Shedding some light on a possible origin of a concept of fractions in China.

Abstract

The article suggests that the mathematical manuscripts from the 3rd and 2nd century BCE recently excavated in China present a terminology for division that is not attested in the mathematical books in Chinese handed down through the written tradition. The only exception to this rule is The Gnomon of the Zhou, the oldest mathematical book handed down, which presents mathematics for the astral sciences and dates partly from ca. 100 BCE. The author argues the manuscripts and The Gnomon of the Zhou refer to a common algorithm for division, which is older than the algorithm to which the verb chu 除 refers and which the latter later replaced. She also puts forward the hypothesis that the concept of fraction with numerator and denominator attested to in the earliest extant mathematical writings in Chinese was tightly connected with this older algorithm.