## Difficult divisions

During Bianchini’s time, European astronomers used the hexadecimal system (base 60) that they inherited from the Babylonians. This hexadecimal system is still used today to write terrestrial and celestial latitudes and longitudes and can divide a full circle into 360 degrees, each degree into 60 minutes, and each minute into 60 seconds; But it is difficult to perform operations like multiplication with hexadecimal numbers. Astronomers need to convert a value to the smallest unit for this.

On the other hand, merchants and accountants had learned to calculate with actual scales and weights, based on which units were divided in various ways. For example, one foot equals 12 inches and three feet equals one yard. To simplify the calculations, Bianchini invented his decimal scheme and defined it as a system for measuring distances in which 30 cm is divided into ten equal parts called untie, each of which is divided into ten minutes (minuta) and then ten seconds ( secunda) are divided; But it was not previously thought that his passion for the ten-day basis would also affect his astrology.

However, according to a treatise called Tabulae primi mobilis B that Bianchini wrote in the 1440s, in some parts he not only used the decimal number system, but also used today’s decimal point.

Bianchini used the decimal point for the first time in the 1440s

Van Brumlen made this discovery while teaching high school math camp. One evening he was describing the Tabulae and trying to translate the Latin word Bianchini. Suddenly, he came across a text in which Bianchini introduced a number with a dot in the middle (10.4) and showed how to multiply it by the number 8. It was at that time that he realized that Bianchini used the decimal point just like today.

The key part of Bianchini’s text was actually a set of trigonometric tables, especially a sine table. Astronomers of that period used spherical trigonometry to calculate the position of celestial bodies on the surface of a sphere. Bianchini converted angles into minutes and seconds, but assigned decimal values of tenths, hundredths, and thousandths to sines, which were interpreted as distances.

Bianchini used a decimal separator to calculate the values between one input and the next number. It is clear that Clevis used the decimal point in exactly this way in 1593. Historians have always wondered why Clevis no longer mentions this innovation. This development was exactly in line with Bianchini’s extensive works. Van Brumlen concludes that Clevis probably inherited the decimal point from his predecessor and it is impossible that he did not know anything about Bianchini.

According to Sarah Hart, a historian of mathematics at the University of London, the beauty of the decimal point is that it makes calculating incorrect numbers as easy as integers. With the decimal checker, you can perform an operation on any number of any size.

Van Brumlen shows that Bianchini’s knowledge in the field of economics probably played an important role in ISIS; Because he did not work with base sixty like other astronomers from the beginning of his career. Rather, his approach was considered revolutionary from the very beginning. Understanding the function of expression required knowing a completely different system than arithmetic.

About a hundred and fifty years later, decimal representation was further developed. Astronomers worked with smaller subdivisions and devised several systems to simplify calculation. Clewis’s research influenced other researchers of decimal fractions, including the Flemish mathematician Simon Stephen, as well as the Scottish astronomer and inventor of the logarithm, John Napper.

Although Biancini’s invention was overshadowed by famous mathematicians after him, historians today must emphasize the importance of his work. The implications of his invention extended beyond astronomy. Decimal fractions inspired scientists to emphasize the nature of nature with greater precision and led to hypotheses that would not have been possible without the decimal point. Among these hypotheses, we can mention infinite decimal numbers that do not stop.

The emergence of the decimal point was based on previous developments, such as the spread of Indo-Arabic numbers to Europe a few centuries ago, and Leonardo Pisano, known as Fibonacci, is considered one of the most influential people in this process. Bianchini’s story shows the constant connection between practical needs, numerical systems and theoretical hypotheses, and also his famous decimal point changed our view of the world.