Until 2023, the earliest known appearance of the decimal point was in the interpolation column of a table of trigonometric sines in Christopher Clavius’s Astrolabium (1593). This is a curious place to introduce such a significant new idea, and the fact that Clavius never exploited it in his later writings has remained unexplained. We can actually trace Clavius’s use of decimal fractional numbering and the decimal point to the work of Giovanni Bianchini (1440), whose decimal system was a distinctive feature of his calculations in spherical astronomy and metrology. While working with his astronomy required working with Bianchini’s decimal system, Regiomontanus only partially copied it. The rest of the European astronomical community followed Regiomontanus, and Bianchini’s system only reappeared with its revival by Clavius. In 2024, while researching late medieval and early Renaissance astronomy, Dr. Van Brummelen, dean of the Faculty of Natural and Applied Sciences at Trinity Western University, noticed an unexpected use of the decimal point in a sine table. While most mathematicians thought that the German Jesuit astronomer Christopher Clavius was the first to use the decimal point in a table showing triangular ratios in 1593, Dr. Van Brummelen discovered that Giovanni Bianchini, an Italian court astrologer, used the decimal point a century earlier. This early dating of the decimal point reveals the richness of medieval scientific activity, dispelling the popular notion that the Middle Ages were a period of intellectual stagnation.
