  Aesop's famous fable The Ant and the Grasshopper emphasizes the choice that
living beings have to make between survival (the Ant) and reproduction (the
Grasshopper). Apis Mellifera colonies face the same dilemma : must they rather
collect nectar in order to produce honey that will enable them to endure the
cold of winter or should they choose to bring pollen back to the hive so as to
raise young bees ? Both, of course, but in which proportion ? And where should
they fly to find the best resources ? We adress these question through a
mathematical perspective, by considering the geometry of resources around the
hive.
