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 (Kr\"ummungs-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.

中文翻译：

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从椭圆导出的面积不变的类似踏板的曲线

我们研究了与椭圆相关的六种类似踏板的曲线，这些曲线对于位于两种形状之一上的踏板点是面积不变的：（i）与椭圆同心的圆，或（ii）椭圆边界本身。情况 (i) 是由 Steiner 在 1825 年证明的曲线的曲率质心 (Kr\"ummungs-Schwerpunkt) 性质的推论。对于情况 (ii)，我们用代数证明了面积不变性。所有不变面积的显式表达式也是假如。