You must be all too familiar with this series. That’s right, it’s the Fibonacci Series. It was named after the 13th century Italian mathematician Leonardo of Pisa (“Fibonacci”). However, there are earlier records of this series in India mentioned in the works of Acharya Pingala. If you notice, the sequence starts with O and 1. After this, each number is the sum of the previous two numbers. It can be represented as:
where ‘n’ is the placeholder for the position of each number. So, for number 5, n=6. But what is special about this series? Rather than being an arbitrary series, The Fibonacci series is observed in nature. Let me show you how!
Flower Petals
Try counting the number of petals in various flowers. You will notice that the number of petals is a part of the Fibonacci series. Most have three (like lilies and irises), five (Rose hips), eight (Cosmea) or thirteen (some daisies).
Pine cones
Find a pine cone and look at it from the bottom. You will notice that there are several spirals originating from the base tip. The spirals are around the cone in both directions. Now, count the spirals. The two resultant numbers will be two consecutive terms in the Fibonacci Series.
The Golden Ratio
Take the ratio of any two consecutive numbers in the Fibonacci sequence. As you go higher, you will notice that the ratio seems to converge; specifically to the number 1.61803398875... which is the Golden Ratio. It is widely applied throughout math and real-life. For example, the ratio of the length of your hand to the length from the wrist to your elbow is equal to the golden ratio. One of the solutions to this equation is the Golden Ratio:
Isn’t this fascinating!
Here is another pattern in the series:
Let’s take 3 numbers, a, b, and c which are consecutive Fibonacci numbers. As you start playing around with these numbers, you may come across this relation:
E.g. 3, 5, 8
There are several examples such as the ones mentioned in real-life. The shape of waves are similar to that of the Fibonacci spiral. Can you find more such applications?
Comments