论文标题
Brocard点的位置在选定的三角家庭上
Loci of the Brocard Points over Selected Triangle Families
论文作者
论文摘要
我们研究了Brocard点的基因座，位于两个选定的三角形家族上：（i）固定在圆周上的2个顶点，第三个顶点将其扫除，（ii）同型椭圆对中的Poncelet 3周期。获得的基因座包括圆圈，椭圆形和泪珠状曲线。我们得出曲线及其区域的表达式。我们还研究了Brocard Triangles的顶点的基因座，在同一个和Brocard-Poristic Poncelet家族上。
We study the loci of the Brocard points over two selected families of triangles: (i) 2 vertices fixed on a circumference and a third one which sweeps it, (ii) Poncelet 3-periodics in the homothetic ellipse pair. Loci obtained include circles, ellipses, and teardrop-like curves. We derive expressions for both curves and their areas. We also study the locus of the vertices of Brocard triangles over the homothetic and Brocard-poristic Poncelet families.
