Biology
and the Golden Ratio
Conclusion: The Bee Hive
��� The geneology of the bee is
a pattern.� This pattern is the result of parthogenesis, the development of an
unfertilized egg into an adult animal without fusion with sperm.� The queen bee mates
only once.� She can then produce either unfertilized eggs or fertilized eggs. �
The unfertilized eggs become male drones, while the fertilized eggs become female workers
or queens.�� In other words, a female bee has two parents, and a male bee has
only one parent; a female.� Female bees reproduce by parthenogenesis during the
spring and summer.� In the fall, the eggs produce both males and females. �
These insects mate, and the females produce fertilized eggs that hatch in the spring.
Family Tree of Drone Bee
He had
1 parent, a female.
He has
2 grand-parents, since his mother had two parents, a male and a female.
He has
3 great-grand-parents: his grand-mother had�two parents but his grand-father had only
one.
The total of all the males and the total of all the females that make each generation
forms an overlapping Fibonacci series repeated twice; One for males and one for
females�
� �
great- ���������� great, great
��� gt,gt,gt
�������������������������������������������������
� grand- ����������grand-
���������� grand
����������� grand
Number of������������ parents:
�������� parents:
�������� parents:
�������� parents:
�������� parents:
of a MALE bee:�������� 1
������������������
2
�����������������
3
������������������
5
������������������
8
of a FEMALE bee:���� 2
������������������
3
����������������
5
�������������������
8
�����������������
13
�
Why does Phi appear in nature?
The arrangements of leaves is the same as for seeds and petals.� All
are placed at 0.618034.. leaves, seeds, or petals, per turn.� In terms of degrees
this is 0.618034 of 360� which is 222.492...�. However, we tend to see the smaller angle
which is (1-0.618034)x360 = 0.381966x360 = 137.50776..�. When you look at properties of
Phi, you will see that 1-phi = phi2 = Phi-2
If there are 1.618... leaves per turn it gives flowers or petals the best
possible exposure to insects to attract them for pollination or exposure to sunlight.� The whole of the plant
seems to produce its leaves, flowerhead petals and then seeds based upon the golden
number.
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