  The present work looks at semiautomatic rings with automatic addition and
comparisons which are dense subrings of the real numbers and asks how these can
be used to represent geometric objects such that certain operations and
transformations are automatic. The underlying ring has always to be a countable
dense subring of the real numbers and additions and comparisons and
multiplications with constants need to be automatic. It is shown that the ring
can be selected such that equilateral triangles can be represented and
rotations by 30 degrees are possible, while the standard representation of the
b-adic rationals does not allow this.
