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| Top Level > Animals & Nature |
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Quotes |
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"There is however, a true music of nature - the song of the birds, the whisper of leaves, the ripple of waters upon a sandy shore, the wail of wind or sea." - John Lubbock (1834-1913) Politician naturalist & archaeologist. |
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Facts |
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What is a Fibonacci number and how does it relate to nature?
A Fibonacci number is any number in the following arithmetical sequence invented by Italian mathematician Leonardo Fibonacci (1170 - 1240) The numbers are known as the Fibonacci series. Each number in the series which begins 1,1,2,3,5,8,13,21,34 - is, after the first two figures merely the sum of the previous two numbers (1+1 =2, 2+1=3, 3+2 =5, 5+3=8 etc.) Yet this simple sequence has other mathematical relationships and with the world of nature.
If, for instance, you examine any plant that sends out individual leaves from a single stem, find two leaves directly above each other, and then count one of the pair plus all the intervening leaves, the total will always be a Fibonacci number. Similarly if you count the clockwise spirals of seeds on the head of a sunflower, and the counterclockwise spirals on the same flower, the figures will not only be a Fibonacci numbers but consecutive Fibonacci numbers. The largest such numbers on record of sunflower spirals are 144 and 233.
Perhaps even more curious is the ratio of successive terms in the Fibonacci series. For instance the numbers 144 and 233 are in the ratio to 1 to 1.61805; and 233 and the following Fibonacci number, 377 are in the ratio 1 to 1.6180257. Successive ratios in the series converge ever more closely on the number 1.618033989 - which is the golden ratio known to mathematicians since at least 300 BC. |
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