Bisecting the trapezoid: tracing the origins of a Babylonian computation of Jupiter's motion
The author published his discovery of the use of trapezoid figures by Babylonian astronomers for calculating the position of the planet Jupiter in his work [Science 351, No. 6272, 482--484 (2016; Zbl 1355.01005)]. In the current article, he takes a more general approach. After briefly introducing the astronomical tablets discussed in his earlier article, he gives a systematic description of the Babylonian mathematical problem texts on trapezoids, which are attested already in Old-Babylonian times (first half of the second millennium BC). Usually, the area of a trapezoid is computed first; different algorithms can be found for right-angled and non-right-angled trapezoids. Furthermore, there are two algorithms for bisection (i.e., dividing into two parts of equal area) documented; the author proposes the existence of two more which could have been the basis for the calculation of Jupiter's motion found in astronomical texts. In a small group of astronomical procedure texts, the displacement of Jupiter is computed with the help of a trapezoid. The daily displacement is assumed to change linearly; for a given time span, the values of the first and last displacement are envisaged as the two parallel sides of a trapezoid; their average is multiplied by the number of days (which corresponds to the length of the trapezoid) to arrive at the total distance traveled. In an appendix presenting transliterations of the texts, the author several times offers improvements on earlier treatments.
scientific article; zbMATH DE number 6882224
scientific article