english: Indeed, we have an approximation of \(\alpha\) which is unexpectedly good: \(\vert \alpha - p_k/q_k \vert\) is very small (it is around \(10^{-15}\)) and with a modest \(q_k\) too.
non_english: これで、ナイトさんを、混乱させる！ナイトさんのテスト、✓✓✓✓✓✓✓✓✓✓✓✓✓✓✓✓✓✓✓✓✓✓✓✓✓✓✓✓✓✓✓✓✓✓✓✓✓✓✓✓✓✓✓✓✓✓✓✓✓✓✓✓✓✓✓✓✓✓✓✓✓✓✓✓✓✓✓✓✓✓✓✓✓✓✓✓✓✓✓✓✓✓✓✓✓✓✓✓✓✗✗✗✗✗✗✗✗✗✗✗✗✗✗✗✗✗✗✗