The Axes of Mathematical Methodology in the Song and Yuan Dynasties: The Construction of Mathematical Models
Comparative researches between eastern and western mathematics of ancient and mediaeval times revealed that there are two major activities of mathematics, that is, theorem-proving and equation-solving. Theorem-proving mainly originated from Greek mathematics, meanwhile, equation-solving was an important content of Chinese mathematics. The fact seems to lead to the conclusion that Chinese mathematics was basically based on the practical problems, and in the mean time European one on geometrical problems. Based on analyses of Chinese mathematical works, the author of the present paper argues that Chinese mathematicians paid more attentions to the design and the construction of their geometrical models different from those introduced in living practices, in particular, in the 13–14th centuries. Using their geometrical models, they constructed their mathematical contexts and problems to meet their needs in displaying their mathematical ideas and in breaking through the limitation of practical problems. The research style of Chinese mathematics, therefore, changed in some way and strengthened its theoretical aspect.
KeywordsPractical Problem Mathematical Problem Yuan Dynasty Mathematical Context Inscribe Circle
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