A1 Vertaisarvioitu alkuperäisartikkeli tieteellisessä lehdessä
Collinearity of points on Poincaré unit disk and Riemann sphere
Tekijät: Fujimura, Masayo; Rainio, Oona; Vuorinen, Matti
Kustantaja: Institute of Mathematics, University of Debrecen
Julkaisuvuosi: 2024
Journal: Publicationes Mathematicae Debrecen
Tietokannassa oleva lehden nimi: Publicationes Mathematicae Debrecen
Vuosikerta: 105
Numero: 1-2
Aloitussivu: 141
Lopetussivu: 169
ISSN: 0033-3883
eISSN: 2064 - 2849
DOI: https://doi.org/10.5486/PMD.2024.9763
Verkko-osoite: https://doi.org/10.5486/PMD.2024.9763
Rinnakkaistallenteen osoite: https://arxiv.org/abs/2212.09037
Preprintin osoite: https://arxiv.org/abs/2212.09037v1
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 Gröbner bases from computer algebra for the solution of polynomial equations.
Julkaisussa olevat rahoitustiedot:
The first author was partially supported by JSPS KAKENHI (Grant No. JP19K03531), and the second author was supported by Finnish Culture Foundation and Magnus Ehrnrooth Foundation.
