  This paper outlines an exact analytic model for self-gravitating thin disc
galaxies with flat rotation curves. It is shown that thin discs of matter alone
can support perfectly flat rotation curves under Newtonian gravity, without
needing extended halos or modified gravity. The method allows disc density to
be inferred from polynomial approximations to the rotation curve. Several
expository models are presented. The model also shows the link between flat
rotation curves and "exponential" discs. It is also shown that reconstructed
discs inherently posses vast mass "hinterlands" in their outer regions, that
can contain the majority of their total mass. Some implications for the problem
of missing mass are discussed.
