We obtain the values concerning $(\theta ,\varphi )=limin{f}_{\left|q\right|\to \infty }\left|q\right|\Vert q\theta -\varphi \Vert$ using the algorithm by Nishioka, Shiokawa and Tamura. In application, we give the values (θ,1/2), (θ,1/a), (θ,1/√(ab(ab+4))) and so on when θ = (√(ab(ab+4)) - ab)/(2a) = [0;a,b,a,b,...].

We consider the values concerning$$ℳ(\theta ,\phi )=\underset{\left|q\right|\to \infty }{lim\; inf}\left|q\right|\left|\right|q^{\theta }-\phi \left|\right|$$where the continued fraction expansion of $\theta$ has a quasi-periodic form. In particular, we treat the cases so that each quasi-periodic form includes no constant. Furthermore, we give some general conditions satisfying $ℳ(\theta ,\phi )=0$.