Persia and Samarkand · c. 1380-1429
Jamshid al-Kashi
Jamshid al-Kashi was mathematician and astronomer. He calculated pi to many sexagesimal places, worked with decimal fractions, and produced highly accurate trigonometric values.
Biographical and historical reference works document Jamshid al-Kashi’s role and the mathematical work summarized on this page.
3-5, 6-8, 9-12, College
The person and the work
Biography
Jamshid al-Kashi was mathematician and astronomer associated with Persia and Samarkand. He calculated pi to many sexagesimal places, worked with decimal fractions, and produced highly accurate trigonometric values.
His Law of Cosines formulation was used for general triangles and astronomical computation. Together, these contributions connect arithmetic, fractions, ratios, and percentages, and trigonometry to the working problems, tools, and questions of the period.
Mathematical contribution
What this hero added or preserved
Core mathematical work
He calculated pi to many sexagesimal places, worked with decimal fractions, and produced highly accurate trigonometric values.
Method, teaching, or application
His Law of Cosines formulation was used for general triangles and astronomical computation.
Why this matters
The larger lesson
Jamshid al-Kashi shows that mathematics grows through proof, calculation, observation, design, teaching, or careful records. The lasting lesson is that arithmetic, fractions, ratios, and percentages, and trigonometry can turn a difficult question into a method another person can inspect and reuse.
Place the work in time
Timeline
- c. 1380
Life and working period
Jamshid al-Kashi worked as mathematician and astronomer in Persia and Samarkand.
- Legacy
Lasting mathematical connection
His Law of Cosines formulation was used for general triangles and astronomical computation.
Key idea
An algorithm is a dependable sequence
Jamshid al-Kashi’s work illustrates how a clear sequence of operations turns a difficult task into repeatable calculation.
Following multiplication before addition gives 7 × 5 + 3 = 38.
Try it yourself
Follow the operation order
Calculate 7 × 5 + 3.
- Multiply first.
- Add the remaining value.
- Check by estimating the size of the result.
Show the answer
7 × 5 = 35, and 35 + 3 = 38.
Math at work
Navigators and pilots use the same habits
Navigators and pilots use arithmetic to plan, compare, test, or communicate decisions. Jamshid al-Kashi’s work provides a historical example of that connection.
Keep curiosity alive
A little-known fact
His Law of Cosines formulation was used for general triangles and astronomical computation.
Jamshid al-Kashi matters because of only one famous formula or anecdote.
The documented record is broader: He calculated pi to many sexagesimal places, worked with decimal fractions, and produced highly accurate trigonometric values.
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.