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 + \frac{4}{2×3×4} − \frac{4}{4×5×6} + \frac{4}{6×7×8} − \frac{4}{8×9×10} + ...

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

It gives these results:

Term | Result (to 12 decimals) |
---|---|

1 | 3 |

2 | 3.166666666667 |

3 | 3.133333333333 |

4 | 3.145238095238 |

... | ... etc! ... |

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