Tracing the Shadow: Mathematical Calculation of Prayer Times Using Spherical Trigonometry (original) (raw)

In this work, complex but not complicated spherical trigonometry functions were used to determine the Islamic prayer times. To the best of our knowledge, it is the first time that a mathematical modelling of the relative shadow height of objects at zenith time has been visually presented for each Julian day of the year in great detail; this is a requirement step for the end and beginning of Zuhr and Asr prayer times, respectively. For practical and proof-of-concept purpose – albeit its applicability to all locations without exception, the prayer times for the capital cities of the under-investigated region of East African countries i.e. Kenya, Somalia, Ethiopia and Djibouti were chosen as case studies for mathematical calculations and data interpretation in addition to Mecca as a benchmark. All the mathematical equations needed for the determination of the beginning for each prayer time were thoroughly reviewed. For data analysis, the widely available MS Excel programme was utilized...