Kerala, India · c. 1350-c. 1425
Madhava of Sangamagrama
Madhava of Sangamagrama was mathematician and astronomer. He developed infinite series for sine, cosine, arctangent, and pi within the Kerala school.
Biographical and historical reference works document Madhava of Sangamagrama’s role and the mathematical work summarized on this page.
9-12, College
The person and the work
Biography
Madhava of Sangamagrama was mathematician and astronomer associated with Kerala, India. He developed infinite series for sine, cosine, arctangent, and pi within the Kerala school.
Correction terms improved the practical accuracy of finite partial sums long before European calculus. Together, these contributions connect trigonometry 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
He developed infinite series for sine, cosine, arctangent, and pi within the Kerala school.
Method, teaching, or application
Correction terms improved the practical accuracy of finite partial sums long before European calculus.
Why this matters
The larger lesson
Madhava of Sangamagrama shows that mathematics grows through proof, calculation, observation, design, teaching, or careful records. The lasting lesson is that trigonometry and calculus and change can turn a difficult question into a method another person can inspect and reuse.
Place the work in time
Timeline
- c. 1350
Life and working period
Madhava of Sangamagrama worked as mathematician and astronomer in Kerala, India.
- Legacy
Lasting mathematical connection
Correction terms improved the practical accuracy of finite partial sums long before European calculus.
Key idea
Triangles connect angle, distance, and direction
Madhava of Sangamagrama’s work uses triangle relationships to turn observations into distances or positions that may be difficult to measure directly.
A right triangle with legs 6 and 8 has hypotenuse 10, a scaled 3-4-5 triangle.
Try it yourself
Complete a right triangle
A right triangle has legs 6 and 8. Find the hypotenuse.
- Square both leg lengths.
- Add the squares.
- Take the square root.
Show the answer
The hypotenuse is 10 because 6² + 8² = 10².
Math at work
Navigators and pilots use the same habits
Navigators and pilots use trigonometry to plan, compare, test, or communicate decisions. Madhava of Sangamagrama’s work provides a historical example of that connection.
Keep curiosity alive
A little-known fact
Correction terms improved the practical accuracy of finite partial sums long before European calculus.
Madhava of Sangamagrama matters because of only one famous formula or anecdote.
The documented record is broader: He developed infinite series for sine, cosine, arctangent, and pi within the Kerala school.
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