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We begin by proving a few general facts about Simson polygons, defined aspolygons which admit a pedal line. We use an inductive argument to show that noconvex $n$-gon, $n\geq5$, admits a Simson Line. We then determine a propertywhich characterizes Simson $n$-gons and show that one can be constructed forevery $n\geq3$. We proceed to show that a parabola can be viewed as a limit ofspecial Simson polygons, called equidistant Simson polygons, and that thesepolygons provide the best piecewise linear continuous approximation to theparabola. Finally, we show that equidistant Simson polygons can be viewed asdiscrete analogs of parabolas and that they satisfy a number of resultsanalogous to the pedal property, optical property, properties of Archimedestriangles and Lambert's Theorem of parabolas. The corresponding results forparabolas are easily obtained by applying a limit process to the equidistantSimson polygons.

On Polygons Admitting a Simson Line as Discrete Analogs of Parabolas