According to multiple sources the following problem would be found in Suanfa tong zong (like on cut-the-knot)

Two reeds of equal height project 3 syaku above the surface of a pond. If we draw the top of one reed 9 syaku in the direction of the shore so that the top is just touching the surface of the water, find the depth of the pond.

(Cut-the-knot claims the book contains the illustration, but another source claims the illustration is Japanese)

Anyhow: I assume Syaku would be an ancient Chinese unit of measurement. But I couldn't retrieve any information on this unit. How is it defined, how much would 1 syaku be in modern units of measurement?

I tried digging up the original problem, but when searching for the original (or any later reprints) I get stuck on the Chinese symbols. Could anyone help me out?

Not sure if "Chinese Language" is the right place for this question. I've been thinking about or "History of Science and Mathematics", but I think the probability of someone owning "Suanfa tong zong" would be the greatest here (?)

  • 1
    Are you certain it's Chinese? Syaku could be referring to Shaku (unit) (Syaku and Shaku are likely different romanisations of the same word in Japanese). It could also very well be referring to Chi (unit), which is where Shaku is supposedly derived from (but apparently a different unit). Both units are around 30-33cm.
    – tangrs
    Commented Jan 24, 2021 at 12:46
  • Well, according to the sources, this would be a translation from the Chinese book "Suanfa tong zong". But I'm not able to find a original source... It might be that it got translated into Japanese (and with the units adjusted), which then later was translated as above.
    – dietervdf
    Commented Jan 24, 2021 at 13:33

1 Answer 1


I believe this is the original text:


It also comes with the following, hard to read, illustration:

enter image description here

This is the measure word you're asking about:


a Chinese foot / one-third of a meter / a ruler / a tape-measure / one of the three acupoints for measuring pulse in Chinese medicine / CL: 支, 把


1 chi; Chinese foot (a traditional Chinese unit of distance based on the human forearm and equal to 10 cun (寸) or 1/10 zhang (丈))
2 (Mainland China) mainland chi; Chinese foot, standardized in 1984 as 1/3 meter
3 (Taiwan) Taiwanese foot, standardized as 10/33 meter and identical to the Japanese shaku
4 (Hong Kong) chek; Hong Kong foot, standardized as 0.371475 meters
5 (informal) imperial foot
6 ruler (straightedge) (Classifier: 把)
7 tape measure

Japanese Shaku is also:

10/33 meter

  • Wow, that is amazing! Thank you very much!
    – dietervdf
    Commented Jan 24, 2021 at 19:25

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