Given a triangle, a trio of circumellipses can be defined, each centered on an excenter. Over the family of Poncelet 3-periodics (triangles) in a concentric ellipse pair (axis-aligned or not), the trio resembles a rotating propeller, where each "blade" has variable area. Amazingly, their total area is invariant, even when the ellipse pair is not axis-aligned. We also prove a closely-related invariant involving the sum of blade-to-excircle area ratios.

中文翻译：

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Poncelet螺旋桨：叶片总面积不变

给定一个三角形，可以定义三个外接圆，每个外接圆的中心都是偏心。在同心椭圆对（轴对齐或不对齐）的Poncelet 3周期（三角形）家族中，三重奏类似于旋转的螺旋桨，其中每个“叶片”的面积均可变。令人惊讶的是，即使椭圆对未与轴对齐，它们的总面积也不变。我们还证明了一个密切相关的不变性，涉及刀片与外圆面积之和。