Mathematics
What do a few math problems have to do with everything we do?
Explaining the Fibonacci Sequence
The Fibonacci sequence is a sequence of numbers, starting with zero and one, is a steadily increasing series where each number is equal to the sum of the preceding two numbers. A very simple sequence but somehow this sequence is very much important to many people in math and investing.
The first 10 numbers of the sequence go as follows:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34…
Every number is picked based on the formula. If we would imagine the numbers in a list with each number having an index one bigger than the one previously then we can put it into an equation like this: Fn = Fn-1 + Fn-2, where n > 1. The index of the number being represented as a lowercase “n.”
Using that formula we can show an example. As an example, 3 is in the 5th index. That means that Fn-1 and Fn-2 have to be index 3 and 4. The 3rd and 4th index values are 1 and 2. If we put that into the formula it is just 1+2=3. It is as simple as that.
But what does this have to do with the golden ratio?
The Golden Ratio
Many people refer to the Golden Ratio as the most beautiful number in the universe (phi =φ ). This is because of the simple fact that it may be depicted practically everywhere, starting with geometry and ending with the human body itself.
It is used in many things such as: architecture, math, painting, nature and investing.
Simply put the golden ratio is a number that equals just about 1.618(1 : 1.6). And the ratio appears when the ratio of two numbers equals the ratio of the ratio of their sum to the larger of the two numbers.
Numerically the golden ratio is represented as:
- Φ = (1+√5)/ 2 = 1.618…
And since this value is irrational the numbers go on forever.
Golden Ratio and Fibonacci sequence
These two things, the golden ratio and the Fibonacci sequence are very closely related. This is because when the numbers in the Fibonacci sequence increase they get closer and closer to the golden ratio.
Conclusion:
The golden ratio and the Fibonacci sequence are used all throughout the world. In art, math, science, plants, nature and even the human body. It is just a seemingly random ratio and a simple math sequence but it somehow has to do with and effects so many things that we do.
