China · fl. 3rd century CE
Liu Hui
Liu Hui was mathematician and commentator. His commentary on The Nine Chapters explained algorithms, justified procedures, and refined approximations to pi.
Biographical and historical reference works document Liu Hui’s role and the mathematical work summarized on this page.
3-5, 6-8, 9-12, College
The person and the work
Biography
Liu Hui was mathematician and commentator associated with China. His commentary on The Nine Chapters explained algorithms, justified procedures, and refined approximations to pi.
He used polygon doubling to approach the area and circumference of a circle. Together, these contributions connect arithmetic, fractions, ratios, and percentages, geometry and measurement, and calculus and change to the working problems, tools, and questions of the period.
Mathematical contribution
What this hero added or preserved
Core mathematical work
His commentary on The Nine Chapters explained algorithms, justified procedures, and refined approximations to pi.
Method, teaching, or application
He used polygon doubling to approach the area and circumference of a circle.
Why this matters
The larger lesson
Liu Hui shows that mathematics grows through proof, calculation, observation, design, teaching, or careful records. The lasting lesson is that arithmetic, fractions, ratios, and percentages, geometry and measurement, and calculus and change can turn a difficult question into a method another person can inspect and reuse.
Place the work in time
Timeline
- fl. 3rd century CE
Life and working period
Liu Hui worked as mathematician and commentator in China.
- Legacy
Lasting mathematical connection
He used polygon doubling to approach the area and circumference of a circle.
Key idea
An algorithm is a dependable sequence
Liu Hui’s work illustrates how a clear sequence of operations turns a difficult task into repeatable calculation.
Following multiplication before addition gives 6 × 5 + 18 = 48.
Try it yourself
Follow the operation order
Calculate 6 × 5 + 18.
- Multiply first.
- Add the remaining value.
- Check by estimating the size of the result.
Show the answer
6 × 5 = 30, and 30 + 18 = 48.
Math at work
Carpenters and builders use the same habits
Carpenters and builders use arithmetic to plan, compare, test, or communicate decisions. Liu Hui’s work provides a historical example of that connection.
Keep curiosity alive
A little-known fact
He used polygon doubling to approach the area and circumference of a circle.
Liu Hui matters because of only one famous formula or anecdote.
The documented record is broader: His commentary on The Nine Chapters explained algorithms, justified procedures, and refined approximations to pi.
Keep exploring
Connected learning paths
Practice these ideas
- AdditionPractice adding whole numbers, integers, and decimals.
- SubtractionPractice subtracting whole numbers, including results below zero.
- MultiplicationBuild multiplication fluency with basic facts and larger values.
- DivisionSolve division problems with whole-number and decimal answers.
- Fractions & DecimalsWork with fractions, decimals, percentages, and conversions.