polygon.rb

class Polygon
  RAD_TO_DEG = (180 / Math::PI)
  DEG_TO_RAD = (Math::PI / 180)

  def self.all(h)
    a = {}
    (3..100).each do |n|
      a[n] = call(h, n)
    end
    a
  end

  def self.call(h, n)
    puts "Height: #{h}"
    odd = n % 2 == 1
    i_angle = 360 / n.to_f
    puts "Interior angle: #{i_angle}"

    i2_angle = i_angle / 2.0
    puts "Half that angle: #{i2_angle}"

    if odd
      cos = Math.cos(i2_angle * DEG_TO_RAD)
      r = h / (cos + 1)
      puts "Radius: #{r}"

      x = n.times.map do |i|
        a = i_angle * (i + 1)
        r * Math.sin(a * DEG_TO_RAD)
      end.max

      w = 2 * x
      puts "w: #{w}"
    else
      r = (h / 2.0) / Math.cos(i2_angle * DEG_TO_RAD)
      puts "Radius: #{r}"

      x = n.times.map do |i|
        a = i_angle * i + i2_angle
        r * Math.sin(a * DEG_TO_RAD)
      end.max

      w = 2 * x
      puts "w: #{w}"
    end

    w
  end
end