Re: fibonacci programme

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#330

From: elhadzil
Date: Mon, 19 Apr 1999 00:00

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Mr Robert AH Prins
Please could you tell me how can I put these two sentences
r5     = sqrt(5)
fib(n) = (((1 + r5) ** n - ((1 - r5)) ** n)) / 2 ** n / r5
in the  procedure of my programme?
Robert AH Prins wrote:

> In article <371B0391.E3122AD7@central.ntua.gr>,
>   elhadzil@central.ntua.gr wrote:
> > do you know how can I create non-recursive programme in pascal that will
> > be able to estimate every term of the Fibonacci sequence?
>
> There is a closed form available to give the mathematical exact value, the one
> below! It's based on the fact that
>
> lim fib(n+1)/fib(n) = (sqrt(5) + 1) / 2 (aka the golden ratio)
> n->oo
>
> r5     = sqrt(5)
> fib(n) = (((1 + r5) ** n - ((1 - r5)) ** n)) / 2 ** n / r5
>
> A quick test in Rexx (which, through it's "numeric digits n" feature, offers
> precision only limited to the amount of storage you throw at it) showed that
> the above formula is correct, well at least up to n = 1000. FYI, fib(1000) =
>
> 434665576869374564356885276750406258025646605173717804024817
> 290895365554179490518904038798400792551692959225930803226347
> 752096896232398733224711616429964409065331879382989696499285
> 16003704476137795166849228875
>
> Robert
> --
> Robert AH Prins
> prinsra@williscorroon.com
>
> -----------== Posted via Deja News, The Discussion Network ==----------
> http://www.dejanews.com/       Search, Read, Discuss, or Start Your Own

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From: elhadzil@central.ntua.gr
Subject: Re: fibonacci programme
Date: 1999/04/19
Message-ID: <371B5271.B8EED898@central.ntua.gr>
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