Square Construction — Rope and Peg Method
Baudhayana Sulba Sutra · 1 · Verse 50
kalpasulbabaudhayanasquare-constructiongeometryrope-peg
Sanskrit Original
समचतुरश्रं चिकीर्षन् — यावत् कर्तुमिच्छति तावती रज्जुं चतुर्धा विभजेत्। तस्य त्रिभागेन पार्श्वं, तद्वर्गाद् अपरं वर्गं मुञ्चेत्। अक्ष्णया रज्जुः समचतुरश्रं करोति॥
samacaturaśraṃ cikīrṣan — yāvat kartum icchati tāvatī rajjuṃ caturdhā vibhajet | tasya tribhāgena pārśvaṃ, tadvargād aparaṃ vargaṃ muñcet | akṣṇayā rajjuḥ samacaturaśraṃ karoti ||
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To construct a square: divide the rope into four equal parts. Use three parts as the side; construct squares on side and hypotenuse separately — the diagonal gives you the perfect square. The Śulba Sūtras provide rope-and-peg constructions equivalent to the ruler-and-compass methods of classical Greek geometry.