R = 1
K = 2

R2 = R * R * 1.0
f = ->(y: Float64) { dy = Math.sqrt(R2 - y * y); (y * dy + R2 * Math.atan(y / dy)) }
s = Math::PI * R2 / (K + 1)

ans = [] of Float64
prev = -R.to_f64
K.times do
  ac = R.to_f64
  wa = prev
  s0 = f.call(prev)
  100.times do
    wj = (ac + wa) * 0.5
    if f.call(wj) - s0 >= s
      ac = wj
    else
      wa = wj
    end
  end
  puts ac
  prev = ac
end