title: Refined quadratic estimations of Shafer's inequality.
abstract: We establish an inequality by quadratic estimations; the double inequality [Formula: see text] holds for [Formula: see text], where the constants [Formula: see text] and 32 are the best possible.
authors.affiliation: General Education, Ube National College of Technology, Tokiwadai 2-14-1, Ube, Yamaguchi 755-8555 Japan.
authors.forename: Yusuke
authors.initials: Y
authors.lastname: Nishizawa
keywords: Shafer’s inequality; a lower bound for arctangent; an upper bound for arctangent