Fibonacci Numbers

Pronunciation: /ˌfib oʊˈnɑ tʃi ˈnʌmb ərz/ ?

Fibonacci numbers
NumberCalculation
0Defined as 0
1Defined as 1
10 + 1 = 1
21 + 1 = 2
31 + 2 = 3
52 + 3 = 5
83 + 5 = 8
135 + 8 = 13
218 + 13 = 21
3413 + 21 = 34
5521 + 34 = 55
...
Table 1: Fibonacci numbers

Fibonacci numbers are a sequence of numbers starting with 0, 1. After the first two numbers, each number in the sequence is calculated by adding the two previous numbers. See table 1.

Fibonacci numbers were first described in (asiatic) Indian mathematics. However, they are named after Leonardo de Pisa [c. 1170 – c. 1250] who introduced them to the western world in his book Liber Abaci (Book of Calculation). Leonardo de Pisa is also know as Fibonacci (son of Bonacci).

The Fibonacci numbers have some interesting properties. Figure 1 shows a sequence of squares. The length of the side each square is one of the Fibonacci numbers. These squares form a rectangle that grows with each Fibonacci number.

Squares whose sides are the length of the next Fibonacci number.
Figure 1: Fibonacci Squares

References

  1. Fibonacci numbers. merriam-webster.com. Encyclopedia Britannica. (Accessed: 2009-03-12). http://www.merriam-webster.com/dictionary/fibonacci numbers.
  2. Laurence Sigler. Fibonacci's Liber Abaci. Springer, November 11, 2003.
  3. lfred S. Posamentier and Ingmar Lehmann. The Fabulous Fibonacci Numbers. Prometheus Books, June 21, 2007.
  4. Nicolai N. Vorobiev and M. Martin. Fibonacci Numbers. Birkhäuser Basel, January 31, 2003.

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Cite this article as:


Fibonacci Numbers. 2010-02-04. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/f/fibonaccinumbers.html.

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Revision History


2010-02-04: Added "References" (McAdams, David.)
2009-02-10: Clarified 'Indian mathematics' as 'Asiatic Indian mathematics' (McAdams, David.)
2008-12-29: Added link to http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Fibonacci.html (McAdams, David.)
2007-07-12: Initial version (McAdams, David.)

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