论文标题
源自椭圆的区域不变的踏板状曲线
Area-Invariant Pedal-Like Curves Derived from the Ellipse
论文作者
论文摘要
我们研究与椭圆形相关的六个类似踏板的曲线，这些曲线是对位于两个形状之一的踏板点不变的：（i）带有椭圆形的圆形同心，或（ii）椭圆形边界本身。病例（i）是曲线的曲率质心（krümmungs-schwerpunkt）特性的推论，由斯坦纳（Steiner）于1825年证明。对于（ii），我们以代数证明了区域不变性。还提供了所有不变区域的明确表达式。
We study six pedal-like curves associated with the ellipse which are area-invariant for pedal points lying on one of two shapes: (i) a circle concentric with the ellipse, or (ii) the ellipse boundary itself. Case (i) is a corollary to properties of the Curvature Centroid (Krümmungs-Schwerpunkt) of a curve, proved by Steiner in 1825. For case (ii) we prove area invariance algebraically. Explicit expressions for all invariant areas are also provided.
