Bee hive order
The honeybee family tree gives a perfectly accurate depiction of the
Fibonacci sequence. The queen bee of the hive lays eggs. Those that are
fertilised by a male bee develop into a female and those that are not
are male. Thus, male bees have only one parent. The family tree
(previous page) with the youngest generation at the bottom will give you
a better idea. Each male bee in the hive has 1 parent, 2 grandparents, 3
great grandparents, 5 great great grandparents, and so on. Now you get
Even if you look at a flower and count its petals, it will be a number
This lily appears to have six petals, however, only
the top three are petals and the bottom three are sepals. And 3 is a
Fibonacci number. Even their seed heads follow the sequence!
There is another interesting pattern formed by the Fibonacci sequence:
the Fibonacci rectangle. Each side of each box has a length equal to a
Fibonacci number and when put into a spiral, each box length is the sum
of the last two, the Fibonacci sequence. When a quarter circle, with a
radius of the box’s length, is drawn in each box a spiral is formed.
This spiral is very similar to Nautilus Shell.
A closer look
Hemachandra, a Jain philosopher, and Gopala, an Indian mathematician,
did studies of these numbers. Hemachendra studied the Sanskrit vowel
sounds that are either long (L) or short (S), and computed how many
cadences of total length could be developed if the long is twice the
length of the short. What he discovered was the Fibonacci sequence.
1 mora: S (forms only one pattern)
2 morae: SS, L
3 morae: SSS, SL, LS
4 morae: SSSS, SSL, LSS, SLS, LL
5 morae: SSSSS, SSSL, SSLS, SLSS,
LSSS, SLL, LSL, LLS
The studies done by Fibonacci initiated new observations in nature and
the Golden Mean. Johannes Kepler showed that if a Fibonacci number is
divided by the Fibonacci number that precedes it in the sequence, the
ratios after 1 divided by 1 settle around one number, the golden mean,
1/1=1, 2/1=2, 3/2=1.5, 5/3=1.6666667, 8/5=1.6, 13/8=1.625 and so on.
Many scientists, including Leonardo DaVinci, have studied
this mean. It is used in art, music, architecture, and has opened a
whole new field of scientific drawing and the study of the human
anatomy. The Golden Mean is also called the Divine Proportion, which has
been used to describe the proportions of the human body. Leonardo
DaVinci used the Divine Proportion in his artwork to accurately draw
human features. His drawing of the Vitruvian Man was the first of such
Do you know that the distance from your wrist to your elbow is the
length of your foot? Five times the width of your eyes is same as the
size of your face! There is one eye length between your eyes! And your
wingspan is your height!
Can you now see these numbers around you?