Mathematically, A Fibonacci sequence is a sequence of numbers in a way that every number is a sum of the previous two. The Fibonacci sequence looks like this when laid out:
1, 1, 2, 3, 5, 8, 13, 21, 34, 55,...
The interesting patter with the Fibonacci Sequence is that when two succeeding elements are divided, the quotient comes closer and closer to the inverse of the Golden Ratio.
1 / 1 = 1
1 / 2 = .5
2 / 3 = .666...
3 / 5 = .6
5 / 8 = .625
...
4181 / 6765 = 0.6180339...
Now we see how the Fibonacci Sequence and the Golden Ratio are correlated. But what is the Golden Ratio? The symbol used for the Golden Ratio is φ. The value of the Golden Ratio is:
φ = [sqrt(5) + 1]/2 = 1.6180339...
The Golden Ratio satisfies the equation:
X^2 - X - 1 = 0
The inverse of the Golden Ratio is: (as shown above by dividing the Fibonacci Sequence)
1/φ = φ - 1 = 0.6180339...
The Golden Ratio and the Fibonacci Sequence can also be found naturally in nature. By measuring parts of your own body right now, you will find out that you are made of the Golden Ratio.
(source)The distance between the finger tip and the elbow / distance between the wrist and the elbow,
The distance between the shoulder line and the top of the head / head length,
The distance between the navel and the top of the head / the distance between the shoulder line and the top of the head.The distance between the navel and knee / distance between the knee and the end of the foot.* the slash means to divide
Many portions of the Parthenon are made of Golden Ratios:
The Fibonacci Sequence and the Golden Ratio can be found in more places in nature such as flowers, plants and shells.
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