Poncelet Propellers: Invariant Total Blade Area

01/25/2021

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by   Dominique Laurain, et al.

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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.