A Special Conic Associated with the Reuleaux Negative Pedal Curve

Liliana Gabriela Gheorghe; Dan Reznik

A Special Conic Associated with the Reuleaux Negative Pedal Curve

Dynamical Systems 2020-10-20 v2 Graphics Complex Variables Metric Geometry

Authors: Liliana Gabriela Gheorghe , Dan Reznik

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.

Keywords

reuleaux triangle negative pedal curve conic poncelet polar duality inversive techniques synthetic proof

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@article{arxiv.2008.08950,
  title  = {A Special Conic Associated with the Reuleaux Negative Pedal Curve},
  author = {Liliana Gabriela Gheorghe and Dan Reznik},
  journal= {arXiv preprint arXiv:2008.08950},
  year   = {2020}
}

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17 pages, 10 figures

A Special Conic Associated with the Reuleaux Negative Pedal Curve

Abstract

Keywords

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