Coordinates of the Midpoint of a Segment in an Extended Hyperbolic Space

Authors : Lyudmila N. ROMAKİNA

Pages : 272-282

Doi:10.36890/iejg.1270550

View : 13 | Download : 6

Publication Date : 2023-04-30

Article Type : Research Paper

Abstract :In this article, we find an analytical characteristic of the type of a line and derive the formulae for calculating the coordinates of the midpoints and quasi-midpoints of elliptic, hyperbolic, and parabolic segments in an extended hyperbolic space $H^3$ in the frame of the first type. The space $H^3$ we consider in the Cayley\\,--\\,Klein projective model as a projective three-dimensional space with an oval quadric $\\gamma$ fixed in it.
Keywords : Extended hyperbolic space, hyperbilic space, hyperbolic space of positive curvature, segment, midpoint, quasi midpoint