Automated triangle constructions in hyperbolic geometry

Abstract

We describe a system for automated ruler and compass triangle constructions in hyperbolic geometry. We discuss key differences between constructions in Euclidean and hyperbolic setting, compile a list of primitive constructions and lemmas used for constructions in hyperbolic geometry, build an automated system for solving construction problems, and test it on a corpus of triangle-construction problems. We extend the list of primitive constructions for hyperbolic geometry by several constructions that cannot be done by ruler and compass, but can be done by using algebraic calculations and show that such extended system solves more problems. We also use a dynamic geometry library to build an online compendium containing construction descriptions, illustrations, and step-by-step animations.