def rad d
    Float(d) * Math::PI / 180.0
  end

  def deg r
    Float(r) * 180.0 / Math::PI
  end

  R = 6371_000.0

  def nps phi
    2 * R * Math::tan(0.25 * Math::PI - 0.5 * phi)
  end

  def nps_inv r
    t = Math::atan(0.5 * r / R)
    Math::PI * 0.5 - 2.0 * t
  end


(1..90).each {|phi|
  r = nps(rad(phi))
  b = deg(nps_inv(r))
  printf("%4.1f %10.1f %9.5f\n", phi, r, b)
}