On Automating Triangle Constructions in Absolute and Hyperbolic Geometry
Vesna Marinkovi\'c (Faculty of Mathematics, University of Belgrade,, Serbia), Tijana \v{S}ukilovi\'c (Faculty of Mathematics, University of, Belgrade, Serbia), Filip Mari\'c (Faculty of Mathematics, University of, Belgrade, Serbia)
TL;DR
This paper introduces an initial system for automating triangle constructions across Euclidean, absolute, and hyperbolic geometries, highlighting differences, primitive steps, and testing on various problems.
Contribution
It presents the first automated system for triangle constructions in absolute and hyperbolic geometries, including a comprehensive list of primitives and an online resource.
Findings
System successfully solves a variety of triangle construction problems
Differences between geometries are systematically addressed
Online compendium provides accessible construction examples
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.
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