Squaring the Circle — Approximate Method
Baudhayana Sulba Sutra · 2 · Verse 9
kalpasulbabaudhayanasquaring-circlepiapproximationancient-mathematics
Sanskrit Original
वृत्तं चतुरश्रं चिकीर्षन् — विष्कम्भमष्टौ भागान् कृत्वा। एकं भागमपोह्याष्टाविंशत्याऽपि तद् भागस्य। चतुर्थोऽष्टभागः शिष्यते — समचतुरश्रं भवति॥
vṛttaṃ caturaśraṃ cikīrṣan — viṣkambham aṣṭau bhāgān kṛtvā | ekaṃ bhāgam apohyāṣṭāviṃśatyā'pi tad bhāgasya | caturtha'ṣṭabhāgaḥ śiṣyate — samacaturaśraṃ bhavati ||
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To square a circle: divide the diameter into 8 parts, subtract 1 part, then subtract 1/29 of that part, and subtract 1/4 of that result. The remaining value gives the side of the equivalent square. This is Baudhayana's approximation — it gives π ≈ 3.088, a remarkable early approximation.