you linked. Yours was a classic "ifpology": you expressed no remorse for your actions. – Viktor Vaughn Nov 26 '17 at 22:37

0 Answers0