论文标题
庞加莱单元磁盘和里曼球体上的积分截线
Collinearity of points on Poincaré unit disk and Riemann sphere
论文作者
论文摘要
我们研究了单位磁盘双曲线几何形状显着的某些点。我们为欧几里得线的交点和黎曼球的大圆圈的立体揭示提供了明确的公式。我们证明了与这些相交点的共线性有关的几个结果，提供了寻找双曲线中点的新方法，并代表了弦中点的公式。这些证明利用来自计算机代数的Gröbner基础来解决多项式方程。
We study certain points significant for the hyperbolic geometry of the unit disk. We give explicit formulas for the intersection points of the Euclidean lines and the stereographic projections of great circles of the Riemann sphere passing through these points. We prove several results related to collinearity of these intersection points, offer new ways to find the hyperbolic midpoint, and represent a formula for the chordal midpoint. The proofs utilize Gröbner bases from computer algebra for the solution of polynomial equations.
