Dripping Faucets and Continued Fractions

 

The note [57] was suggested by observing a dripping faucet in the bath tub: two drops were falling from different sides of the spout taking turns, in a very precise fashion. This problem leads naturally to studying the combinatorial problem of the pattern of intersections between a straight line in the plane with a square lattice. The ``dripping pattern” turns out to be related to continued fractions and to the so-called Morse-Thue sequences.