Fractional decimal notation uses a decimal point (in some places a comma is used) to separate the integer part from the fraction of a quantity. However, the origins of this notation are not entirely clear and have remained obscure for a long time.

Recently, researchers have shed new light on this subject, allowing tracing the evolution of this system from its early appearances in the fifteenth century.

One of the first people to use a fractional decimal system was the Italian mathematician and astronomer Giovanni Bianchini in the mid-fifteenth century. In one of his treatises on metrology called Compositio instrumenti, Bianchini introduced a notation for measurements that divided the foot into ten parts called untie, which were in turn divided into ten parts called minuta.

By representing distances decimally using points to separate the units, Bianchini effectively created one of the first known fractional decimal systems.

Later, Bianchini extended the use of this decimal system to his works on spherical astronomy, highlighting his text Tabulae primi mobilis. In it, he used sine tables with a radius of the base circumference of 120,000, which implied decimal values.

In addition, his interpolation columns contained two numbers separated by a space or period, anticipating calculations with fractional decimal notation. In this way, Bianchini profoundly transformed mathematical astronomy by introducing a decimal arithmetic system.

Another key figure influenced by Bianchini’s work was the humanist astronomer Regiomontanus. Although the latter only partially adopted Bianchini’s innovations, he contributed to their dissemination by publishing works such as his Astronomical Tables. However, fractional decimal notation did not become widely adopted at that time.

Nearly a century and a half later, the German Jesuit Christopher Clavius unexpectedly reintroduced the decimal point in a sine table contained in his work The Astrolabe of 1593. Like Bianchini, Clavius used the point to separate numbers in interpolation columns, demonstrating skill in decimal calculations. However, Clavius did not further develop the system, and it fell into oblivion again.

Thanks to recent research, it has been established that Clavius borrowed the structure and decimal notation from Bianchini’s tables, which he surely had access to. Thus, it was Bianchini and not Clavius who actually introduced the decimal point in Europe in the mid-fifteenth century. However, due to the limited following of his works, the origin of this crucial notation remained unknown for a long time.

This finding sheds new light on the evolution of the fractional decimal system and the decimal point specifically. Additionally, it reveals the importance of lesser-known figures like Bianchini in the development of fundamental mathematical concepts for modern science.


Sources

Glen Van Brummelen, Decimal fractional numeration and the decimal point in 15th-century Italy. Historia Mathematica, doi.org/10.1016/j.hm.2024.01.001


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