\textit{Sangaku} problems about ellipses: why primary sources matter (Q2094396)

In this paper, the author studies some interesting problems regarding the Sangaku problems for ellipses. As the author remarks, because the Japanese thought of ellipses as sections of cylinders, they naturally understood the affine relationship between the diameters of cylinders and the axes of an ellipse based on it, and they relied heavily on this knowledge to solve problems. Four discussions are presented by the author and this cases can be thought of as short case studies that illustrate the difference between the Japanese approach and more modern ones. Using the affine geometry, an interesting problem is presented. More exactly, the problem of inscribed ellipses in parallelograms. The Japanese often applied affine transformations method to take ellipses to circles and vice versa. The paper is interesting not only from the history of mathematics viewpoint but also from the affine and analytical geometry point of view.