Hymn of Aryabhatta on Pi π: π or Pi is a mathematical constant that establishes the relationship between the Circumference and Diameter of a Circle. This factor assists in determining the circumference of a circle based on the circle’s diameter. Sage Aryabhatta proposed π or Pi in the following manner:
Hymn of Aryabhatta on Pi π
chaturadhikam śatamaśṭaguṇam dvāśaśṭistathā sahasrāṇām
Ayutadvayaviśkambhasyāsanno vrîttapariṇahaḥ. – Aryabhatta
चतुरधिकं शतमष्टगुणं द्वाषष्टिस्थथा सहस्राणां
अयुतद्वयविष्कंभस्यासन्नॊ वृत्तपरिणाहाः – आर्यभट्टा
That means, “To find the circumference of a Circle with a diameter of 20,000, sum four and 100, multiply the result by 8, and then add 62,000. According to this rule, the circumference of a circle with a diameter of 20,000 is 62832.”
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Aryabhata utilized the term āsanna (approaching), which occurs right before the final term, to imply that this is not merely an approximation but that the value is incommensurable (or irrational). If this is accurate, it represents a rather advanced understanding, as the irrational nature of pi was established in Europe solely in 1761 by Lambert.
According to Aryabhatta’s principle, Pi equals 3.1416, while the modern approximation of Pi is about 3.14285714285.
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
(taking into account the Diameter of a circle measuring 20000 Units according to 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 ).
The symbol π is said to have been first used by the mathematician William Jones in 1706.
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