# Śulbasūtras

**Type:** Work  
**Domain:** Indian Mathematics  
**Composed:** c. 800–200 BCE  
**Language:** Sanskrit (sūtra style — brief, aphoristic rules)  
**Codex URL:** /mathematics/indian-mathematics/sulbasutras/  
**Entry status:** Live — v1.0 (2026-05-27)

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## Summary

Sanskrit geometric manuals for constructing Vedic fire altars. The Baudhāyana Śulbasūtra (c. 800 BCE) explicitly states the Pythagorean theorem and lists specific Pythagorean triples (3,4,5), (5,12,13), (8,15,17), (7,24,25), (12,35,37). Contains √2 ≈ 577/408 accurate to 5 decimal places. Methods for combining, transforming, and doubling geometric areas.

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## Key texts

| Text | Date | School |
|------|------|--------|
| Baudhāyana Śulbasūtra | c. 800–600 BCE | Taittirīya |
| Āpastamba Śulbasūtra | c. 600–450 BCE | Taittirīya |
| Kātyāyana Śulbasūtra | c. 300–200 BCE | Śukla Yajurveda |
| Mānava Śulbasūtra | c. 600–300 BCE | Maitrāyaṇīya |

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## Pythagorean theorem (BSS 1.12)

"The cord stretched along the diagonal of a rectangle produces an area which the vertical and horizontal sides together produce." Stated ~200+ years before Pythagoras.

## √2 approximation (BSS 1.61–62)

√2 ≈ 1 + 1/3 + 1/(3·4) − 1/(3·4·34) = 577/408 ≈ 1.4142156 (actual: 1.4142135)

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## Sources

### Tier 1
- Plofker, K. (2009). *Mathematics in India*. Princeton University Press. pp. 17–39.
- Sen, S.N. and Bag, A.K. (1983). *The Śulbasūtras*. Indian National Science Academy.

### Tier 2
- Hayashi, T. (2003). Indian mathematics. In *Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences*. Johns Hopkins. pp. 118–130.

### Tier 3
- Joseph, G.G. (2011). *The Crest of the Peacock*. 3rd ed. Princeton University Press. pp. 229–240.

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*Mathematics Codex entry v1.0 — added 2026-05-27 — thecodex.expert/mathematics/*