Decimal separator: Decimal numbers are 150 years earlier than expected

German mathematician and Jesuit priest Christopher Clavius Not only was he responsible for major parts of the reform of the Gregorian calendar in 1582, but he is also credited with the first use of the decimal separator as we know it today. In his nearly 900-page work “The Astrolabe,” which… Spherical astronomy Clavius, who rejected the Copernican worldview despite all his research until the end of his life, used a dot in the sine tables to separate pre-decimal and post-decimal places in a number.

This notation, which is still common today, has simplified many calculations and made them more efficient; Previously, using symbols such as rational numbers was relatively laborious. Having said that Clavius ​​was the first to consciously use the interval, it is surprising that this period does not appear again in any of his works.

Talented businessman

How could someone invent such a powerful computational system and then stop using it, let alone claim ownership of it? This is asking Glenn van Bromelen In his book, which was recently published in the specialized magazine “Historia Mathematica”. a job. A mathematics historian from Trinity Western University in Canada may now have an answer. It takes you 150 years into the past, to Italy, specifically to Ferrara.

A merchant of Venice lived there Giovanni Bianchini (ca. 1410 – 1469). He worked in the service of the ruling family at that time DestiBetween 1440 and 1460, the mathematically educated official also wrote several astronomical works.

Complex calculations

In Bianchini's time, astronomers used this in their calculations The sexagesimal systemWhich dates back to the Babylonians. The base of the number system is 60, not 10 as in the decimal system. It is still used today for lines of longitude and latitude because this basis is well suited for circles and angles. Other operations – such as simple multiplication – are very complex in this number system because they require analysis and intermediate calculations.

For traders at that time, calculations were not easy at all; Many measurements had inconsistent denominators, for example, a foot had twelve inches, but a yard had three feet.

Great idea

According to van Brummelen, Bianchini used a self-made decimal system for commercial calculations. However, there was no evidence that he also used such a system in his astronomical works – until recently, when the Canadian historian stumbled upon the decimal point while translating one of Bianchini's treatises (“Tabulae primi mobilis B”) from medieval Latin: there Clues He enters a number “with a dot in the middle” – 10.4 – and shows how to multiply it by 8.

“I realized he was doing it just like we do today,” van Brummelen told Nature News of his moment of realization. The core of the treatise was trigonometric tables, including the sine table – which scientists of the time used to calculate celestial orbits. The decimal point was used in the same context as Clavius ​​150 years later, van Brummelen explains. He must have almost taken over from Bianchini. Since then, the period or comma has become increasingly common. According to the historian, the new spelling was perhaps initially too revolutionary to be immediately understood. Sometimes it takes a while for a good idea to take hold.