# What is meant by Fibonacci series?

## Fibonacci sequence formula

Absolutely nothing.

The Fibonacci sequence has no bearing on epistemology, metaphysics, logic or ethics.

,One could argue that it somehow falls into aesthetics.

In my opinion, one would be wrong in all but the most trivial way.

## What is the Fibonacci sequence used for

The Fibonacci sequence, as you know, reflects patterns of growth spirals found in nature.

That doesnt make it important as such it just makes it a natural phenomenon, like seeing ripples in a pond or noticing the five-fold pattern of digits at the ends of each of our limbs.

There is an underlying geometry in the evolution of living things.

And that is important.

Why? Because most people are unaware of this.

Even Darwin never mentioned it in his theory of natural selection.

Once the underlying geometry of evolution becomes common knowledge it will cease to be that important.

Or rather it will be as important as you want it to be depending on what your interests are.

,The Fibonacci sequence is much more than just a number sequence, just as my hands are much more than the fingers at the end of my arms.

,At the moment I am researching the Fibonacci spirals connection with obsessive behaviour.

I dont expect a mathematician to comment on this because its not their area.

The Fibonacci pattern is also found in the musical scale.

Again this does not make it important.

Its simply something that exists as a number pattern that may or may not have deeper significance.

At this stage, the Fibonacci sequence and spiral seems to be a natural feature in many areas of life.

Its up to researchers to discover how and where it can be applied.

,A simple astronomical fact is that the mean tropical year of 365.

242 days divided by the Fibonacci ratio 13/8 equals 224.

7 days - the orbit of Venus.

What beautiful precision! Astronomers never mention this, but astrologers love this fact because Venus rules aesthetics and beauty - the popular attributes of the golden ratio.

## Fibonacci sequence Python

In simplified C++, you would do something like this:,i=0;a=1; b=fibon(a); if(b % 2==0, goto loop, goto next);loop:printb,, ,;i=i+b; next:a++;if(a<50, goto2, discard=0;printTotal ==, i,Output: 2 , 8 , 34 , 144 , 610 , 2584 , 10946 , 46368 , 196418 , 832040 , 3524578 , 14930352 , 63245986 , 267914296 , 1134903170 , 4807526976 , Total == 6293134512It loops through the first 50 terms and lists the even ones and sums them up.

## Fibonacci calculator

Itu2019s NOT.

Recursion is an extraordinarily inefficient way to calculate Fibonacci numbers.

On the other hand, it is a great example of how recursion works (and why you donu2019t always want to use it).

## Fibonacci golden ratio

Itu2019s not Fibonacciu2019s.

About 700 years ago, he wrote a problem about multiplying rabbits that leads to whatu2019s called the Fibonacci sequence: 1, 1, 2, 3, 5, 8, 13, 21, etc.

Thereu2019s a connection between the Fibonacci sequence and the golden ratio, but Fibonacci didnu2019t know that as he never said anything about either.

,The first construction of the golden ratio still surviving appeared in Euclidu2019s Elements Proposition II.

11 about 2300 years ago.

Thatu2019s in preparation for Proposition IX.

11 in which he constructed a regular pentagon.

In book XIII itu2019s used in the construction of dodecahedra and icosahedra.

Itu2019s not Euclidu2019s invention though.

Earlier geometers analyzed the regular pentagon at least 150 years earlier.

Unfortunately, earlier writings didnu2019t survive.

,The golden ratio has other applications including its use in finding the sine and cosine of 36u00b0 and 72u00b0.

Those are needed to construct trig tables as those of Ptolemy 1900 years ago.

,The golden ratio wasnu2019t associated with beauty at all until about 400 years ago with Pacioli and da Vinciu2019s book Divina proportione (the Divine Proportion) was published.

They connected the golden ratio not just to geometry (pentagons, dodecahedra, and icosahedra as in the Elements) but also to religion, architecture, and proportions of the human body.

Except for the geometry, itu2019s all rather fanciful.

,The golden ratio, frac12(1+sqrt 5), is as perfect as any other number.