Who created the fibonacci sequence?

Question

2. What is the fibonacci sequence?

3.How is the fibonacci sequence produced?

4.How does golden ratio relate to the fibonacci sequence?

5.Name two different ways the fibonacci sequence is found in nature
If u noe the answer 2 any of these ?'s can u please answer them

Answer 1

Leonardo of Pisa known as Filius Bonacci (son of Bonacci). His father was an Italian merchant who traded in North Africa which is where the boy grew up and became exposed to Arabic mathematics. It was through contacts like this that Arabic and Indian mathematical ideas entered mainstream European culture,

He was led to the sequence by considering the problem of the growth of a rabbit population and published his findings in his influential book Liber Abaci (Book of the Abacus) in 1202,

He considered the growth of an idealised (biologically unrealistic) rabbit population, assuming that:

(a) in the first month there is just one newly-born pair,
(b) new-born pairs become fertile from their second month on
(c) each month every fertile pair begets a new pair, and
(d) the rabbits never die

He argued thus: Let the population at month n be F(n). At this time, only rabbits who were alive at month n−2 are fertile and produce offspring, so F(n−2) pairs are added to the current population of F(n−1). Thus the total is F(n) = F(n−1) + F(n−2).

(3) And that is the generating rule for the Fibonacci sequence. Each term is the sum of the previous two terms.

(2) Conventionally it begins with 0, 1 and continues 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657 ...

(4) The Golden Ratio, Phi 1.618033989 .., and its inverse phi (0.618033989 ...) are both produced by considering how the ratios of successive terms of the Fibonacci sequence converge (from either side) on the Golden Ratio.

3/5 = 0.6
5/8 = 0.625
8/13 = 0.61538 ...
13/21 = 0.61904 ...
21/34 = 0.61765 ...
34/55 = 0.61818 ...
55/89 = 0.61797 ...
89/144 = 0.61805 ...

10946/17711 = 0.618033990 ...
17711/28657 = 0.618033988 ...

AND SIMILARLY

5/3 = 1.666 ...
8/5 = 1.6
13/8 = 1.625
21/13 = 1.61538 ...

17711/10946 = 1.618033985 ...
28657/17711 = 1.618033990 ...

(5) The two best-known examples of Fibonacci numbers appearing in nature are in the arrangements of sunflower heads and pine cones.

Answer 2

Who Invented The Fibonacci Sequence

Answer 3

fibonacci sequence made by a genius dude NAMED fibonacci

the fibonacci sequence is made by adding the number before it
start out with
1
1+0=1
1+1=2
2+1=3
3+2=5
5+3=8
8+5=13
and so on so you get
11235813 :]

Answer 4

1) The Fibonacci numbers are named after Leonardo of Pisa, known as Fibonacci, although they had been described earlier in India

2&3) In mathematics, the Fibonacci numbers form a sequence defined recursively - after two starting values,each number is the sum of the two preceding numbers.

4) The golden ratio (phi), is defined as the ratio that results when a line is divided so that the whole line has the same ratio to the larger segment as the larger segment has to the smaller segment. Expressed mathematically, normalising the larger part to unit length, it is the positive solution of the equation.

5) Fibonacci sequences appear in biological settings, such as branching in trees, the curve of waves, the fruitlets of a pineapple, and the arrangement of a pine cone. Przemyslaw Prusinkiewicz advanced the idea that these can be in part understood as the expression of certain algebraic constraints on free groups, specifically as certain Lindenmayer grammars.

Answer 5

Fibonacci is one of the greatest mathematicians who is almost unknown to the general public. In addition to the Fibonacci sequence he is also credited with formulating the mathematics that allow bankers, brokers and financiers to do present value calculations, a cornerstone of determining whether an investment is worthwhile. The Fibonacci sequence describes series of fractions found in the natural world. These sequences occur naturally in the spacing of leaves and branches to maximize light penetration, in the normal proportions of arms and legs to trunk length in humans and in the spacing of spirals in certain molusks. The Fibonnaci sequence is directly applicable to Art, Architecture Botany and Zoological sciences because these naturally occurring numbers help describe the correct function and optimum physical structure of living things and structures. Leonardo DaVinci and the builders of the pyramids are among those who have used the so-called "golden proportions and Fibonnaci sequences in their work.

Answer 6

1. Fibonacci, in 1202, first wrote of the sequence.

2. 0,1,1,2,3,5,8,13,....

3. each number in the sequence is the sum of the previous 2: a[n] = a[n-1]+a[n-2]

4. as you proceed down the sequence, the ratio of consecutive numbers (3/2, 5/3, 8/5, ...) approaches the golden ratio, (1 + √5)/2.

5. the sequence is found in seashell spirals, pinecones and pineapples, in the population of reproducing rabbits (Fibonacci's original context), in the branching of plants, in Pascal's Triangle, and endlessly on.

Answer 7

The fibonacci sequence was actually not invented by Leonardo Fibonacci. Leonardo Pisano Bigollo (nickname, Fibonacci) only referenced the sequence in his book "Liber Abaci". It was only named after him because this was the first time the sequence had been introduced in western mathematics.

Answer 8

1) Fibonacci created the Fibinacci series.
2) 1,1,2,3,5,8,13,21,34,55,89.....
3) Each term is the sum of the 2 previous terms.
4) The ratio of any 2 adjacent terms approaches the golden ratio as n approaches infinity. It gets fery close very fast.
5) the golden ration is seen in a lot of places.

Answer 9

3. it's made of a recursive function
each of its sentence are made of adding two sentences just before it
For example the sequence is : 1,1,2,3,5,8,13,...
after 13 we have (13+8)=21

4. The golden ratio is the ratio of two of its sentences which are came just after each other
for example the sequence is: 1,1,2,3,5,8,13...

Golden ratio~13/8 or 8/5 or 5/3 ...

Answer 10

Here you go:

http://en.wikipedia.org/wiki/Fibonacci

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