Noumerico: Journal of Technology in Mathematics Education
Vol. 4 No. 1 (2026): Noumerico, March 2026

Clifford's Algebraic Approach in Determining the Direction of Qibla

Muhamad Imam Mutamaqin (Unknown)
Muhamad Safa’udin (Unknown)



Article Info

Publish Date
31 Mar 2026

Abstract

While classical methods and hisab methods based on spherical trigonometry and vector algebra are commonly used, this article introduces a more elegant, purely geometric alternative using Clifford Algebra (within the framework of Geometric Algebra). This method uses unit vectors in three-dimensional space to represent the positions of the observer and the Kaaba, then projects these vectors onto the local horizontal plane using geometric operations such as the dot product and the outer product. The results of the Qibla direction calculations for five major cities in Indonesia—Jakarta, Surabaya, Medan, Bandung, and Makassar—when compared with the spherical trigonometry and vector algebra methods, show high consistency, with a maximum difference of less than 0°. Further validation using data from the Qibla Locator also confirms the method's accuracy. Clifford Algebra has proven to be an accurate, intuitive, and computationally efficient approach, with great potential for applications in digital navigation systems, augmented reality, and science education. Thus, this method offers a powerful modern alternative for determining the direction of the Qibla through hisab

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Journal Info

Abbrev

noumerico

Publisher

Subject

Computer Science & IT Education Mathematics Social Sciences

Description

The aim of this Journal is to promote a principled approach to research on technology in mathematics education and related concerns by encouraging enquiry into relationship between theoretical and practical studies. The journal welcomes contributions in such areas of current analysis in: 1. Use of ...