  We consider flow directions on the translation surfaces formed from double
$(2n+1)$-gons, and give a sufficient condition in terms of a natural gcd
algorithm for a direction to be hyperbolic in the sense that it is the fixed
direction for some hyperbolic element of the Veech group of the surface. In
particular, we give explicit points in the holonomy field of the double
heptagon translation surface which are not so-called connection points. Among
these are the central points of the heptagons, giving a negative answer to a
question by P.Hubert and T.Schmidt.
