The use of decimals is 1.5 centuries older than historians believe.

From Bianchini’s “Composition of Instruments.” Reproduced with permission from the Biblioteca Estense di Modena (Cod. Lat. 145, f. 7r). Credit: History of Mathematics (2024). DOI: 10.1016/j.hm.2024.01.001

A historian of mathematics at Canada’s Trinity-Wester University has found that the decimal was used by a Venetian merchant 150 years before the use of the German mathematician Christopher Clavius. In his paper published In the journal History of MathematicsGlen Van Brummelen describes how he found evidence of the use of decimals in a volume called “Tabulae” and its importance in the history of mathematics.

The invention of the decimal point led to the development of the decimal system, and as a result it became easier for people working in many fields to calculate fractions as easily as whole numbers. Before this new discovery, the earliest use of decimals was by Christopher Clavius ​​when he was making astronomical tables—the resulting work was published in 1593.

This new discovery was made in a section of a manuscript written by Giovanni Bianchini in the 1440s—Van Bremlin was discussing a section of trigonometric tables with a colleague when he noticed that some of the numbers had a dot in the middle. is also included. An example was 10.4, which Bianchini then multiplied by 8 in the same way as is done with modern arithmetic. The finding shows that a decimal to represent non-whole numbers occurred about 150 years earlier than previously thought by historians of mathematics.

Giovanni Bianchini worked as a merchant in Venice for several years, before being appointed to a management role with a large estate owned by the powerful d’Este family. In this role, he also managed assets and investments, giving him a strong background in mathematics. He also published works on astronomy, demonstrating his ability to plot planetary motions and predict solar eclipses.

The findings suggest that Bianchini played an increasingly important role in the development of the fundamental principles of mathematics. Von Bromlein notes that, as a merchant, Bianchini would have traveled widely, including to places in the Islamic world where mathematical concepts were being developed, possibly because of his use of non-whole numbers and their influenced the ways of easily representing

More information:
Glen Van Brummelen, Decimals and the Decimal Point in 15th-Century Italy, History of Mathematics (2024). DOI: 10.1016/j.hm.2024.01.001

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