9 citations · 12 across the 7 of their papers we have counts for
7 papers
Theorem of three squares across three geometries
Kazuhiro Ichihara, Akira Ushijima
In Euclidean geometry, the Pythagorean theorem is presented as an equation involving three squares. This paper explores how analogous expressions may be identified in spherical and…
A Proof of Irrationality of by Contraposition
Akira Ushijima
We point out that the proof of irrationality of by Niven can be modified to a proof by contraposition. As a warm-up, we also give a proof of irrationality of and $\s…
On the maximal volume of three-dimensional hyperbolic complete orthoschemes
Kazuhiro Ichihara, Akira Ushijima
A three-dimensional orthoscheme is defined as a tetrahedron whose base is a right-angled triangle and an edge joining the apex and a non-right-angled vertex is perpendicular to the…
Strongly invertible knots, rational-fold branched coverings and hyperbolic spatial graphs
Kazuhiro Ichihara, Akira Ushijima
A construction of a spatial graph from a strongly invertible knot was developed by the second author, and a necessary and sufficient condition for the given spatial graph to be hyp…
A classification of hyperbolic manifolds related to the three-dimensional torus
Akira Ushijima
L. Paoluzzi constructed a family of compact orientable three-dimensional hyperbolic manifolds with totally geodesic boundary, which were, by construction, closely related to the th…
A volume formula for hyperbolic tetrahedra in terms of edge lengths
Jun Murakami, Akira Ushijima
We give a closed formula for volumes of generic hyperbolic tetrahedra in terms of edge lengths. The cue of our formula is by the volume conjecture for the Turaev-Viro invariant of…