A general theory of proportion is presented and applied to proportional systems based on the golden mean, root 2, and root 3. These proportions are shown to be related to regular star polygons and to the law of repetition of ratios. The additive properties of these proportions are presented in terms of both irrational and integer series. The geometrical and number theoretic properties of the root 3 system are focused on since this system has not been previously reported in the literature. An architectural Rotunda is presented. The relationship between systems of proportion and the symbolic dynamics of chaos theory is presented.