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Fibonacci Numbers in Nature. Getting the Maths Right in Flowers.

Fibonacci Numbers? Leonardo Fibonacci, the man responsible for for re-discovering the amazing Fibonacci Numbers, was an Italian mathematician who was born somewhere around 1170. In 1202 he published a book called 'Liber Abaci' (Book of Calculation).

He was also the man who gave us our decimal numbering system. He figured out that it was far more efficient than the Roman Numeral System, which did not even contain a '0' - zero.

Helianthus whorl

Helianthus (Sunflower).

Tournesol (4)

Another Sunflower.

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, _

(Each number is the sum of the previous two numbers).

Fibonacci numbers

Fibonacci Numbers from one Maths point of view.


Fibonacci and the Golden Ratio.

Mathematicians can explain it so well, but Fibonacci numbers can be seen everywhere. If you can see a pattern in the sunflowers and finish the number sequence above, then you're well on the way to understanding them. That's all we need. Just to observe and appreciate the intricacy and realize that there's a plan, a map, a 'rule' even, that nature adheres to, is enough.

Fibonacci had a specific problem: "A certain man put a pair of rabbits in a place surrounded on all sides by a wall. How many pairs of rabbits can be produced from that pair in a year if it is supposed that every month each pair begets a new pair, which from the second month on becomes productive?"

He soon worked it out using a special sequence of numbers and also what is called the 'Golden Ratio' which he found in an ancient Sanskrit manuscript and this sequence answered his problem. The sequence is 1, 1, 2, 3, 5,8,13, etc, where each number is the sum of the two preceding numbers.

Basically, for example, if there were no Fibonacci Numbers, then a flower would show up as a straight line! In Nature, a flower needs something to tell it when to turn, rather than go on forever. So this amazing sequence does just that. (In liason with the DNA molecules of course).

Pflanze-Sonnenblume1-Asio (cropped)

Fibonacci spirals of Sunflower seed head.

Aloe polyphylla spiral

Aloe polyphylla spiral.

Red Cabbage cross section showing spirals

Even the humble Cabbage.

As it was soon discovered from his research - and that of later scholars, this 'Golden Ratio' shows up in Nature as a whole (but not in everything), proving so many different things to be ordered in this manner. Rabbits of course, flowers, cells, pine cones, DNA, the Solar System, the leaf node positions on a plant, the Nautilus shell, the Ammonite (the Fibonacci Fossil), even the universe itself; an endless list. 

This site deals with the Rabbits and other 'things'.

Even just looking at the pictures on the above sites gives us enough to understand and ponder.

Home. Return from Fibonacci Numbers to Parts of a Flower.

"To see a world in a grain of sand,

And a heaven in a wild flower,

Hold infinity in the palm of your hand,

And eternity in an hour".

William Blake.