Napiers bones, the slide rule… they work because addition and substraction of logs is multiplication and division of the subjects …
as in X/Y = z ^ ( log z X - log z Y ) … for any z
That’s nothing. Not when you consider the fact that 6π[sup]5[/sup] = proton to electron mass ratio
My favorite:
pi^4 + pi^5 = e^6
Never saw that before. Excellent. Thanks!
The fact that pi would show up in something spherical is simply geometry. Nothing surprising at all.
Pretty sure that’s an approximation, not a perfect equation.
[Quote=Hellestal]
Originally Posted by standingwave
My favorite:
pi^4 + pi^5 = e^6
Pretty sure that’s an approximation, not a perfect equation.
[/quote]
Whoosh. And whoosh. Unless I’m being whooshed (twice).
True. A very close approximation to be sure, like the second xkcd toon posted above. Close enough to drive people nuts.
It would have been less misleading to write π[sup]4[/sup] + π[sup]5[/sup] = e[sup]5.999999956…[/sup]Wikipedia has a nice page of such close approximations, but I can’t find that page right now. Is this one on it? Anyway, it does seem remarkable!
Another famous approximation is e[sup]π √163[/sup] = 262537412640768743.999999999999…
This is related to some number theory; how about π[sup]4[/sup] + π[sup]5[/sup] = e[sup]5.999999956…[/sup] ?
Oops. I should have added a few more digits
e[sup]π √163[/sup] = 262537412640768743.999999999999250…
to emphasize that the infamous .99999999999999999999999999999… (which is an integer) was not intended. 