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Journals / International Electronic Journal of Geometry / 2026 / Volume: 16 Issue: 1

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

Lyudmila N. Romakina(Saratov State University)0000-0002-3695-2076
Pages
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Publication Date
2023-04-30
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

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.

📌 3 Key Takeaways

🎯
Objective & Hypothesis: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.
📊
Key Findings & Data: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.
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Conclusion & Impact: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.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Extended hyperbolic space · hyperbilic space · hyperbolic space of positive curvature

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.

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Cite This Article

Romakina, L. N. (2023). Coordinates of the Midpoint of a Segment in an Extended Hyperbolic Space. International Electronic Journal of Geometry, Volume: 16 Issue: 1. https://doi.org/10.36890/iejg.1270550

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