A Vector-Algebraic Reconstruction of the Medieval Arab Formula for the Shadow of a Gnomon

2025/10/14 by Fabrizio Patuzzo, Patuzzo, Fabrizio · 1 voice
Arts and Humanities · Mathematics · Physics and Astronomy · #FOS: Mathematics #Historical Astronomy and Related Studies #Historical, Religious, and Philosophical Studies #History and Overview (math.HO) #History and Theory of Mathematics #math.HO

paper · pdf · doi:10.48550/arxiv.2510.12913

openalex publication_date 2025/10/14 · arxiv published 2025/10/14 · arxiv updated 2025/10/14 · openalex created_date 2025/10/17 · openalex updated_date 2026/07/28

Abstract

We present a modern reconstruction of the classical formula, first derived by medieval Arab astronomers, that describes the trajectory of the tip of a gnomon's shadow during the day as a function of latitude, solar declination, and gnomon height. Unlike the traditional derivations based on spherical trigonometry, our approach uses only elementary vector algebra and rotation matrices. The same vector framework naturally extends to other classical relations used in sundial construction.

Discussions

• Fabrizio Patuzzo: A Vector-Algebraic Reconstruction of the Medieval Arab Formula for the Shadow of a Gnomon https://arxiv.org/abs/2510.12913 https://arxiv.org/pdf/2510.12913 https://arxiv.org/html/251 [bsky, 0 points, 0 comments]

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