BRUTE_FORCE_PI.md

Brute Force Pi Calculation

Making use of the observation that Pi is the area of a circle with diameter equal to one, a brute force calculation of Pi would be to:

1. randomly generate points in a square
2. count the points within the circle and the total number of points
3. multiple the ratio of points in the circle to total number of points by the area of a square with a side the length of the diameter of the circle (in this case two (2))

Usage

BruteForcePi.estimate_pi # Estimated value of π: 3.2 (accuracy: 98.1408%)
BruteForcePi.estimate_pi(iterations: 10_000) # Estimated value of π: 3.1164 (accuracy: 99.1981%)

brute-force-pi.rb

class BruteForcePi
  def self.estimate_pi(iterations: 10)
    points_in_circle = 0
    total_points = 0

    iterations.times do
      x = rand(-1.0..1.0)
      y = rand(-1.0..1.0)

      points_in_circle += 1 if Math.sqrt(x**2 + y**2) <= 1
      total_points += 1
    end

    pi = 4.0 * (points_in_circle.to_f / total_points)
    accuracy = 100.0 - ((pi - Math::PI).abs / Math::PI * 100.0).round(4)

    puts "Estimated value of π: #{pi} (accuracy: #{accuracy}%)"
  end
end