All Sides to an Oval: Properties, Parameters, and Borromini's Mysterious Construction

Introduction.- Properties of a polycentric oval.-F .- Ruler/Compass constructions of simple ovals.- Ovals with given symmetry axis lines.- Ovals with unknown axis lines.-Inscribing and circumscribing ovals - The frame problem.- The stadium problem and the running track.- Parameter formulas for simple ovals and applications.- Parameter formulas for simple ovals.- Limitations for the frame problem.- Measuring a four-centre oval.- Optimisation problems for ovals.- Ovals with 4n centres.- Remarkable four-centre ovals .-Appendix.-References.-Acknowledgements.