The Fibonacci Series
Italian mathematician, Leonardo Fibonacci, in one of his books discussed the following problem....... "A certain man put a pair of rabbits in a place surrounded on all sides by a wall. If it is supposed that each pair gives birth to another pair every month, beginning in its second month, how many rabbits will be there in an year ?"
The answer : One pair will be born in the second month, one pair in the third, two in the fourth, three in the fifth, five in the sixth and so on, in a series which occurs in nature with a mathematical precision of an astonishingly high order.
When written out the Fibonacci series runs........ 0,1,1,2,3,5,8,13,21,34. . . . . . . . Each number after 1 being equal to the sum of its two predecessors. So the number of pairs of rabbits in each month equals to the sum of the pairs born in the preceding two months. In an year they will be 233 pairs
This series is very often found in nature. The petal like florets in the head of a sunflower, for example, form two overlapping spirals, one clockwise and the other counter-clockwise. There are 21 florets in the clockwise spiral and 34 in counter-clockwise spiral........ and both 21 and 34 are found in the Fibonacci series.
Spirals can also be seen in the structure of pinecones. Usually there are 8 clockwise spirals and 5 counter-clockwise ones. On the outside of a pineapple there are normally 8 spirals in one direction and 13 in the other!
The way in which shoots are arranged on plant stems also seems to be in accordance with the Fibonacci series. Compared with the one beneath it, each shoot is offset so that it doesn't shade its neighbour. The angle between one shoot and the next, expressed as a fraction of the circumference of the stem, is generally found to be given by two numbers from the Fibonacci series........... 1/2 for grasses, 1/3 for beech and hazel, 2/5 for oak and fruit trees, 3/8 for rose and poplar, 5/13 for willows , almond trees and leeks.
Wait........ there's more. As the Fibonacci series progresses the ratio of each number to its predecessor is close to 1.62:1. Since the time of ancient Greeks, this has been known as golden ratio and regarded as being aesthetically pleasing. The ratio can be seen in the proportions of many classical buildings. Even architects as Le Corbusier have incorporated the proportions based on the Fibonacci series in modern cities like Chandigarh. In this way art imitates life, and the golden ratio is used the world over by counless architects and artists to whom Fibonacci's rabbits mean nothing
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