# # a run with floats
# puts pi
#
# 2012-08-30 08:11:17 -0500
# Found it with 426183 terms
# 2012-08-30 08:11:19 -0500
# 3.1415949999995694
#
# # a run with rational numbers
# puts pi(false)
#
# 2012-08-30 08:11:44 -0500
# Found it with 426183 terms
# 2012-08-30 08:33:02 -0500
# 3.141594999999669
#
# # Don't add rationals with differing denominators in a tight loop

# Given that Pi can be estimated using the function
# 4 * (1 – 1/3 + 1/5 – 1/7 + …) with more terms giving greater accuracy,
# write a function that calculates Pi to an accuracy of 5 decimal places.
#
def pi(fast=true)
  puts Time.now
  previous_value = i = running_multiplier = 1
  while ('%0.5f' % previous_value.to_f) != ('%0.5f' % (previous_value=(4*running_multiplier)).to_f) do
    new_term = (Rational(1,1+(i*2)) * (-1)**i)
    new_term = new_term.to_f if fast
    running_multiplier += new_term
    i += 1
  end
  puts "Found it with #{i} terms"
  puts Time.now
  (4*running_multiplier).to_f
end