On the theory of regular polygons in traditional Japanese mathematics: Reconstruction of the process for the calculation of the degree of \textit{Kaihōshiki} appearing in the \textit{Taisei Sankei} by Seki and Takebe brothers (Q2713746)

In this particularly interesting article, the author explains how the three Japanese mathematicians, authors of the unpublished mathematical manuscript \textit{Taisei sankei} -- Seki Takakazu and the two Takebe brothers, invented a new technique for the calculation of the area of regular polygons inscribed into a circle: while the older method previously used in Japan (and of course elsewhere) was dependent on Archimedean-like numerical calculations, they devised a general method based on the geometrical derivation of a polynomial having the length of the side of the sought polygon as one of its roots. A detailed reconstruction of the whole process and a specific example is given.