三角形族上Brocard点的轨迹
Loci of the Brocard Points over Selected Triangle Families
摘要：
本文研究了两类三角形上的Brocard点的轨迹：（i）固定在圆周上的两个顶点和第三个顶点，（ii）位似椭圆对中的Poncelet 3-xs。获得的位点包括圆、椭圆和泪滴状曲线。我们推导出这两条曲线及其面积的表达式。我们还研究了位似和Brocard-poristic Poncelet家族的Brocard三角形顶点的轨迹。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
