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

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International Electronic Journal of Geometry
Volume:16 Issue:1
Coordinates of the Midpoint of a Segment in an Extended Hyperbolic Space

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

Pages : 272-282

View : 73 | Download : 11

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

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