arXiv:2101.10456
Poncelet Propellers: Invariant Total Blade Area
Poncelet Propellers: Invariant Total Blade Area
著者: Dominique Laurain, Daniel Jaud, Dan Reznik
分類: math.MG, cs.CG, cs.RO, math.DS
原文アブストラクト
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.