## Wednesday, March 18, 2015

### Go, pi

I have a friend who used to know $$\pi$$ to about 50 places. I can barely remember nine. But on pi day last weekend, I wrote a little Go program that approximates $$\pi$$ by calculating many terms of an infinite series (Nilakantha's Series).

You can express Nilakantha's series as: $$\pi = 3 + \frac{4}{2\times3\times4} - \frac{4}{4\times5\times6} + \frac{4}{6\times7\times8} - \frac{4}{8\times9\times10} + \dots$$

Here's the Go program:

  package main

import (
"fmt"
"os"
"strconv"
)

const ndefault = 10000

func main() {
// How many iterations?
n := ndefault
if (len(os.Args) > 1) {
n,_ = strconv.Atoi(os.Args[1])
}
if n == 0 { n = ndefault }
fmt.Println("n =", n)

pi := 3.0
s  := 1.0    // Sign for alternating terms

// Nilakantha series.
for i := 2.0; i <= float64(n*2); i += 2 {
pi = pi + s * (4 / (i * (i + 1) * (i + 2)));
s = -s
}
fmt.Printf("%1.20f\n", pi)
}


Not perfect, but not bad (maybe I'm doing something wrong):
                     Starts
going off
rails here.
|
approx: 3.14159265358953820879
actual: 3.141592653589793238462643383279502884197

If you really want to know more about the history and the mathematics, there's a nice paper here from the Mathematical Association of America: The Discovery of the Series Formula for $$\pi$$. And the Wikipedia page on $$\pi$$.