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A Special Conic Associated with the Reuleaux Negative Pedal Curve (2008.08950v2)
Published 20 Aug 2020 in math.DS, cs.GR, math.CV, and math.MG
Abstract: The Negative Pedal Curve of the Reuleaux Triangle w.r. to a point $M$ on its boundary consists of two elliptic arcs and a point $P_0$. Interestingly, the conic passing through the four arc endpoints and by $P_0$ has a remarkable property: one of its foci is $M$. We provide a synthetic proof based on Poncelet's polar duality and inversive techniques. Additional intriguing properties of Reuleaux negative pedal are proved using straightforward techniques.
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