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Scientific Secrets of Jainism
a circle at several points and the inner exterior polygon mutually joining several points on the circumference of the circle, Archimedes, the Greek mathematician went on increasing the sides of both the polygons to the largest possible number and tried to find the ratio between the diameter and circumference of a circle. And he was very successful.?
Since Archimedes tried to find the exact value of n, a large number of mathematicians in Europe have been trying to find the value of n. They have given various formulae. The German mathematician and philosopher, G. Leibnitz, the Swiss mathematician L. Euler, the British mathematicians, J. Wallis and Lord Brounker are among them. The formulae given by these four mathematicians are respectively as under> :
f ---1-- 2
1 3
+
1 - 5
-
1 - 7
+
1 9
---
-
1 11
etc.
1 2 2 4 4 --=-XX -XX 4 1 3 3 5
6 6 -X-etc. 5 7
1+-
2-
12
32
In all the above four methods, there are infinite components. But we can make calculations only with a definite number of components. In this calculation, therefore, the larger the number of components that we use, the truer is the value.
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