Fibonacci number

From Wikipedia, the free encyclopedia
(Redirected from Fibonacci sequence)
Jump to: navigation, search
A Fibonacci spiral created by drawing arcs connecting the opposite corners of squares in the Fibonacci tiling; this one uses squares of sizes 1, 1, 2, 3, 5, 8, 13, 21, and 34; see Golden spiral

The Fibonacci numbers are a pattern of numbers in mathematics named after Leonardo of Pisa, known as Fibonacci. Fibonacci's 1202 book Liber Abaci introduced the pattern to Western European mathematics, although this pattern was already described in Indian mathematics.[1][2]

The first number of the pattern is 0, the second number is 1, and each number after is equal to the two numbers before it added together. For example 0+1=1 and 3+5=8.

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

Fibonacci numbers in nature[change | edit source]

Sunflower head displaying florets in spirals of 34 and 55 around the outside

Fibonacci sequences appear in many places in nature.[3] Some examples of the Fibonacci sequence being used in nature are tree branches, the pattern of leaves on a stem, the fruitlets of a pineapple,[4] the flowering of artichoke, the uncurling of a fern and the arrangement of a pine cone.[5] The Fibonacci numbers are also found in the family tree of honeybees.[6]

References[change | edit source]

  1. Parmanand Singh. "Acharya Hemachandra and the (so called) Fibonacci Numbers". Math. Ed. Siwan, 20(1):28-30, 1986. ISSN 0047-6269
  2. Parmanand Singh,"The So-called Fibonacci numbers in ancient and medieval India." Historia Mathematica 12(3), 229–44, 1985.
  3. S. Douady and Y. Couder (1996). "Phyllotaxis as a Dynamical Self Organizing Process" (PDF). Journal of Theoretical Biology 178 (178): 255–274. doi:10.1006/jtbi.1996.0026. http://www.math.ntnu.no/~jarlet/Douady96.pdf.
  4. Jones, Judy; William Wilson (2006). "Science". An Incomplete Education. Ballantine Books. pp. 544. ISBN 978-0-7394-7582-9.
  5. A. Brousseau (1969). "Fibonacci Statistics in Conifers". Fibonacci Quarterly (7): 525–532.
  6. http://www.cs4fn.org/maths/bee-davinci.php

Other websites[change | edit source]