Fibonacci--Fun Background You've Never Heard  

Are you a Geek?

If you have the smallest amount of geek in you, you will find the following information fascinating. If you are the Anti-Geek and could care less about why things are and how they came to be and other such stuff.... if that describes you, may God have mercy on your soul.

However, if you, like me, find background information, the hows and whys, and math, and geometry, and slightly famous Italian Mathemeticians spectacularly interesting; then you will love this post. As an added bonus, I am going to tell you some things you probably have never heard if you have only read about Fibonacci ratios from Forex sites or other such sources.

Who is Fibonacci and why do we Care?

Leonardo Bonacci, aka Leonardo of Pisa, was a 13th century mathematician who introduced the Arabic Numeral system to Europe. His father ran, or more accurately managed, a Pisan trading post in Algiers where the bright young Leo was introduced to the superior arithmetic used in the Arab world. At age 35 he published a book Liber Abaci (Book of Abacus or Book of Calculation) which described counting in Arabic numerals, processes of multiplication, conversions including currency and profit (hence he was involved in Forex!), formulas for arithmetic and geometric series, and other such subjects. Surprisingly, the book was a great hit among the 13th century elite and he won a salaried (sort of a tenure) position with the Roman Emperor Frederick II. He was given the name Fibonacci posthumously which means "little one of Bonacci"

In one chapter of the book, he addressed the very pressing problem of rabbit farmers in medieval Europe expressed as, "How many rabbits can be bred in one year?". The resulting answer was the following series of numbers:

1,1,2,3,5,8,13,21,34,55,..... where each subsequent number F is represented by the formula F_n = F_(n-1) + F_(n-2).

So why is this sequence important? The sequence grows at a rate 0f 61.8% which is the Golden Ratio and designated by the ancient Greeks as 'φ'. (Actually, the growth of the sequences approaches φ and it is only approximate with the early numbers of the sequence.)

It appears that this sequence and the Golden Ratio appear a lot in nature and in the heavens. It also is found in architecture both ancient and modern. It is used in Computer Science theory. More than a few doctoral dissertations have centered on it. And some very successful stock, commodity, and Forex traders have used it to amass fortunes.

Forget Rabbits, what about Honey Bees?

Not everyone believes in the magic of Fibonacci numbers in Forex or market trading in general. Some people even scoff at the notion and say that these ratios only work because everyone is using them. I think such naysayers are nincompoops. But before we discuss the use of the Fibonacci sequence and the Golden Ratio in Forex, I want to share some fun information.

Everyone has heard the story about the rabbits. Fibonacci skeptics will tell you how rabbits don't really reproduce the way Leo described it. Well, then let me introduce you to honey bees. I ripped the following snippet from a Dr. Ron Knott who has a bunch of accreditations following his name: Ph.D, M.Sc, B.Sc (Pure Maths), C.Math, FIMA, C.Eng, MBCS, CITP. I'm sure he's a lot smarter than me.

Honeybees and Family Trees

There are over 30,000 species of bees and in most of them the bees live solitary lives. The one most of us know best is the honeybee and it, unusually, lives in a colony called a hive and they have an unusual Family Tree. In fact, there are many unusual features of honeybees and in this section we will show how the Fibonacci numbers count a honeybee's ancestors (in this section a "bee" will mean a "honeybee").

First, some unusual facts about honeybees such as: not all of them have two parents!
In a colony of honeybees there is one special female called the queen.

There are many worker bees who are female too but unlike the queen bee, they produce no eggs.

There are some drone bees who are male and do no work.

Males are produced by the queen's unfertilised eggs, so male bees only have a mother but no father!

All the females are produced when the queen has mated with a male and so have two parents. Females usually end up as worker bees but some are fed with a special substance called royal jelly which makes them grow into queens ready to go off to start a new colony when the bees form a swarm and leave their home (a hive) in search of a place to build a new nest.

So female bees have 2 parents, a male and a female whereas male bees have just one parent, a female.

Here we follow the convention of Family Trees that parents appear above their children, so the latest generations are at the bottom and the higher up we go, the older people are. Such trees show all the ancestors (predecessors, forebears, antecedents) of the person at the bottom of the diagram. ....

Let's look at the family tree of a male drone bee.

1. He had 1 parent, a female.
2. He has 2 grand-parents, since his mother had two parents, a male and a female.
3. He has 3 great-grand-parents: his grand-mother had two parents but his grand-father had only one.
4. He has 5 great-great-grand parents [--edited by me]
5. He has 8 great-great-great grand parents. [--edited by me]
6. He has 13 fourth-generation grand parents. [--edited by me]
7. He has 21 fifth-generation grand parents. [--edited by me]
8. and so on ...

... [thus we see the Fibonacci sequence in the number of grand parents in each increasing generational level --edited by me]

Source: The Fibonacci Sequence as it appears in Nature by S.L.Basin in Fibonacci Quarterly, vol 1 (1963), pages 53 - 57.

Even the bee does Fibonacci!!

Its Easy to Draw Fibonacci