Changes and Continuities in the Use of Diagrams Tu in Chinese Mathematical Writings (Third Century to Fourteenth Century) [I]

Abstract

This article aims at highlighting a radical change in the materiality of tu between the time when they were first mentioned in Chinese mathematical texts in the third century commentaries on Canons and the thirteenth century, from which there are abundant illustrations in treatises. Moreover, it intends to highlight that the meaning of the word tu 圖, as used in mathematical writings, greatly changed over the same time span. It argues that third century tu 圖 were material objects, cut in paper with squared-grid, and worked out in specific ways. They probably always displayed particular dimensions and only represented objects for plane geometry. Their areas, and not their points, were marked, and they were marked by characters or colors. Areas were cut into pieces and rearranged. Such is the contribution mathematical texts can offer for capturing the nature of tu for these early periods. In contrast to this, thirteenth century tu 圖 to which mathematical texts refer were East

The Diversity of Mathematical Cultures: One Past and Some Possible Futures

“…In summary, and in contrast to what later documents attest, the mathematical activity evidenced by our first cluster of writings is based on books containing only text and also on three types of object: rods, blocks and diagrams [5].…”

Different cultures of computation in seventh century China from the viewpoint of square root extraction

“…These sources will help us answer the questions raised above. 11 Karine Chemla discusses the use of diagrams, and how they changed, in Chinese mathematical writings, see (Chemla, 2010a). To me, many questions still need to be solved concerning the geometrical facets of the history of mathematics in China.…”