I here with give what Aryabhatta told us about a factor which is called Pi,π in mathematics. This factor is deduced by relating two entities or parameters of a circle – Diameter and Circumference of a circle.
A circle’s circumference is calculated by multiplying its diameter with pi,π which is 22/7 in modern mathematics. This 22/7 approximates to 3.14285714285.
It is our pride that our ancestor Sage Aryabhatta gave the factor to the approximation of 3.1416 centuries back. Let us look at what he said about this equation and how it is understood now.
chaturadhikam śatamaśṭaguṇam dvāśaśṭistathā sahasrāṇām
చతురధికం శతమష్టగుణం ద్వాషష్టిస్థథా సహస్రాణాం
"Add four to 100, multiply it by eight and then add 62,000. By this rule the circumference of a circle of diameter 20,000 can be approached."
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.
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 )
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