Determining the Qibla Direction by Astronomical and Geometrical Methods
Duaa Abdullah
TL;DR
The paper surveys historical and modern methods for determining the Qibla direction, contrasting folk astronomical practices with systematic geometric and trigonometric approaches. It presents compass- and astrolabe-based methods, formalizes Qibla azimuth calculations via spherical trigonometry and vector-based formulations, and demonstrates a C++-based computational model for real-time application. The work synthesizes geometric constructions, spherical-trigonometry formulas, and algorithmic implementation to provide precise Qibla guidance, bridging Islamic astronomical heritage with contemporary computation. Its practical contributions include explicit methods, derivations, and a portable program suitable for mobile use, advancing accurate Qibla determination across diverse locations.
Abstract
This paper investigates the determination of the Qibla direction using both astronomical and geometrical approaches. The study reviews historical and classical methods employed by Muslim scholars and astronomers including the use of instruments such as the astrolabe and compass. It further explores spherical trigonometry techniques to precisely calculate the Qibla azimuth from any given location on Earth. The research clarifies geometric constructions and presents a computational model implemented in C++ to facilitate accurate Qibla determination. This interdisciplinary analysis underscores the rich tradition of Islamic astronomy and geometry in solving practical religious requirements, providing both theoretical frameworks and practical algorithms for modern application.