Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665512013ON HYPERBOLIC AREA OF THE MODULI OF Ɓ|ACUTE TRIANGLES191200ENNaomiKanesakaHiroakiNakamuraA -acute triangle is a Euclidean triangle on the plane
whose three angles are less than a given constant . In this note, we
shall give an explicit formula computing the hyperbolic area A() of
the moduli region of -acute triangles on the PoincarLe disk. It turns
out that A() is a period in the sense of Kontsevich-Zagier if cot is a
nonnegative algebraic number.No potential conflict of interest relevant to this article was reported.Acta Medica Okayama122006Some classical views on the parameters of the Grothendieck-Teichmüeller group123133ENHiroakiNakamura<p>We present two new formulas concerning behaviors of the standard parameters of the Grothendieck-Teichmüller group GT , and discuss their relationships with classical mathematics. First, considering a non-Galois etale cover of P<sub>1</sub> {0 1 infinity} of degree 4, we present a newtype equation satisfied by the Galois image in GT . Second, a certain equation in GL <sub>2</sub> (Z||Z<sub>2</sub> ) satisfied by every element of GT is derived as an application of (profinite) free differential calculus.</p>
No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664612004Eigenloci of 5 Point Configurations on the Riemann Sphere and the Grothendieck-Teichm・ler GroupENPierreLochakHiroakiNakamuraLeilaSchnepsNo potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15665212010BELYI FUNCTION ON X<sub>0</sub>(49) OF DEGREE 7ENKenjiHoshinoHiroakiNakamuraNo potential conflict of interest relevant to this article was reported.