Posted by: Alexandre Borovik | August 24, 2008

Pappus on bees

Bees were endowed with a certain geometrical forethought …. There being, then, three figures which of themselves can fill up the space round a point, viz. the triangle, the square and the hexagon, the bees have wisely selected for their structure that which contains the most angles, suspecting indeed that it could hold more honey than either of the other two.

Pappus of Alexandria



  1. According to some biologists, bees have the second-most sophisticated communications language on earth, after humans.

    And the University of Queensland Brain Institute in Australia has just invested in a bee flight research lab, as part of major research into (human) brain functions.

  2. I am just curious, are there any insects or animals who have chosen the wrong geometry for their actions and insist on it?

  3. There is one well-known and tragic example: insects fly to a candle along a logarithmic spiral because they normally navigate keeping a constant angle between the direction of their flight and the Moon. When they are duped into belief that a candle is Moon, they fly at a constant angle with direction to the candle, which make to spiral closer and closer to the candle. See details in

    K. N. Boyadzhiev, Spirals and Conchospirals in the Flight of Insects. The College Mathematics J. 30 no.~1 (1999) 23–31;

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