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Authors: Harish Chandra Rajpoot
In this paper, the principal geometric parameters of a spherical triangle are derived using elementary geometry and trigonometry. The resulting formulae are practical and straightforward to apply for computing key quantities such as the solid angle subtended at the center, the covered spherical surface area, and the interior angles. The analysis is further extended to the corresponding plane triangle obtained by joining the vertices of the spherical triangle with straight line segments, allowing for the evaluation of its geometric parameters. In addition, the derived relations are applied to the right pyramid formed by connecting the vertices of a spherical triangle to the center of the sphere, enabling analytical computation of parameters such as the normal height, angles between consecutive lateral edges, and the area of the base.
Comments: 11 Pages, 3 Figures
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[v1] 2026-02-22 21:45:57
Unique-IP document downloads: 74 times
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