what information do you have on it off the top of your head? please do not give me the sequence (0, 1, 1, 2, 3, 5...) or tell me how the sequence works. do not answer with "i don't know" or anything meaning the same thing either.
2006-11-24 06:27:20 · 9 answers · asked by echo 5 in Science & Mathematics ➔ Mathematics
the odd thing about them is that they naturally occur in nature in many places. just like pi and the golden number. Somehow nature chooses these proportions.
check out these sites. you'll like the info there:
http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat.html#Rabbits
http://www.goldenmeangauge.co.uk/fibonacci.htm
http://library.thinkquest.org/27890/applications5.html
ahem...may i please get the best answer?
2006-11-24 06:33:25 · answer #1 · answered by Mugen 2 · 0⤊ 0⤋
We now know (after lots of hard work) that the only
powers in this sequence are 1,1,8 and 144.
Also, the largest triangular number in this sequence
is 55 and 89 u is the largest Fibonacci number
of the form n² -n + 1.
The fact that the only Fibonacci cubes are 1,1, and 8
is equivalent to the solution of a problem of Gauss
stating that the last imaginary quadratic field
with unique factorisation is Q(sqrt(-163)).
There are some things we don't know about
this sequence.
1).Are there infinitely many primes in the Fibonacci sequence?
2). Let p be a prime number. Is the first Fibonacci
number divisible by p ever divisible by p² ?
It turns out that if Fermat's last theorem holds
in Q(sqrt(5)) then the answer to the last question is "no".
So you can see we find these numbers at
some of the deepest levels of mathematics.
There is a journal called the Fibonacci Quarterly
where you can get much more information on this
sequence and its associated Lucas sequence.
2006-11-24 17:01:35 · answer #2 · answered by steiner1745 7 · 0⤊ 0⤋
Fibonacci numbers are the sequence of numbers (fn) goes to infinity where n=1(assumption as a theoritical part)
fn = (fn-1) + (fn-2)
this series can be used in programming languages like C++(as an example of usage area)
2006-11-24 14:51:42 · answer #3 · answered by cgds_81 1 · 0⤊ 0⤋
I believe the guy is the one who finally got Europeans to dump Roman numerals and use the decimal system.
So F(n)=F(n-1)+F(n-2) defines the Fibonacci sequence. The ratio of consecutive Fibonacci numbers converges to phi=1.618... (the golden ratio).
2006-11-24 14:45:02 · answer #4 · answered by Anonymous · 0⤊ 0⤋
Originally it had to do with a rabbit (not rat) population. It represents the (idealized) growth of the population. The ratio of consequtive numbers tends to the golden ratio as n tends to infinity. It shows up in the arrangement of seed on a sunflower, the leaves along a stalk of a plant, and other places. There are other sequences with interesting properties.
2006-11-24 15:20:34 · answer #5 · answered by modulo_function 7 · 0⤊ 0⤋
Fibonacci poem (the number of syllabi increases in sequence):
I
see
the sky
what a night!
a moon is in sight
can i grab a start tonight?
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Fibonacci in flower petals
Fibonacci in the geometric positioning of squares that traces out a shell.
---
2006-11-24 14:36:43 · answer #6 · answered by Nautilus 2 · 0⤊ 0⤋
The ratio (n+1)/n tends to the golden ratio for large n.
2006-11-24 14:35:13 · answer #7 · answered by 1,1,2,3,3,4, 5,5,6,6,6, 8,8,8,10 6 · 0⤊ 0⤋
Fibonnacci constructed a recurrent relation that enabled him to predict the number of rats after a given period.
2006-11-24 14:29:56 · answer #8 · answered by gjmb1960 7 · 0⤊ 0⤋
He is Italian, and the sequence is found in sunflowers and pineapples and such.
2006-11-24 14:30:04 · answer #9 · answered by nom 1 · 0⤊ 0⤋