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 mer phi
    R * Math::atanh(Math::sin(phi))
  end

  def mer_inv r
    Math::asin(Math::tanh(r / R))
  end


(0..79).each {|phi|
  r = mer(rad(phi))
  b = deg(mer_inv(r))
  printf("%4.1f %10.1f %9.5f\n", phi, r, b)
}