The Origins of the Decimal Point: Tracing Back to Giovanni Bianchini in the 15th Century
Some inventions are so ingrained in our daily lives that we often forget someone had to come up with them. One such invention is the decimal point, a crucial symbol in our numerical system. But have you ever wondered who first introduced this revolutionary concept? According to a recent paper by Glen Van Brummelen, a Professor of Mathematical Sciences at Trinity Western University, the origins of the decimal point can be traced back to Giovanni Bianchini in the 15th century.
Previously, it was believed that the earliest appearance of the decimal point was in Christopher Clavius’s Astrolabium in 1593. However, Van Brummelen challenges this notion and argues that Clavius was not the true originator of the decimal point. Instead, he credits Giovanni Bianchini, a Venetian merchant and administrator for the d’Este family, for introducing this significant mathematical concept.
Although Bianchini was not a renowned mathematician, he demonstrated an interest in mathematics through a short paper on geometry he wrote in the 1440s. In this paper, he used an instrument called a biffa to develop an equivalent to the metric system. He divided a line into ten equal parts called “untie,” which were further divided into ten parts called “minuta.” Bianchini’s treatise stood out not because he was the first to use decimal expansion, but because of the particular notation he employed – a small dot to separate whole units from fractional parts.
Van Brummelen highlights Bianchini’s notation as a significant breakthrough. In his paper, Bianchini referred to lengths that required more than one unit of measurement and named each unit accordingly. However, when it came to multiplication, division, and extracting roots, Bianchini abbreviated the representation using his decimal notation. For instance, he represented the quantity 746 secunda as “.746.” This innovative approach to notation caught the attention of influential mathematician astronomers, including Clavius and Johannes Müller von Königsberg, also known as Regiomontanus.
Regiomontanus learned from Bianchini and adopted many of his innovations, further expanding on the paradigms established by Bianchini. On the other hand, Clavius’s use of the decimal point in an interpolation column in a Sine table can be explained by his access to Bianchini’s work. Clavius had copied the structure of Bianchini’s Sine table, which explains why he introduced the decimal point in that particular context but never used it again.
While Bianchini’s contribution to the development of the decimal point may seem like a small footnote in history, it played a crucial role in shaping our numerical system. Van Brummelen’s research sheds light on this often overlooked aspect of mathematical history and highlights the significance of Bianchini’s notation.
The paper by Glen Van Brummelen, published in the journal Historia Mathematica, invites us to appreciate the origins of the decimal point and recognize the contributions of Giovanni Bianchini, a Venetian merchant whose mathematical innovations continue to impact our lives centuries later.