Prof. Dr. Hilmi Hacısalihoğlu

The mathematics of animal (behaviour)

I. The mathematics of bees
II. The mathematics of spiders
III. The mathematics of fish

I. God ordained the bees to be examples to the human. 65-75 thousand bees practice a very clear mathematics program. They are equipped a beehive with a honeycomb that will serve as a beehive. The honeycombs are furnished with uniform hexagonal prisms starting from everywhere inside of the hive, the same type of prisms are built and finished. From a mathematical point of view it seems that bees choose the best possible shape of the combs cells which is optimal regarding spent material ensuring a maximum strength. The wax needed to build combs has been extruded from the worker bee glands under their abdomen. A foreign bee is not allowed to enter the hive. For the safety of the hive, guard bees located at the entrance of the hive are responsible. This discipline and diligence is also very interesting and worthy to notice. The inner arrangement of the honeycombs is also another story. At the bottom is a room for the queen, a separate second room at the top is for the eggs, a separate room at top of it for the larvae, and the last room is arranged for honey. Each bee follows the same rigor to all this unique structure. The size of the fractals is 1.
II. Spiders can be found everywhere all over the world. Spiders construct webs by producing the silk. Webs allow a spider to catch prey without having to expend energy by running it down. Thus it is an efficient method of gathering food. However, constructing the web is in itself an energetically costly process because of the large amount of protein required, in the form of silk. All male spiders are killed by their females, except those who can escape and survive immediately after mating. They do not need anything but a fixed point to construct their webs. Spider webs are used for hunting and feeding purposes, and they form the webs with same method. The webs are fractals of size 1.
III. Long-distance migrations of animals represent one of the great wonders of the natural world. In the marine environment, migratory movements sometimes reach astonishing extremes: for example, some sea turtles, salmon, sharks, and elephant seals travel distances that exceed the width of oceans before returning to their home areas to reproduce. How animals find their way during such migrations has remained a central mystery of sensory and behavioral biology.