《孫子算經卷中》 "Sun Tzŭ's Computational Classic: Volume II"
§16. Side length of a square of given perimeter

This section gives a worked example of computing the side length of a square given its perimeter.

The relevant unit conversion for length is

1 \unit{pace~(步)} = 6 \unit{rules~(尺)}.

See Vol. I §1 (Units of length).

Translation

Chinese source text: Version A, Version B, Version C, Version D.
Unless noted otherwise, I follow the text from Version D, 《知不足齋叢書》本.

Source text Target text Notes
今有索長五千七百九十四步、欲使作方。問幾何。
答曰、一千四百四十八步三尺。		 Suppose there be rope of length five thousand seven hundred [and] ninety-four paces, [and we] wish to make [it] construct [a] square. [We] ask, how much [be its edge]?
Answer saith: one thousand four hundred [and] forty-eight paces [and] three rules.
術曰、置索長五千七百九十四步。以四除之、得一千四百四十八步、餘二步。 Method saith: put [down the] rope's length five thousand seven hundred [and] ninety-four paces. Dividing it by four, resulteth in one thousand four hundred [and] forty-eight paces, remainder two paces.
以六因之、得一丈二尺。以四除之、得三尺。 Multiplying it by six, resulteth in one rod [and] two rules. Dividing it by four, resulteth in three rules.
  • 因： multiplying

    As in times tables, 九因歌, "[the] Song of Nine Multiples".

通計、即得。 Calculating [the] total, [we] are done.
  • 通： total; lit. throughout
  • In modern notation, the side length of the square is
    \begin{aligned} \frac{5794 \unit{paces}}{4} &= 1448 \unit{paces} + \frac{2 \unit{paces}}{4} \times \frac{6 \unit{rules}}{\unit{pace}} \\[\tallspace] &= 1448 \unit{paces} + 3 \unit{rules}. \end{aligned}

Cite this page

Conway (2023). "Sun Tzŭ's Computational Classic: Volume II §16". <https://yawnoc.github.io/sun-tzu/ii/16> Accessed yyyy-mm-dd.