Collinearity of points on Poincar\'e unit disk and Riemann sphere

Autor:	Fujimura, Masayo, Rainio, Oona, Vuorinen, Matti
Rok vydání:	2022
Předmět:	Mathematics - Metric Geometry 51M10 (Primary) 51M09 (Secondary)
Druh dokumentu:	Working Paper
Popis:	We study certain points significant for the hyperbolic geometry of the unit disk. We give explicit formulas for the intersection points of the Euclidean lines and the stereographic projections of great circles of the Riemann sphere passing through these points. We prove several results related to collinearity of these intersection points, offer new ways to find the hyperbolic midpoint, and represent a formula for the chordal midpoint. The proofs utilize Gr\"obner bases from computer algebra for the solution of polynomial equations. Comment: 26 pages, 7 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2212.09037 Zobrazit plný text záznamu View this record from Arxiv