Golden_Ratio

Golden Ratio The Fibonacci series after Leonardo of Pisa or, alias Leonardo Fibonacci, born in 1175, whose great book The Liber Abaci, on arithmetic, was a standard work for 200 years and is still considered the best book written on arithmetic. It was the principal means of demonstrating and introducing the enormous advantages of the Hindu Arabic system of numeration over the Roman System. Leonardo's reputation amongst scholars was deservedly great. It was so outstanding that King Frederick II, visiting Pisa in 1225, held a public competition in mathematics to test Leonardo's skill and he was the only one able to answer the questions. |One of the most spectacular examples of the Fibonacci Series in nature is in the head of the sunflower. Scientists have measured the number | |of spirals in the sunflower head. They found, not only one set of short spirals going clockwise from the centre, but also another set of | |longer spirals going anti clockwise, These two beautiful sinuous spirals of the sun flower head reveal the astonishing double connection | |with the Fibonacci series. The New Scientist Dec. 81 featured on its cover a daisy head showing the double spiral. The article then went on | |to discuss the Fibonacci series, showing other examples of the double spirals in nature and comparing them to computer generated double | |spirals. The writers also postulated an explanation for the way plants' growth illustrates the Fibonacci series in the position and spacing | |of the leaves. | |It is the ratio between the perimeter of a circle where the larger part A, is to the smaller part B, as the larger part A is to the whole | |A+B. Our old familiar Golden Proportion premise here seen in yet another guise. The other example of the Golden Proportion is concerned with| |the number of leaves between one leaf and the next one directly overhead and the number of rotations before this position is reached. Some | |trees like Elmwood and basswood, the leaves along a stem seem to occur alternately on two opposite sides and we speak of 1/2 phyllotaxis. In| |the beech and hazel the passage from one leaf to the next is I/3 of a turn. |