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 wereSome of the results presented in this paper derive from a research carried out during the summer of 2001 and presented at the conference “ From Image to Action: The Function of Tu-Representations in East Asian Intellectual Culture ”, Paris, September 3–5, 2001. The preprint handed out during the conference can be found at http://halshs.ccsd.cnrs.fr/halshs-00000103, with the slight difference that I added to it references to illustrations that I presented at the time, but have not yet put online. Due to personal circumstances, I have not yet published the results and the arguments underlying them. These results benefited from the contributions made by participants in the seminar I organized in Paris between 1996 and 2002 on mathematical diagrams, within the framework of my project “History of Science, History of Text.” I am grateful to Michela Bussotti for the fine remarks she communicated to me at the time on the preprint I circulated. I also express my thanks to the anonymous referees and the participants of the workshop « Specialized Knowledge in Traditional East Asian Contexts », organized by Kim Yung Sik (June 2009, Yang Ming University, Taipei) for their perceptive comments. Rachel Rudolph played a key part in preparing the final version of the article. My heartfelt thanks to her and to Dirk Schlimm.included in the texts themselves and hence articulated with the discourse on the surface of the page. Moreover, the extension of what could be represented in a tu 圖 increased tremendously. However, as I show in part II of this paper, in the thirteenth century, several traditions must be distinguished, regarding the nature of tu 圖and the way in which they were integrated into the text. Moreover, part II shows that despite this break in the nature of tu 圖, some thirteenth century mathematicians inherited ways of working with tu 圖from earlier times. I argue that this occurred within the framework of a specific mathematical domain, that is, a given subtradition. The mathematicians operating within this framework brought into play the same markers (colors, characters) for areas and adapted the operations onto paper. However, what is most interesting is that they made use of these traditional ways of working with figures while bestowing new mathematical meanings upon them. This thus presents an interesting case of continuity and rupture within a given tradition. All these uses of figures, in their variety, are specific to China and differ from the way in which other traditions used figures in mathematics.