More magic: Exp(Pi*Sqrt(n))

Exp(Pi*Sqrt(n)) PageThis table lists values of Exp(Pi*Sqrt(n)), for some selected values of n up to 1000. Some of these values are very close to integers. A prize will be awarded to anyone who can either convincingly argue that this is coincidence, or who can explain why this is so in terms

Re: More magic: Exp(Pi*Sqrt(n))

Hal Finney wrote: ``Unfortunately it does not seem likely that an explanation suitable for a college senior is available, unless he is willing to educate himself for several months on higher mathematics.´´ I suspect that Roy Williams Clickery included this condition so that he always has an

Re: More magic: Exp(Pi*Sqrt(n))

Hi Saibal, Very interesting! I didn't know that one. The chances that this is just a coincidence seems very low, but 1) it should be verified whether this propertyholds to much larger numbers, which should be no problem with nowadays computers, 2) Whether it holds to other bases, e.g.