Sunday, May 25, 2008

Fibonacci number

Fibonacci number

A tiling with squares whose sides are successive Fibonacci numbers in length

In mathematics, the Fibonacci numbers are a sequence of numbers named after Leonardo of Pisa, known as Fibonacci. Fibonacci's 1202 book Liber Abaci introduced the sequence to Western European mathematics, although the sequence had been previously described in Indian mathematics.

A tiling with squares whose sides are successive Fibonacci numbers in length

A tiling with squares whose sides are successive Fibonacci numbers in length

The first number of the sequence is 0, the second number is 1, and each subsequent number is equal to the sum of the previous two numbers of the sequence itself. In mathematical terms, it is defined by the following recurrence relation:

That is, after two starting values, each number is the sum of the two preceding numbers. The first Fibonacci numbers (sequence A000045 in OEIS), also denoted as Fn, for n=0,1,2, … ,20 are:

F0

F1

F2

F3

F4

F5

F6

F7

F8

F9

F10

F11

F12

F13

F14

F15

F16

F17

F18

F19

F20

0

1

1

2

3

5

8

13

21

34

55

89

144

233

377

610

987

1597

2584

4181

6765


posted by: Andy Says   Jump to Message Thread on HM Google Group...

0 comments: