Baudhāyana: The Pythagorean Theorem
Written in Sanskrit — 800 BCE
Pythagoras of Samos was born around 570 BCE. The theorem that bears his name states that in a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides (a² + b² = c²). For most of the world's students, this theorem has one name and one origin.
The Baudhāyana Śulbasūtra, composed approximately 800 BCE — 230 years before Pythagoras was born — contains the following statement: "The diagonal of a rectangle produces [an area] which both the vertical side and the horizontal side produce together." This is the Pythagorean theorem. Written in Sanskrit. As a practical geometric rule for constructing fire altars.
The Śulbasūtras (sutras of the cord) are a class of ancient Indian texts that provide geometric rules for constructing Vedic fire altars (yajñavedi) in precise shapes and areas. They are applied geometry of the highest order — and they contain mathematics that the Western world would not independently arrive at for centuries.
The Actual Text — Baudhāyana Śulbasūtra 1.12
दीर्घचतुरश्रस्याक्ष्णया रज्जुः पार्श्वमानी तिर्यङ्मानी च
(dīrghacaturaśrasyākṣṇayā rajjuḥ pārśvamānī tiryaṅmānī ca yatpṛthagbhūte kurutastadubhayaṃ karoti)
"The diagonal of a rectangle produces [an area] which both the vertical and horizontal sides produce together."
This is the Pythagorean theorem in Sanskrit, dated to approximately 800 BCE. The text continues to give specific Pythagorean triples: 3-4-5, 5-12-13, 8-15-17, 12-35-37 — all integer solutions to a² + b² = c², listed for practical use in altar construction.
Source: Baudhāyana Śulbasūtra 1.12, translated by Bibhutibhushan Datta, The Science of the Śulbas, Calcutta University Press (1932)
Baudhāyana's Value for √2
The Baudhāyana Śulbasūtra also gives a rational approximation for √2 in the context of converting a square to a circle of equal area:
√2 ≈ 1 + 1/3 + 1/(3×4) − 1/(3×4×34)
= 1.4142156...
Correct value: 1.41421356...
This approximation is accurate to five decimal places — far more precise than what was needed for practical altar construction, suggesting that Baudhāyana was pursuing mathematical accuracy as a goal in itself.
Source: Kim Plofker, Mathematics in India, Princeton University Press (2009), p. 18
"The Śulbasūtras contain a great deal of mathematics. They provide rules for constructing geometric shapes, for transforming one shape into another of equal area, and for computing square roots with remarkable precision."
— Kim Plofker, Mathematics in India, Princeton University Press (2009)
Sources
- • Baudhāyana Śulbasūtra, translated by Bibhutibhushan Datta, The Science of the Śulbas, Calcutta University Press (1932)
- • Kim Plofker, Mathematics in India, Princeton University Press (2009)
- • George Gheverghese Joseph, The Crest of the Peacock, Princeton University Press (2011)
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