Abstract
We study the envelope of the family of lines which bisect the interior region of a simple, closed curve in the plane. We determine this ‘bisection envelope’for polygons and show that polygons with no parallel pairs of sides are characterized by their bisection envelope. We show that the bisection envelope always has at least three and an odd number of cusps. We investigate the winding numbers of bisection envelopes, and use this to show that there are an infinite number of curves with any given bisection envelope and show how to generate them. We obtain results on the intersections of bisecting lines. Finally, we give a relationship between the ‘internal area’of a curve and that of its bisection envelope.
Citation
Noah Fechtor-Pradines. "Bisection envelopes." Involve 8 (2) 307 - 328, 2015. https://doi.org/10.2140/involve.2015.8.307
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