Straight Line motion with rigid sets
Metric Geometry
2014-01-21 v1
Abstract
If one is given a rigid triangle in the plane or space, we show that the only motion possible, where each vertex of the triangle moves along a straight line, is given by a hypocycloid line drawer in the plane, and a natural extension in three-space. Each point lies on a circle which rolls around, without slipping, inside a larger circle of twice its diameter.
Cite
@article{arxiv.1401.4743,
title = {Straight Line motion with rigid sets},
author = {Robert Connelly and Luis Montejano},
journal= {arXiv preprint arXiv:1401.4743},
year = {2014}
}