### FSU Mathematics

### Opal Graham

A Correspondence Between Projective Geometry and Circle Geometry

There is a correspondence between the geometric objects of Projective Space ${\mathrm{\mathbb{R}\mathbb{P}}}^{3}$ and the geometric objects of Circle Space $\mathfrak{C}\left({\mathbb{S}}^{2}\right)$- the space of circles of radius between $0$ to $\mathrm{\pi}$ on the $2$-sphere. We go through this correspondence and discuss how this relationship can be exploited to analyze rigidity of circle polyhedra and rigidity of projective polyhedra.