The Magic of Fibonacci numbers

Let us look in the real world to find the traces of Fibonacci. In every bee hive, there is one female bee (queen) who lays all the eggs. If an egg is not fertilized, it ultimately hatches into a male bee, called a drone.

If an egg is fertilized by a male bee, then the egg produces a female bee (i.e, worker bee), who doesn't lay any eggs herself (unless she is fed something called royal jelly, in that case she will turn into a queen to challenge the existing one or fly off and start a new hive).

Now let's look at the family tree of a male. If we will count the numbers of parent, grand parent, great grandparents, great-great grandparents, great-great-great grandparents, great-great-great-great grandparents and so on of a male bee, we will find the Fibonacci sequence. 1, 1, 2, 3, 5, 8, 13...

These numbers are then used to derive the Golden Ratio. The Golden Ratio is 1.618. It appears naturally in almost all aspects of life i.e, family trees in bunnies, petals on a rose, body ratio’s in humans. It is said that people that are considered ‘naturally beautiful’ have a face and body that follows the golden ratio. Both the Fibonacci numbers and the Golden Ratio appear in Honeybees.
If you divide the number of female bees by the number of male bees you get 1.618, the golden ratio. This mathematical sequence work for any honeybee hive at any give time. Commonly, honeybee hives are always used to explain the Fibonacci Sequence and Golden Ratio.