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A Special Conic Associated with the Reuleaux Negative Pedal Curve
August 20, 2020 · Declared Dead · 🏛 arXiv.org
"No code URL or promise found in abstract"
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Authors
Liliana Gabriela Gheorghe, Dan Reznik
arXiv ID
2008.08950
Category
math.DS
Cross-listed
cs.GR,
math.CV,
math.MG
Citations
1
Venue
arXiv.org
Last Checked
2 months ago
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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