《孫子算經卷中》 "Sun Tzŭ's Computational Classic: Volume II"
§15. Dividing a cube into smaller cubes

This section gives a worked example of computing the number of smaller cubes which make up a bigger cube.

The relevant unit conversion for length is

1 \unit{rule~(尺)} = 10 \unit{inches~(寸)}.

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
今有木方三尺、欲方五寸作枕一枚。問得幾何。 Suppose there be [a] wooden cube [of edge] three rules, [and we] wish [that each] cube [of edge] five inches [thereof] construct one pillow. [We] ask, how many result?
  • Version B and Version C have 高三尺 after 木方三尺.
  • 枚

    Classifier, omitted in the English.

答曰、二百一十六枚。 Answer saith: two hundred [and] sixteen [pillows].
術曰、置方三尺、自相乘、得九尺。以高三尺乘之、得二十七尺。 Method saith: put [down the] cube's [edge] three rules, [which], multiplied with itself, resulteth in nine rules. Multiplying it by [the] height three rules, resulteth in twenty-seven rules.
以一尺木八枕乘之、即得。 Multiplying it by eight pillows of [each] one rule of wood, [we] are done.
  • 一尺： one rule

    This is a cubic rule, as are the 27 rules above.

  • In modern notation, the number of pillows is
    (3 \unit{rules})^3 \times \frac{8}{1 \unit{rule}^3} = 216,
    where we have used the fact that 1 \unit{rule} = 2 \times 5 \unit{inches}, and that 2^3 = 8.

Cite this page

Conway (2023). "Sun Tzŭ's Computational Classic: Volume II §15". <https://yawnoc.github.io/sun-tzu/ii/15> Accessed yyyy-mm-dd.