The Fibonacci Sequence:
When Maths Turns Golden UNBOUND Learn how to see, and realize that everything connects to everything else: Leonardo Da Vinci Fibonacci Sequence has captivated Mathematicians, artists, designers, and scientists for centuries. Wondering what’s so special about it? Let us begin with the history. The original problem that Leonardo Fibonacci investigated (in the year 1202) was about how fast rabbits could breed in ideal circumstances. Suppose a newly-born pair of rabbits, one male, and one female are put in a field. Rabbits are able to mate at the age of one month so that at the end of its second month, a female can produce another pair of rabbits. Suppose that our rabbits never die and that the female always produces one new pair (one male, one female) every month from the second month on. The puzzle that Fibonacci posed was... How many pairs will there be in one year? Think! No? Let me help you. At the end of the first month, they mate, but there is still one only 1 pair. At the end of the second month, the female produces a new pair, so now there are 2 pairs of rabbits in the field. At the end of the third month, the original female produces a second pair, making 3 pairs in all in the field. At the end of the fourth month, the original female has produced yet another new pair, the female born two months ago produces her first pair also, making 5 pairs. Can you see the pattern here? 1, 1, 2, 3, 5, 8, 13, 21, 34…… The solution, generation by generation, was a sequence of numbers later known as Fibonacci numbers. Fibonacci Sequence is a set of numbers that start with a one, followed by a one, and proceeds based on the rule that each number is equal to the sum of the preceding two numbers. The Fibonacci numbers can be thought of as Nature’s numbering system. They appear everywhere in Nature, from the leaf arrangement in plants to the pattern of the florets of a flower, the bracts of a pinecone, or the scales of a pineapple. The Fibonacci numbers are therefore applicable to the growth of every living thing, including a single cell, a grain of wheat, a hive of bees, and even all of mankind. In the seeming randomness of the natural world, we can find many instances of a Mathematical order involving the Fibonacci numbers themselves and the closely related “Golden” elements. Let’s add one more interesting thing here: If we take the ratio of two successive numbers in Fibonacci’s series, (1, 1, 2, 3, 5, 8, 13, ..) and we divide each by the number before it, we will find the following series of numbers: 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... The ratio seems to be settling down to a particular value, which we call the ‘golden ratio’ or ‘the golden number’. It has a value of approximately 1·618034 and we denote it by “Phi”. Now, let’s get acquainted with some of the endless examples that make Fibonacci a wonder or ‘Golden’ sequence. Flower petals: The number of petals in a flower consistently follows the Fibonacci sequence. Famous examples include the lily, which has three petals, buttercups, which have five, the chicory’s 21, the daisy’s 34, and so on. Each petal is placed at 0.618034 per turn (out of a 360° circle) allowing for the best possible exposure to sunlight and other factors. Seed heads: The head of a flower is also subject to Fibonaccian processes. Typically, seeds are produced at the centre and then migrate towards the outside to fill all the space. Sunflowers provide a great example of these spiraling patterns. l know it's possible." ~ Gloria Steinem
