# Fibonacci series! Debunked!

Ok, this is not strictly music based, but urgh, I do get annoyed with all the mysticism and nonsense around the Fibonacci series and the Golden Ratio...and it's time to bust a few myths...

**Quick recap:**

Fibonacci series: 1,1,2,3,5,8,13,21,34,55,89....

Golden ratio = 1.618033..

**Myth 1:There's something uniquely special about the Fibonacci series' ability to generate the golden ratio by dividing two consecutive numbers**

> There isn't actually anything special about the Fibonacci series' ability to generate the golden ratio in this way. **ANY series of consecutively added numbers increasingly approximate the golden ratio as the numbers get bigger:**

Fibonacci series:

2/1 = 2

3/2 = 1.5

5/3 = 1.667

21/13 = 1.615

...

89/55 = **1.618**

Lucas' numbers (starting numbers 1 and 3): 1,3,4,7,11,18,29,47,76,123...

18/11 = 1.63

29/18 = 1.611

...

123/76 = **1.618**

Random pair (let's start with 5 & 12): 5,12,19,31,50,81,131,212

212 / 131 = **1.618**

So when people measure the Parthenon and the human body and magically find 1,3,5,8 everywhere, it doesn't prove a thing. They could be looking for 1,4,7,11 or 5,12,19. Look hard enough for small enough numbers in hard-to-accurately-measure things and you will find what you're looking for - and that's Numberwang!

**Myth 2:There's still something oh-so-special about the Fibonacci series and the Golden Ratio. **

The Fibonacci series isn't even the best or most logical series to use if you're really insistent on the whole adding-consecutive-numbers-together-to-get-the-golden-ratio thing. You should be using the Lucas series as shown above, and for a very interesting and cool reason:

> Lucas' numbers (starting numbers 1 and 3): 1,3,4,7,11,18,29,47,76,123...

> Now, let's raise the Golden Ratio to its subsequent powers and round them off:

Phi ^ 1 = 1.618 (phi being the Greek letter for the golden ratio, raised to the power 1)

Phi ^ 2 = 2.618 ~ 3

Phi ^ 3 = 4.23 ~ 4

Phi ^ 4 = 6.85 ~ 7

Phi ^ 5 = 11.09 ~ 11

Phi ^ 6 = 17.94 ~ 18

Phi ^ 7 = 29.03 ~ 29

Look! Raising the golden ratio to subsequent powers produces a series of numbers that approximates the Lucas series. **And if that's not Numberwang I bloody well don't know what is. **

*Thanks to a chapter in Matt Parker's 'Things to Make and Do in the Fourth Dimension' which the above intel comes from. *