0, 1, 1, 2, 3, 5, 8, 13, 21, 34, …
If you think I have started hurling random numbers at you, look a little more closely.
Try and observe a pattern.
When you see it, read on. (If you can’t, scroll to the bottom of the article for a hint, for I know curiosity kills the cat.)
Now gather a ruler and a scale and make squares with these widths.
What you will observe is a spiral, appearing as if by magic.
Are you up for one last fun exercise? Take any two successive numbers from this sequence and divide them by each other.
What you get is 1.618034, which is also called the Golden Ratio.
Go on, pick any two numbers from the sequence.
This isn’t just an arbitrary sequence, it lies at a core of many a phenomenon, most of which you must be encountering in your everyday life and overlooking.
Although named after Leonardo Pisano Bogollo, who lived between 1170 and 1250 in Italy, and had the nickname Fibonnaci, it wasn’t first observed by him. The Fibonacci sequence appears in Indian mathematics, in connection with Sanskrit prosody.
In the Sanskrit tradition of prosody, there was interest in enumerating all patterns of long (L) syllables that are 2 units of duration, and short (S) syllables that are 1 unit of duration. Counting the different patterns of L and S of a given duration results in the Fibonacci numbers: the number of patterns that are m short syllables long is the Fibonacci number Fm + 1.
So let’s get our detective glasses on and discover this amazing pattern in nature, shall we?
Ever looked at a plant and marveled at the way the leaves are arranged in a specific way to receive optimum sunlight?
By dividing a circle into Golden proportions, where the ratio of the arc length is equal to the Golden Ratio, we find the angle of the arcs to be 137.5 degrees. In fact, this is the angle at which adjacent leaves are positioned around the stem.
In the case of tapered pinecones or pineapples, we see a double set of spirals – one going in a clockwise direction and one in the opposite direction. When these spirals are counted, the two sets are found to be adjacent Fibonacci numbers.
Similarly, sunflowers have a Golden Spiral seed arrangement. This provides a biological advantage because it maximizes the number of seeds that can be packed into a seed head.
The inside of fruits, the branching point of stems and the number of petals are all exhibited in Fibonnaci Order. Fibonacci numbers also appear in the pedigrees of idealized honeybees, according to the following rules:
- If an egg is laid by an unmated female, it hatches a male or drone bee.
- If, however, an egg was fertilized by a male, it hatches a female.
Thus, a male bee always has one parent, and a female bee has two.
If one traces the pedigree of any male bee (1 bee), he has 1 parent (1 bee), 2 grandparents, 3 great-grandparents, 5 great-great-grandparents, and so on. This sequence of numbers of parents is the Fibonacci sequence. The number of ancestors at each level, Fn, is the number of female ancestors, which is Fn−1, plus the number of male ancestors, which is Fn−2.[65] .
An enthusiast could also arrange nachos in this way!
It is also worthwhile to mention that we humans have 8 fingers in total, 5 digits on each hand, 3 bones in each finger, 2 bones in 1 thumb, and 1 thumb on each hand.
The ratio between the forearm and the hand is the Golden Ratio!
The Golden Ratio is seen in the proportions in the sections of a finger.
Fascinating, isn’t it?
How there is order within what seems like chaos, how symbols and sequences jump out of theories and pages, hiding in plain sight, waiting to be discovered.
How Mathematics interwines with nature to produce the lovechild called Fibonnaci sequence.
This November 23rd (11/23, get it? Get it?) let everyone know.
(P.S The next number in the sequence is found by adding up the =previous two numbers. Example 1+0=1, 1+1=2, 2+1=3, 3+2=5, you get the drift.)