Approximate Value of √2 — Baudhayana
Baudhayana Sulba Sutra · 2 · Verse 12
kalpasulbabaudhayanasquare-rootsqrt2mathematicsapproximation
Sanskrit Original
समस्य द्विकरणी — प्रमाणं तृतीयेन वर्धयेत्। तच्चतुर्थेनात्मचतुस्त्रिंशोनेन — समासेत्। साविशेषः॥
samasya dvikaraṇī — pramāṇaṃ tṛtīyena vardhayet | tac caturthenātmacatustriṃśonena — samāset | sāviśeṣaḥ ||
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The diagonal of a square = side × (1 + 1/3 + 1/(3×4) − 1/(3×4×34)). This gives √2 ≈ 1 + 1/3 + 1/12 − 1/408 = 1.4142156... — correct to 5 decimal places. A remarkable rational approximation obtained by Baudhayana centuries before any Western mathematician.