@article{article_1512613, title={Envelopes of Bisection Lines of Polygons}, journal={International Electronic Journal of Geometry}, volume={17}, pages={421–436}, year={2024}, DOI={10.36890/iejg.1512613}, author={Marques Da Silva, Joel and Craizer, Marcos}, keywords={Envelopes of families of lines, area bisection lines, discrete envelopes, discrete cusps, half-area polygons, three vertices theorem}, abstract={A bisection line divides a convex planar curve into two parts with equal areas. It is natural to study the envelope of these lines, which in general present singularities. The polygonal case is particularly interesting, since there are several different notions of a discrete envelope. In this paper, we study three different notions of discrete envelopes of bisection lines and the connections between them.}, number={2}, publisher={Kazım İlarslan}