2021/04/09 by Temel Ermiş, Ermiş, Temel, Özcan Gelişgen +1 · 1 citation
Computer Science · Mathematics · #51F99 #51K05 #51N20 #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric and Algebraic Topology #Mathematics and Applications #Metric Geometry (math.MG) #math.MG #msc:51F99 #msc:51K05 #msc:51N20
paper · pdf · doi:10.48550/arxiv.2104.04274
arxiv created 2021/04/09 · openalex publication_date 2021/04/09 · arxiv updated 2021/04/12 · openalex created_date 2021/04/26 · openalex updated_date 2026/07/31
In geometry, Monge's theorem states that for any three nonoverlapping circles of distinct radii in the two dimensional analytical plane equipped with the Euclidean metric, none of which is completely inside one of the others, the intersection points of each of the three pairs of external tangent lines are collinear. So, it is clearly observed that Monge's theorem is an application of Desargues' theorem. Our main motivation in this study is to show whether Monge theorem is still valid even if the plane is equipped with the metrics alpha and Lp.