Wednesday, October 24, 2018

#PythaShastri π/4 series

π/4 = 1/1 - 1/3 + 1/6 - 1/10 + 1/15 - 1/21 + . . . . . . . .

What are these 1, 3, 6, 10, 15, 21 . . . . . . .  ?

These are numbers from #PythaShastri pattern. Please refer to #PythaShastri pattern posted earlier in this blog. It was a brilliant ( it seemed to me !!) pattern between rational numbers and a series of natural numbers.

And now it seems to be approaching π/4 when expressed in denominators with + and - signs alternated. I have not checked it completely. But two places 0.78 was approached.

π/4 is tough to reach. Madhava of Sangamagrama gave a series of π/4. My measuring behaviour equation gave π/2. Then there was one π/3√3.

You may think I am being proud. I am not at all proud but I am writing so in praise of God.

3 comments:

Kirtivasan Ganesan said...

I am sorry for the error.
It is not pi by 4.
Error is regretted.

Kirtivasan Ganesan said...

I am wrong here. Madhava of Sangamagrama pi is most beautiful. It is pi by 4 = 1 - 1/3 + 1/5 - 1/7 + 1/9 . . .

Kirtivasan Ganesan said...

1 + 1/3 + 1/6 + 1/10 + 1/30 + 1/60 + 1/100 + 1/300 + 1/600 + 1/1000 + 1/3000 + 1/6000 + 1/10000 + ..... is 1.666666666