Counting-rod arrays
Arranging numbers in columns made it possible to multiply and subtract entire conditions systematically.
11 / ANTIQUITY TO THE RENAISSANCE
Liu Hui
Two purchases can tell you the prices of two kinds of grain. Make one part of the purchases match, then remove it.
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01 / ELIMINATION
Cancel what matches
A green sack and a copper sack have different prices. You know what two purchases cost.
Double one purchase so the green sacks match. Then everything that matches cancels, leaving one sack and its price. The counting-rod board beside it does the same, column by column.
What does each sack cost?
Two market purchases. Every green sack has one price; every copper sack has another.
Purchase totals:
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THE IDEAMultiplying a whole equation keeps it true. Subtracting two equations removes matching terms and leaves a simpler problem.
The person behind the ideas
- His commentary on the Nine Chapters dates to 263 CE.
- He explained why procedures work, including operations on counting-rod arrays.
- His work also developed geometric reasoning about areas, volumes and circles.
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Reasons behind rules
Liu Hui connected procedures to explanations, including geometric arguments for measurement.