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

Year 2023, Volume: 16 Issue: 1, 272 - 282, 30.04.2023

Lyudmila N. Romakina

https://doi.org/10.36890/iejg.1270550

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

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