Al-Samaw’al’s Curious Approach to Trigonometry

Al-Samaw’al’s work Exposure of the Errors of the Astronomers contains a single numerical table, a highly unusual table of sines. In order to avoid the problem of approximating sin(1 degree), al-Samaw’al redefines the number of degrees in a circle from 360 to 480. In the accompanying chapter, al-Samaw’al criticizes his predecessors for deviating from geometrical precision and explains how his table is to be calculated. However, our analysis demonstrates that al-Samaw’al did not follow his own instructions, simply interpolating his entries from a traditional sine table.