Mathematics & Computer Science
Infinite series for pi, sine and cosine
c. 1340-1425 CEMadhava of Sangamagrama (Kerala School)Works via Nilakantha's Tantrasangraha; Jyeshthadeva's YuktibhasaUttar Pradesh
1340
Power-series expansions for arctangent, sine and cosine, and a series for pi (the 'Madhava-Leibniz' series).
- Dated
- 1340–1425
- As scholars put it
- c. 1340-1425 CE
- Originator
- Madhava of Sangamagrama (Kerala School)
- Source text
- Works via Nilakantha's Tantrasangraha; Jyeshthadeva's Yuktibhasa
- Region
- Uttar Pradesh
- Discipline
- Mathematics & Computer Science
- Evidence
- Documented
- Confidence
- High
- Verification
- Verified-web
Meanwhile in the West
Rediscovered in Europe by Gregory, Newton and Leibniz.
Fair to say
The Kerala School did not build a full calculus with a general theory of limits; it produced specific series and convergence insights.
Path to modern innovation
These are the seeds of calculus and modern analysis.
1340Infinite series for pi, sine and cosine
1530Builds on
Transmission
Independent European rediscovery ~250-300 years later; no proven transmission, though contact via Jesuits is debated.
Primary sources
References
- 1Yuktibhasa (c.1530)
- 2Plofker (2009)
- 3Joseph, The Crest of the Peacock
Further reading
Corrections and additional sources: edit IND-005 on GitHub.