Abstract
We classify all convex polygons whose area-bisecting deltoids or perimeter-bisecting deltoids are similar to those for a triangle, that is, they are tri-cusped and tri-concave-out closed curves. The additional condition that these two kinds of deltoids are segment-free makes no difference to the first classification and restricts the second to one that is much more similar to the first. We show that, up to similarity, the restricted second class is a complete system of representatives for the first class modulo affine equivalence.
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Acknowledgements
Stefan Catoiu’s research was supported in part by Faculty Summer Research Grants from the University Research Council (2017) and the College of Science and Health (2019) at DePaul University.
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Feb. 26, 2021. This paper is in final form and no version of it will be submitted for publication elsewhere.
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Berele, A., Catoiu, S. The classification of convex polygons with triangular area or perimeter bisecting deltoids. Beitr Algebra Geom 63, 95–114 (2022). https://doi.org/10.1007/s13366-021-00572-5
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DOI: https://doi.org/10.1007/s13366-021-00572-5
Keywords
- Area-bisecting deltoid
- Bisecting area
- Bisecting perimeter
- Bisecting line
- Deltoid
- Envelope
- Perimeter-bisecting deltoid
- Triangular deltoid