03-14-2019-pi2

 Calculating Pi Yourself

There are many special methods used to calculate π and here is one you can try yourself: it is called the Nilakantha series (after an Indian mathematician who lived in the years 1444–1544).

It goes on for ever and has this pattern:

3 + 42×3×444×5×6 + 46×7×848×9×10 + ...

(Notice the + and pattern, and also the pattern of numbers below the lines.)

It gives these results:

TermResult (to 12 decimals)
13
23.166666666667
33.133333333333
43.145238095238
...... etc! ...

Get a calculator (or use a spreadsheet) and see if you can get better results.