A random question for mathematicians regarding i and the Fibonacci sequence.
#2
(08/07/2011, 11:17 PM)robo37 Wrote: What is the Fibonacci root of i, or to put it another way, what is the equation of x when ((1+sqrt 5)/2)^x-((-1)^x/((1+sqrt 5)/2)^x)))/sqrt 5=n?
You did not rationalize your denominator.
The numerical solutions to Fibonacci(x)=i are
x ~ -.42709179162288762 - .22105741463869769 * I
and
x ~ 1.67226840550786450 + 3.2642638352534426 * I.
I do not know of any closed forms for those numbers.
For an inverse to the Fibonacci function, there are no result found in terms of standard mathematical functions.
Please remember to stay hydrated.
ฅ(ミ⚈ ﻌ ⚈ミ)ฅ Sincerely: Catullus /ᐠ_ ꞈ _ᐟ\
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RE: A random question for mathematicians regarding i and the Fibonacci sequence. - by Catullus - 06/27/2022, 12:06 AM

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