Loci of the Brocard Points over Selected Triangle Families
Metric Geometry
2020-10-01 v2 Computational Geometry
Abstract
We study the loci of the Brocard points over two selected families of triangles: (i) 2 vertices fixed on a circumference and a third one which sweeps it, (ii) Poncelet 3-periodics in the homothetic ellipse pair. Loci obtained include circles, ellipses, and teardrop-like curves. We derive expressions for both curves and their areas. We also study the locus of the vertices of Brocard triangles over the homothetic and Brocard-poristic Poncelet families.
Keywords
Cite
@article{arxiv.2009.08561,
title = {Loci of the Brocard Points over Selected Triangle Families},
author = {Ronaldo Garcia and Dan Reznik},
journal= {arXiv preprint arXiv:2009.08561},
year = {2020}
}
Comments
10 pages, 7 figures, 1 table, 4 videos