A study on the content related to pi and calculating the area of a circle in Joseon-Sanhak

This study examines the characteristics of calculation methods for pi and area of a circle and examples of changes over time in the way they are interpreted and handled in Joseon-Sanhak.For this purpose, We analyzed four Joseon-Sanhak books, including <Muksajipsanbeop>, <Juseogwangyeon>, <Guiljip>, and <Gosasibiijip>, representing the late 17th and 18th centuries.The specific analysis results are as follows.First, all Joseon-Sanhak books recognized that precision can be adjusted by appropriately selecting approximations of various pi according to the situation, and they still placed emphasis on Gobeob() for convenience of calculation.Regarding the properties of pi, the ratio property that reveals the relationship between diameter and circumference and the approximation property due to infinity were relatively well revealed, but the remaining properties were recognized in a limited way.In addition, Joseon-Sanhak books were using various methods of calculating the area of a circle, and all methods of calculating the area of a circle contained a consistent logic of creating a rectangle with the diameter and circumference and then calculating the area in proportion to the area of the square.Meanwhile, from the late 17th century to the 18th century, cases of a gradual shift from calculation methods to strict mathematical logic related to circles were confirmed.Gujangmundab of <Juseogwangyeon> argue why all calculation methods for the area of circles are based on the area of squares, present numerical calculation results as the basis for comparing the precision of pi, and provide a general method for obtaining a more precise pi.The principles of Halwonsul were developed logically.These cases can be seen as a movement of change that seeks to reason and justify strictly logically.This change suggests that Joseon-Sanhak are advancing to a stage where they value mathematical precision beyond the practical purpose of simply applying calculation methods.