On Automating Triangle Constructions in Absolute and Hyperbolic Geometry

Abstract

We describe first steps towards a system for automated triangle constructions in absolute and hyperbolic geometry. We discuss key differences between constructions in Euclidean, absolute and hyperbolic geometry, compile a list of primitive constructions and lemmas used for constructions in absolute and hyperbolic geometry, build an automated system for solving construction problems and test it on a corpus of triangle-construction problems. We also provide an online compendium containing construction descriptions and illustrations.