geometry of bees

chris cambré, Aug 27, 2017

Honeybees build hives to stock honey, eggs and larvae. In Ancient Greece and Rome the shape of the cells raised the intrest of mathematicies and even today hives are studies by scientists. In this GeoGebrabook you'll find tesselations and the theorema of Pythagoras. We'll use minimalisation techniques with derivates. In the last worksheet you can find some links to additional information.


  • 1. geometrical bees
  • 2. regular polygons
  • 3. pointed cells
  • 4. diagonal d
  • 5. diagonal D
  • 6. area of a cell
  • 7. minimal area
  • 8. angles

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geometrical bees

the shape of a honey comb
The Roman scholar Varro, in his 1st century BC book-long poem De Agri Cultura (“On Agriculture”), briefly states: “Does not the chamber in the comb have six angles, the same number as the bee has feet? The geometricians prove that this hexagon inscribed in a circular figure encloses the greatest amount of space.”[br] [br]There are some quotes by Aristoteles to, but the attribitions are uncertain[br]Fact is that Greek and Romans saw that the honeybees didn't build the combs at random and noticed that the shape is mathematially interesting.[br]
Pappos of Alexandria (300 A.D.)
Pappos of Alexandria described a honeycomb as a tiling of six angled prisms.
Giacomo Filippo Maraldi (1712)
Giacomo Filippo Maraldi, astronomer at the Paris observatory noticed that the back plates of the cells weren't flat shaped. They are formed by three non coplanair rhombusses. He measured the angles of the rhombus as 109.47° and 70.53°.[br]The upper cell is placed with the pointed top fitted in the hole upon the point were three sells meet
Questions
Ask yourself some questions raised by the observations of Pappos and Maraldi.[br]In the following worksheets we will explore how and why of the shape of the cells.
– chris cambré

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Information