The decimal point is 150 years older than historians thought, newly discovered observations from 15th-century Italy reveal.
Decimal points are so simple, they seem to have been around forever. These handy math tools break integers into tenths, hundredths, and thousandths, making calculations much easier than doing math with fractions. Some versions of decimals have been around since the 19th century (in Damascus) or the 12th century (in China).
But a consistent system of decimals was not fully established until 1593, when the German mathematician Christopher Clavius used decimals in an astronomical treatise. Now, new research suggests that Clavius was playing with an ancient tradition, adapting the use of decimals from a 15th-century Venetian merchant named Giovanni Bianchini.
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Bianchini's work dates from between 1441 and 1450, making the decimal point a century and a half older than Clavius's use of it, according to the authors of the new research.
While teaching math camp to middle school students, Glenn van BromelenA historian of mathematics at Trinity Western University in Canada noted the use of the decimal point in one of Bianchini's theses.
“I remember running up and down the halls of my dormitory on my computer trying to find anyone who was awake, shouting: ‘Look at this, this guy is doing decimal points in the 1440s!’” Van Brummelen said. Nature News.
The idea of dividing whole numbers into parts is very old, but most mathematicians before the Middle Ages used fractions. Astronomers have used decimals, but not in the familiar base 10 system that elementary school students learn today. Instead, they used base-60 decimal numbers, created by dividing 360-degree circles into 60 minutes, which could then be divided into 60 seconds.
Sometimes, mathematicians used symbols reminiscent of the current decimal system, van Brummelen wrote in a paper published online for the journal History of mathematics. But these ideas tended to fade away rather than spread from one mathematician to another.
“Thus, trying to identify a ‘first’ among this group of different players may be a fool’s errand, depending on one’s criteria for the historical actor’s level of appreciation for the power of operations with decimals and the persistence of their systems,” Van Bromelin wrote.
However, it is easier to determine the date with a decimal point a point — a symbol that persists to this day, he wrote. This notation first appeared in Bianchini's Tabulae primi mobilis B, a text on calculating stellar coordinates. Bianchini was a merchant who became the administrator of the ruling family of Venice at the time, the d'Este family. As part of this job, he was responsible for calculating horoscopes and astrology. In some tables in his text, he uses the decimal point just as mathematicians do today.
Although the blog post was slow to spread, Clavius knew about Bianchini, José Chabas, an astronomy historian at Pompeu Fabra University in Barcelona, Spain, told Nature News. Writers inspired by Clavius picked up the decimal point and ran with it. Finally, Scottish mathematician John Napier, inventor of logarithms, established the decimal point in mathematics in the early 17th century.
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