# Distributing fire stations in a circular city

How to distribute k points inside a disc so to minimize the distance of any point inside the disc to the closest of the k points? Does this problem have a name? Is the solution a famous sequence of geometric graphs?

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Instead of circle, do you mean disk? –  Joel Reyes Noche Feb 25 '13 at 0:51
Yes, pardon for the imprecision. –  Leo Arruda Feb 25 '13 at 15:27

This is the (finite) covering problem in the plane. According to Boroczky's book "Finite packing and covering", the answer is only known (provably) up to $k = 10$, due to the work of K. Bezdek and G. Fejes Toth. I don't know if the solutions are a famous sequence of geometric graphs.