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I know of the Fibonacci Number as the Golden Ratio. It has an interesting
relationship:
1
----------- = 1 + GoldenRatio
GoldenRatio
or
1
---------- = 1.61803...
0.61803...
In English:
The reciprocal of the number is equal to one plus the number.
Is that the off-topic buzzer I hear?
ttfn
David Pearson
Nortel, Public Carrier Networks
Ottawa, Ontario, Canada
dpearson@no*.ca*
In message "Fibonacci series", you write:
> Actually, the big thing is not as much a "Fibonnacci series" as
> Fibonacci's number (correct spelling).
>
> Fibonacci's number:
> Start with ANY two numbers (typically 1 and 1, not 0 and 1, according to
> Webster). The next number in the series is the sum of the two last
> numbers:
> N(1) = 1
> N(2) = 1
> N(3) = N(1) + N(2) = 2
> N(4) = N(2) + N(3) = 3
> ...
> N(m) = N(m-2) + N(m-1)
> ...
>
> The BIG thing:
> The interesting particularity of this series is that the ratio of N(m-1)
> / N(m) converges very fast towards the number 0.618..., regardless of
> the two original numbers. Calculating Fibonacci's number (number towards
> which the ratio converges) to a desired precision is often the first
> computer program people write.
>
> Check-out the following two series, using different starting points.
> They both converge extremely fast.
>
> Index Number Ratio Index Number Ratio
> 1 1 1 13
> 2 1 1.00000 2 15 0.86667
> 3 2 0.50000 3 28 0.53571
> 4 3 0.66667 4 43 0.65116
> 5 5 0.60000 5 71 0.60563
> 6 8 0.62500 6 114 0.62281
> 7 13 0.61538 7 185 0.61622
> 8 21 0.61905 8 299 0.61873
> 9 34 0.61765 9 484 0.61777
> 10 55 0.61818 10 783 0.61814
>
> Even more interesting, 0.618 or so is an appealing number to humans.
> Notice how everything you look at is rectangular, not square. Of course,
> the length of the short side divided by the length of the long side on
> most rectangles does not always give 0.618, but the closer it is, the
> most appealing the shape is (so my High School math teacher says).
>
> Hope this answers your questions,
> PierreC
> >----------
> >From: A.Appleyard[SMTP:A.APPLEYARD@fs*.mt*.um*.ac*.uk*]
> >Sent: Tuesday, September 24, 1996 2:29 AM
> >To: Techdiver@terra.net
> >Subject: Fibonacci series
> >
> > Scott Leimroth <anscott@ns*.co*.au*> wrote (Subject: Deco):-
> >> Fibonnacci sequence.????? Can somebody please explain what this is to this
> >> poor fool. Thanks in advance, Scott
> >
> >I think it is the series of integers 0 1 1 2 3 5 8 13 21 34 etc, where each
> >element is the sum of the two previous elements.
> >--
> >Send mail for the `techdiver' mailing list to `techdiver@terra.net'.
> >Send subscription/archive requests to `techdiver-request@terra.net'.
> >
> --
> Send mail for the `techdiver' mailing list to `techdiver@terra.net'.
> Send subscription/archive requests to `techdiver-request@terra.net'.
>
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