What is the Fibonacci sequence for?

Answer 1

In nature:
The sequence is an example of a recursive sequence. The Fibonacci Sequence defines the curvature of naturally occurring spirals, such as snail shells and even the pattern of seeds in flowering plants.

In computing:
It is an approximate doubling/halfing WITHOUT multiplication/divisoin or even shifts. This have applications in old computer science which remains in use today. eg Fibonacci search in accordance with binary search.

In number theory:
It has many brilliant divisibility patterns. It is periodic mod evry prime number! This has many applications in primality proving of huge numbers. Just notice mod 2:
odd odd even odd ood even ...
(It is provable even by a child.)

Because of its basic definition based only on addition, it may have MANY fundamental applications in all branchs of sciences. The above are only a few of them.

BUT EVEN IF IT HAD NO APPLICATION AT ALL
IT WAS WORTH OF INTEREST BECAUSE OF ITS PURE BEAUTY.

Answer 2

What is it for? I'm not sure what this question means. Here are a couple of possibilities:

1. It contains interesting pairs of numbers. Rectangles with adjacent numbers as their sides come closer to the golden rectangle as you get further in the sequence. The golden rectangle is used in classical and modern architecture to make beautiful buildings (think: the Parthenon) among other things. [Adjacent numbers are also used for paper sizes, e.g., 3x5 cards, 5x8 cards]

2. It appears in nature in a lot of places. Consider pine cones, where if you count the leaves of the cone going one way around you get, say, 13 and 21 in the other -- adjacent Fibonacci numbers.

3. Self-similar spirals (e.g., Nautilus shells) are also related to the Fibonacci sequence.

4. The ratios between adjacent numbers converge on a cool number, the Golden Ratio, which is at the heart of all these natural findings. Interestingly enough, any sequence started with two positive numbers and formed by adding the last two numbers to get the next one also converges on the same ratiio (e.g., 1 3 4 7 11 18 ... etc.) does the same thing eventually.

5. Reproductive success is a Fibonacci sequence as well. Suppose you have a pair of rabbits, and that it takes two reproductive cycles for a pair to become mature enough to reproduce, and that each mature pair can produce one pair per cycle. Then the first and second cycles you have 1 pair, the third cycle you have 2, the third you have 3, the fourth you have 5, 8, 13, etc.

Answer 3

The Fibonacci sequence (1, 1, 2, 3, 5, 8, 13, etc. where each term is the sum of the previous 2) is not often used "for" any particular application. It's just a good study of sequences and ratios.

Though the classic real-life application is that it shows you the number of pairs of rabbits (to use the traditional example) you have after an initial pair starts breeding, assuming that the time it takes a newborn pair to reach breeding age is the same time it takes for a pair to breed after it already bred once. You start off with one pair (1). They breed to make a second pair (2). The original pair is ready to breed again (3). Then the first two pairs breed (5) while the third pair is still growing, etc.

Fibonacci numbers also show up a lot in nature (number of leaves on a branch, curvature of sunflower faces and nautilus shells, etc.) because a lot of things in nature reproduce in this kind of way.

Answer 4

It is based on an old geometry question. Given two points A and B, and the straight line connecting them, cut the line at point C such that the ratio of AC to CB is equal to the ratio of CB to AC.

This is arbritarily letting CB be greater than AC.

If A corresponds to zero, and B corresponds to one, then the point C is located at 0.618033...., which is the one of the numbers that pops out of the fibonacci sequence.

Answer 5

The Fibonacci sequence is a series of numbers where the two numbers' sum give the sum of the next number. It was also used as a code in the book "The Da Vinci Code"

Answer 6

the rectangle with the L/W ratio of two consecutive numbers of this sequence is considered perfect rectangle.
like 1 and 1
1 and 2
2and 3
etc..
and for example the ratio of 1 to 8 is not considered a nice rectangle.

Answer 7

Fibonacci numbers are the sum of previous two numbers. For example:

1,1,2, 3,5,8,13,21,34 etc etc.

Hope this helps.

Answer 8

the drawing toy called a spirograph.
the curvature of a perfect shell.
the sex of a bee.
the golden ration.
fractals.


see here for more info:
http://en.wikipedia.org/wiki/Fibonacci_number
http://images.google.com/images?q=fibonacci+sequence&hl=en&client=safari&rls=en&um=1&sa=X&oi=images&ct=title

Answer 9

The great Hungarian composer Bela Bartok used it in his piece "Music for Strings, Percussion and Celesta."

Math Rules (and sometimes sounds good too!)

Answer 10

it's not for anything, it is just a sequence of numbers, nothing less and nothing more.

they are a set of numbers where the previous two numbers add up to the third number

0,1,1,2,3,5,8.....

they have no significance other than that.