  An elementary geometric construction is used to relate the space of lattices
in a plane to the space exp_3(S^1) of the subsets of a circle of cardinality at
most 3. As a consequence we obtain new proofs of a theorem of Bott which says
that exp_3(S^1) is homeomorphic to a 3-sphere and a theorem of Shchepin which
says that points of exp_3(S^1) that correspond to one-point subsets form a
trefoil knot in this 3-sphere.
