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Dergiler / 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
Sayfa
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Yayın Tarihi
2023-04-30
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

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 Maddede Bu Makale

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Amaç & Hipotez: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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Temel Bulgular & Veri: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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Sonuç & Katkı: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.
🔬Tür:Modelleme & Sayısal Simülasyon
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler: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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Bu Makaleye Atıf Yap

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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Kaynakça (15)

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  10. Romakina, L., Ushakov, I.: The Chaos game in the hyperbolic plane of positive curvature. In: Abstracts of Satellite International Conference on Nonlinear Dinamics $\&$ Integrability and Scientific School “Nonlinear days” (NDI\,--\,2022), June 27\,---\,July 1/2022, Yaroslavl, RUSSIA. YarSU, 86-88 (2022).
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