2021/12/18 by Ariel Kellison, Kellison, Ariel
Computer Science · Engineering · #3D Modeling in Geospatial Applications #Computational Geometry and Mesh Generation #FOS: Computer and information sciences #Logic in Computer Science (cs.LO) #Model-Driven Software Engineering Techniques
paper · pdf · doi:10.48550/arxiv.2112.11182
openalex publication_date 2021/12/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A direct proof of the Steiner-Lehmus theorem has eluded geometers for over 170 years. The challenge has been that a proof is only considered direct if it does not rely on reductio ad absurdum. Thus, any proof that claims to be direct must show, going back to the axioms, that all of the auxiliary theorems used are also proved directly. In this paper, we give a proof of the Steiner-Lehmus theorem that is guaranteed to be direct. The evidence for this claim is derived from our methodology: we have formalized a constructive axiom set for Euclidean plane geometry in a proof assistant that implements a constructive logic and have built the proof of the Steiner-Lehmus theorem on this constructive foundation.