It has been known since antiquity that the trigonometric chords or sines of certain arcs or angles can be determined with geometric exactitude, while others can be computed only approximately. In particular, the chord or sine of any integer multiple of three degrees, or of any angle derived from any such multiple by repeated bisection, can be found exactly. But because of the theoretical impossibility of trisecting an angle under Euclidean constraints, it is not possible to construct exactly the chord or sine of one degree. However, those very quantities were necessary for mathematicians to produce tables of trigonometric functions. In this talk we sketch the history of mathematical techniques for computing the sine of one degree that were described in Arabic, Persian, Sanskrit and European sources.
SPEAKERS: Clemency Montelle (University of Canterbury), Kim Plofker (Union College), and Glen Van Brummelen (Trinity Western University)