# Interpreting Algorithms Written in Chinese and Attempting the Reconstitution of Tabular Setting: Some Elements of Comparative History

• Charlotte-V. Pollet
Chapter
Part of the Mathematics Education in the Digital Era book series (MEDE, volume 11)

## Abstract

The mathematics of 12th–14th-century China is known for its beautiful algebraic texts. Unfortunately, information concerning their context of transmission and instruction is scarce. One interesting pattern is that many of the texts share a predisposition for tabular setting and several of these texts refer to the same algebraic procedure named tian yuan 天元 (Celestial Source) used to set up polynomial equations. The setting of these equations on a counting surface is the result of a specificity of using counting rods for the algorithm of division. Precisely, the role of division for setting up and solving equations is fundamental to the algorithm. This chapter presents an excerpt borrowed from Li Ye’s 李冶 Yigu yanduan 益古演段 (the Development of Pieces [of Area according to the Collection] Augmenting the Ancient [Knowledge], 1259). It presents first a basic example of the Celestial Source procedure, then attempts reconstitution of polynomials on the counting surface and ends with comparative observations related to the chapter on the Bījagaṇitāvataṃsa (BGA) written by Nārāyaṇa in 14th-century India. The description of the algorithm for setting up a quadratic equation is interesting from a comparative perspective. The way in which lists of operations are ordered shows that Indian and Chinese authors had different interests, addressed different difficulties and understood mathematical concepts differently, while referring to division, using tabular setting and “model” equations.

## Keywords

Algorithm Division Algebra Song dynasty China Li Ye

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