Aryabhatta’s Pi, π

π or Pi is a mathematical constant which defines the relation between Circumferance and Diameter of a Circle. Sage Aryabhatta defined it as follows:

chaturadhikam śatamaśṭaguṇam dvāśaśṭistathā sahasrāṇām
Ayutadvayaviśkambhasyāsanno vrîttapariṇahaḥ. – Aryabhatta

चतुरधिकं शतमष्टगुणं द्वाषष्टिस्थथा सहस्राणां
अयुतद्वयविष्कंभस्यासन्नॊ वृत्तपरिणाहाः – आर्यभट्टा

“In order to obtain the circumference of a Circle having a diameter of 20,000, add four to 100, multiply it by 8 and then add 62,000. By this rule the circumference of a circle of diameter 20,000 becomes 62832.”

Aryabhata used the word āsanna (approaching), appearing just before the last word, as saying that not only that is this approximation, but that the value is incommensurable (or irrational). If this is correct, it is quite a sophisticated insight, for the irrationality of pi was proved in Europe only in 1761 by Lambert.

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And as per the principle of Aryabhatta Pi works out to 3.1416 and modern Pi is approximated to 3.14285714285.

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100+4= 104  ( chaturadhikam= Add four to 100 )

104*8=832 ( śatamaśṭaguṇam= multiply it by eight )

832+62000=62832 ( dvāśaśṭistathā sahasrāṇām = add 62000 to the resultant )

22/7 *20000= 62832

( considering Diameter of a circle of having 20000 Units as per Aryabhatta)

62832/20000= 3.1416 ( factor that is pi,π as per Aryabhatta designating relation between Diameter and circumference )

22/7= 3.14285714285 ( present day pi,π ).

Actually the symbol π is claimed to have been used first by mathematician William Jones in 1706.

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