26 Jul
2008
26 Jul
'08
9:42 p.m.
<<
(Yes, Henry, ln phi = asinh 1/2 .-)
I'm not even managing to clamber in on the ground floor here. _Why_ is it true?
Lessee: sinh(x) := (e^x - e^-x)/2, so one branch (the usual one) of the inverse function is asinh(y) = ln(x + sqrt(x^2 + 1). So asinh(1/2) = ln( 1/2 + sqrt(5/4) ) = ln(phi). --Dan _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele