A remark on Chapple-Euler Theorem in non Euclidean geometry

2020/12/30 by Noda, Takeo, Yasutomi, Shin-ichi · 1 citation
#51M09 #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2101.01554

Abstract

In non-Euclidean geometry, there are several known correspondings to Chapple-Euler Theorem. This remark shows that those results yield expressions corredponding to the well-known formula d=√(R(R-2r)).

Cited by

• Egan conjecture holds

Related

• Non-Euclidean Pythagorean triples, a problem of Euler, and rational points on K3 surfaces
• An application of Pappus' Involution Theorem in euclidean and non-euclidean geometry
• ON CURVES AND TUBES IN ℝⁿ
• Non-euclidean shadows of classical projective theorems
• The Reciprocal of the Fundamental Theorem of Riemannian Geometry