Approximation of π *_* Aryabhata worked on the approximation for pi (π) and may have come to the conclusion that π is irrational. In the second part of the Aryabhatiyam (gaṇitapāda 10), he writes: चतुराधिकं शतमष्टगुणं द्वाषष्टिस्तथा सहस्राणाम्। अयुतद्वयस्य विष्कम्भस्यासन्नो वृत्तपरिणाहः॥ caturadhikaṃ śatamaṣṭaguṇaṃ dvāṣaṣṭistathā sahasrāṇām ayutadvayaviṣkambhasyāsanno vṛttapariṇāhaḥ. 'Add four to 100, multiply by eight, and then add 62,000. By this rule, the circumference of a circle with a diameter of 20,000 can be approached.' *_* This implies that the ratio of the circumference to the diameter is ((4 100) × 8 62000)/20000 = 62832/20000 = 3.1416, which is accurate to five significant figures. *_* It is speculated that Aryabhata used the word āsanna (approaching), to mean that not only is this an approximation but that the value is incommensurable (or irrational). If this is correct, it is quite a sophisticated insight, because the irrationality of pi (π) was proved in Europe only in 1761 by Lambert. - Study24x7
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Approximation of π *_* Aryabhata worked on the approximation for pi (π) and may have come to the conclusion that π is irrational. In the second part of the Aryabhatiyam (gaṇitapāda 10), he writes: चतुराधिकं शतमष्टगुणं द्वाष...

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