论文标题
椭圆形的三角形中心的有趣不变
Intriguing Invariants of Centers of Ellipse-Inscribed Triangles
论文作者
论文摘要
我们描述了椭圆形的三角族中心的不变式，其两个顶点固定在椭圆边界上，第三个扫除了它。我们证明：（i）如果三角形中心是barycenter and ortheCenter的固定仿射组合，则其位点是椭圆形； （ii）以及上述仿产组合的家族，上述基因座的中心横扫了一条线； （iii）在平行固定顶点的家族上，Loci刚刚沿第二行翻译。此外，我们研究了椭圆基因座的包膜的不变性，这是椭圆上两个固定顶点的组合。
We describe invariants of centers of ellipse-inscribed triangle families with two vertices fixed to the ellipse boundary and a third one which sweeps it. We prove that: (i) if a triangle center is a fixed affine combination of barycenter and orthocenter, its locus is an ellipse; (ii) and that over the family of said affine combinations, the centers of said loci sweep a line; (iii) over the family of parallel fixed vertices, said loci rigidly translate along a second line. Additionally, we study invariants of the envelope of elliptic loci over combinations of two fixed vertices on the ellipse.
