A study on geometrical diagrams for 3-D objects in pre-modern East-Asian mathematical texts (The study of the history of mathematics 2017)

Abstract

In this paper, we discuss features of geometrical diagrams in different cultures, especially representations of 3-D objects in East Asia. There is no Chinese diagram in the first millennium or earlier that survives to this day. In the second millennium, there are some interesting features. In the first half of the second millennium, Chinese diagrams for 3-D objects are usually contextualised; in the second half, the diagrams became more abstract. Korean and Japanese mathematicians used very creative ways, such as parallel line segments or shadows, to draw 3-D objects. Japanese scholars also put a middle curve in a 2-D diagram to create the sense of the third dimension. For sangaku diagrams, they also put different colours on the two regions divided by the middle curve, as if those regions are different "faces".