## PI approximation using Leibniz formula.
##
## PI/4 = 1 - 1/3 + 1/5 - 1/7 + 1/9 - ...

from math import abs, PI

pi_by_4 = 0; sign = -1
for i in 1..100000
	sign    *= -1
	pi_by_4 += sign * 1/(2*i - 1)
end

pi = 4 * pi_by_4
assert(abs(pi - PI) < 0.00002)

print('PI =', pi)