#! /usr/bin/awk -f

### pi.awk, https://en.wikipedia.org/wiki/Pi
# In 1706 John Machin used the Gregory–Leibniz series to produce an algorithm
# that converged much faster. Machin reached 100 digits of π with this
# formula. Other mathematicians created variants, now known as Machin-like
# formulae, that were used to set several successive records for calculating
# digits of π. Machin-like formulae remained the best-known method for
# calculating π well into the age of computers, and were used to set records
# for 250 years, culminating in a 620-digit approximation in 1946 by Daniel
# Ferguson–the best approximation achieved without the aid of a calculating
# device.

function pi() {
    return 4*(4*atan2(1,5) - atan2(1,239))
}

BEGIN {
    (ARGV[1] > 0) ? fig = ARGV[1] : fig = 6
    str = "%." fig "g\n"
    printf(str, pi())
}