#Fibonacci spiral series

Read on and find out all about the history and importance of 'nature's secret code.' The Fibonacci Sequence Explained Throughout History & NatureĪs we mentioned above, the Fibonacci Sequence can be found in many natural elements, and it has been used throughout history in renowned music compositions, works of art, and building structures. This mysterious yet perfect sequence can be found in different natural phenomena, from a seashell to a whole galaxy. Each digit in the Fibonacci sequence results from the sum of the previous two numbers, and it can be repeated until infinity. Its relevance can be seen in its visual effect that describes a growth pattern in nature. The Fibonacci Sequence was discovered in 1202 by Leonardo of Pisa, although it was later proved that ancient Indian mathematicians already knew about it. This article talks about this famous symbol through history and explains its importance.

#Fibonacci spiral series

Do you suppose.INSIDE: The Fibonacci Sequence is a series of numbers in which each digit comes from the sum of the two previous ones. Returning to mankind's application of the Golden Ratio: While I was stationed in Europe many years ago, I learned to appreciate the fact that converting between miles and kilometers was simplified because they were related to each other by the reciprocal factors 1.6 and 0.6. Even though the curvature is slight, any dentist knows that he must pull a tooth in the right direction. Most of nature's horns, claws and teeth (including your own) exhibit a Fibonacci spiral. A pine cone has two spirals of 5 and 8 arms, and a pineapple has spirals of 5, 8 and 13-all Fibonacci numbers (I must confess that, although I was finally able to identify the spirals on a pineapple in the supermarket, I got hopelessly lost on a white spruce cone).īut these are only a sampling. These are two adjacent Fibonacci numbers. The individual florets in the head of a daisy grow in two spirals extending out from the center. Most are so commonplace that we never take notice of them. Nature finds a myriad of ways to put these numbers to work. Eventually,the quotients become precisely the numbers in the Golden Ratio and remain that way. (and 3 divided by 2 equals 1.5), but 21 divided by 34 equals 0.6176.

For example, 2 divided by 3 equals 0.6666. If you take the quotient of any two numbers in the Fibonacci series, you will find that the further you go up the line, the closer the value converges on the 'perfect' ratio. It is permissible at this point to ask what all this has to do with the Golden Ratio, and therein lies the beauty. This deceptively simple-looking series is obtained merely by sequentially adding numbers which are the sum of the preceding two. Fibonacci reasoned that, if the rabbits reached maturity two months after birth and produced an additional pair every month thereafter, the total population of rabbit pairs would increase monthly according to the series 1, 2, 3, 5, 8, 13, 21, 34. The 'Fi' part of his name meant 'son of.' The Bonacci part meant 'simpleton.'Īlthough history does not record the mental acuity of Fibonacci's father, it does relate that the boy took an early interest in the number of rabbits that could be raised in a year if one began with a single pair. Historically, credit for recognition of the peculiar mathematical properties of this ratio must go to a 13th century Italian known as Fibonacci. The earlier column told only half the story of the Golden Ratio, however. It is also found in nature, reflected in essentially every spiral form from a snail shell to the arms of a galaxy. Thus, the shape seems to be subliminally pleasing to the human eye, as witnessed by the many ways in which it is used in art and in construction. Rectangles with sides proportioned 0.618034 to 1 (or 1 to 1.618034) are often the shape taken by such commonplace items as picture frames and playing cards. To recapitulate briefly, the Golden Ratio consists of the two numbers 1.618034 and 0.618034, each of which is the reciprocal of the other. The interest shown seems to justify a sequel. Seldom has an article appearing in this space generated the volume of reader response as did last month's column on the Golden Ratio.