An Infinite, Converging, Sequence of Brocard Porisms
Metric Geometry
2020-10-08 v3 Computational Geometry
Graphics
Robotics
Abstract
The Brocard porism is a known 1d family of triangles inscribed in a circle and circumscribed about an ellipse. Remarkably, the Brocard angle is invariant and the Brocard points are stationary at the foci of the ellipse. In this paper we show that a certain derived triangle spawns off a second, smaller, Brocard porism so that repeating this calculation produces an infinite, converging sequence of porisms. We also show that this sequence is embedded in a continuous family of porisms.
Keywords
Cite
@article{arxiv.2010.01391,
title = {An Infinite, Converging, Sequence of Brocard Porisms},
author = {Dan Reznik and Ronaldo Garcia},
journal= {arXiv preprint arXiv:2010.01391},
year = {2020}
}
Comments
20 pages, 6 figures, 2 tables, 4 video links