Fibonacci Sequence



The Fibonacci sequence is a mathematical series of numbers, discovered by Leonardo de Pisa.. It was introduced to western mathematics in his book Liber Abaci, written in 1202.   By definition, the first two numbers in the sequence are 0 and 1, and each subsequent number is the sum of the previous two. The first 13 numbers in the sequence are as follows:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144

The following formula could be used:

    Fn= Fn-1 + Fn-2

 The number 144 is the 13th number in the sequence, so F13=144  

    F13=F12+F11

   144=89+55

Graphically, when you look at this equation you will notice that it creates a spiral, and as the numbers continue to grow the distance from the original point becomes greater, as you can see below.

Equally important to the understanding of the Fibonacci sequence is the understanding of the golden ratio. Two numbers satisfy the golden ratio if the ratio of the sum of two quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller quantity. As the Fibonacci sequence reaches higher numbers, the golden ratio becomes more precise.

Equation:         Equation with numbers:             Average Golden Ratio Value:

(a+b)/a =b/a          (89+55)/89  = 89/55                      ≈1.618                                                

Why is this mathematical representation significant?  To understand, you must realize that there is an abundance of examples in nature that perfectly exemplify this sequence.  When looking at the seeds on a sunflower, starting at the middle most seed and working your way out, you’ll notice a spiral almost identical to the spiral in the pictures above.  The branching of trees also is an example of this sequence.

Perhaps the most incredible example within nature is the ancestry of honey bees.  A female honey bee will lay an egg, if that egg goes unfertilized the resulting offspring will be a male drone bee.  But if the egg is fertilized by a male bee, the resulting offspring will be a female.  If you look at the ancestry of a single male honey bee(one bee) you will find he has one parent, two grandparents, three great-grandparents, five great-great-grandparents, eight great-great-great-grandparents and an exact continuous Fibonacci sequence of ancestors.

This is significant because it proves nature operates within its own code.  According to some theories concerning simulated reality, at some point in the future, we will create an advanced enough computer system that will possess the capability to recreate the entire universe as we know it with identical laws involving physics. Our entire reality is theoretically programmable.  By using the data hidden in nature, we may be able to uncover truths about ourselves we never thought possible.

Written by @username_SDX

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