China · c. 1010-c. 1070
Jia Xian
Jia Xian was mathematician. He developed methods for extracting roots and arranged binomial coefficients in a triangular array.
Biographical and historical reference works document Jia Xian’s role and the mathematical work summarized on this page.
3-5, 6-8, 9-12, College
The person and the work
Biography
Jia Xian was mathematician associated with China. He developed methods for extracting roots and arranged binomial coefficients in a triangular array.
The coefficient triangle was later explained and popularized by Yang Hui. Together, these contributions connect arithmetic and algebra and functions to the working problems, tools, and questions of the period.
Mathematical contribution
What this hero added or preserved
Core mathematical work
He developed methods for extracting roots and arranged binomial coefficients in a triangular array.
Method, teaching, or application
The coefficient triangle was later explained and popularized by Yang Hui.
Why this matters
The larger lesson
Jia Xian shows that mathematics grows through proof, calculation, observation, design, teaching, or careful records. The lasting lesson is that arithmetic and algebra and functions can turn a difficult question into a method another person can inspect and reuse.
Place the work in time
Timeline
- c. 1010
Life and working period
Jia Xian worked as mathematician in China.
- Legacy
Lasting mathematical connection
The coefficient triangle was later explained and popularized by Yang Hui.
Key idea
An algorithm is a dependable sequence
Jia Xian’s work illustrates how a clear sequence of operations turns a difficult task into repeatable calculation.
Following multiplication before addition gives 11 × 11 + 19 = 140.
Try it yourself
Follow the operation order
Calculate 11 × 11 + 19.
- Multiply first.
- Add the remaining value.
- Check by estimating the size of the result.
Show the answer
11 × 11 = 121, and 121 + 19 = 140.
Math at work
Engineers and architects use the same habits
Engineers and architects use arithmetic to plan, compare, test, or communicate decisions. Jia Xian’s work provides a historical example of that connection.
Keep curiosity alive
A little-known fact
The coefficient triangle was later explained and popularized by Yang Hui.
Jia Xian matters because of only one famous formula or anecdote.
The documented record is broader: He developed methods for extracting roots and arranged binomial coefficients in a triangular array.
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.
- Pre-AlgebraBridge arithmetic and algebra with integers, ratios, and equations.