Fractions in the Suan Shu Shu (China, Beginning of the 2nd Century BCE)

TL;DR

This paper thoroughly analyzes the diverse representations of fractions in the ancient Chinese text Suan Shu Shu, highlighting the linguistic structures and syntax used for expressing fractions around the 2nd century BCE.

Contribution

It provides a complete description of the different forms and syntactic structures of fractions in the Suan Shu Shu, including the use of predicative phrases and lexicalized forms.

Findings

Identification of mono-dimensional and bidimensional fraction forms

Description of the syntactic role of the morpheme zh{}i

Analysis of lexicalized fraction expressions like 1/3, 1/2, 2/3

Abstract

The Su{\`a}n Sh{\`u} Sh{\=u} contains 301 instances of regular expressions for fractions. They can be "mono-dimensional" (formed with one integer name only) for unit fractions, "bidimensional" (with two integer names) for both unit and non-unit fractions, or lexicalized only for 1/3, 1/2 and 2/3. The present paper gives a complete description of the diversity of these forms. Bidimensional expressions are predicative phrases: the name n f{\=e}n of a unit fraction 1/n acts as subject and the numerator's name as predicate; according to the syntactic context, the morpheme zh{\=i} can be used as an optional marker of this predicative relation.