3 papers
math.NT2023
Rational angle bisectors on the coordinate plane and solutions of Pell's equations
Takashi Hirotsu
On the coordinate plane, the slopes and of two straight lines and the slope of one of their angle bisectors satisfy the equation Rece…
math.CO2022
Normal-sized hypercuboids in a given hypercube
Takashi Hirotsu
In a given hypercube, draw grid lines parallel to the edges, and consider all hypercuboids (or hypercubes) whose edges are lying on the grid lines or the boundary. We find the limi…
math.NT2022
Diophantine equation related to angle bisectors and solutions of Pell's equations
Takashi Hirotsu
It is important in drawing techniques to find combinations of two straight lines and their angle bisectors whose slopes are all rational numbers. This problem is reduced to solving…