由椭圆导出的面积不变的类踏板曲线
Area-Invariant Pedal-Like Curves Derived from the Ellipse
摘要：
我们研究了六个踏板状曲线与椭圆是面积不变的踏板点躺在两个形状之一：（i）一个圆同心的椭圆，或（ii）椭圆边界本身。情形（i）是Steiner在1825年证明的曲线曲率质心（Krümmungs-Schwerpunkt）性质的推论。对于情况（ii），我们证明面积不变性代数。还提供了所有不变区域的显式表达式。
英文摘要：
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.
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