  We establish a new connection between sails, a key notion in the geometric
theory of generalised continued fractions, and arithmetic of totally real
number fields, specifically, universal quadratic forms and additively
indecomposable integers. Our main application is to biquadratic fields, for
which we show that if their signature rank is at least 3, then ranks of
universal forms and numbers of indecomposables grow as a power of the
discriminant. We also construct a family in which these numbers grow only
logarithmically.
