GOLDEN RATIO NUMBERS SERIES

Phi is usually rounded off to 1.618 and this is a common number throughout nature. The golden ratio is a special number found by dividing a line into two parts so that the longer part divided by the smaller part is also equal to the whole length divided by the longer part.Īs with pi (the ratio of the circumference of a circle to its diameter), the digits go on and on, theoretically into infinity. Interesting as you go to higher numbers in the sequence, the ratio of two successive numbers approaches the golden ratio. It just looks best when using these numbers. If you count the rows of petals on my Angel Rose you can see the first row has 2, then 3, then 5, then 8. It just always looks more aesthetically pleasing. Leonardo has been called ‘Fibonacci’ ever since.Now I have developed the rose further for larger roses and the rows of petals always fall into these numbers below.

In the 1870s, the French mathematician Edouard Lucas assigned the name “Fibonacci” to the number sequence that is the solution to the famous “Rabbit Problem” in Leonardo Pisano’s book, Liber Abaci (1228). Remarkably, it was yet another hundred years before Leonardo would once again be acknowledged academically and given the credit to which he is due. This was in 1797, over five centuries after Leonardo had died. This remarkable endorsement did not resuscitate Leonardo’s legacy, however, and his name was once more quickly forgotten.įor another three hundred years historical anonymity obscured the achievements of Leonardo Pisano until one day, by slim chance, a mathematics historian named Pietro Cossali (1748-1815) noticed Pacioli’s reference and began researching Leonardo’s works on his own. No biographies were written about him or his many accomplishments in math even mathematicians did not know who he was until 1494, when a respected Italian mathematician named Luca Pacioli (1447-1517) briefly mentioned Leonardo’s name in the introduction to a book of his own, Summa, giving credit to him for most of the ideas presented in his own book. Master Leonardo Pisano (not to be confused with Leonardo da Vinci) was a beloved public servant of Pisa, Italy, who achieved fame during his lifetime (ca.1170 – ca.1250) but was forgotten within two hundred years. The formula for Golden Ratio is: F(n) = (x^n – (1-x)^n)/(x – (1-x)) where x = (1+sqrt 5)/2 ~ 1.618 The Golden Ratio represents a fundamental mathematical structure which appears prevalent – some say ubiquitous – throughout Nature, especially in organisms in the botanical and zoological kingdoms. Phi and phi are also known as the Golden Number and the Golden Section. CB/AC – is the same as the ratio of the larger part, AC, to the whole line AB. In the image below, the ratio of the smaller part of a line (CB), to the larger part (AC) – i.e. Phi (Φ), 1.61803 39887…, is also the number derived when you divide a line in mean and extreme ratio, then divide the whole line by the largest mean section its inverse is phi (φ), 0.61803 39887…, obtained when dividing the extreme (smaller) portion of a line by the (larger) mean. After these first ten ratios, the quotients draw ever closer to Phi and appear to converge upon it, but never quite reach it because it is an irrational number.

GOLDEN RATIO NUMBERS SERIES

When a number in the Fibonacci series is divided by the number preceding it, the quotients themselves become a series that follows a fascinating pattern: 1/1 = 1, 2/1 = 2, 3/2 = 1.5, 5/3 = 1.666…, 8/5 = 1.6, 13/8 = 1.625, 21/13 = 1.61538, 34/21 = 1.619, 55/34 = 1.6176…, and 89/55 = 1.618… The first ten ratios approach the numerical value 1.618034… which is called the “Golden Ratio” or the “Golden Number,” represented by the Greek letter Phi (Φ, φ). Related to the Fibonacci sequence is another famous mathematic term: the Golden Ratio.

Golden ratio numbers