Planarity conditions and four-body central configurations equations with angles as coordinates
Mathematical Physics
2020-06-12 v1 math.MP
Abstract
We discuss several conditions for four points to lie on a plane, and we use them to find new equations for four-body central configurations that use angles as variables. We use these equations to give novel proofs of some results for four-body central configuration. We also give a clear geometrical explanation of why Ptolemy's theorem can be used to write equations for co-circular central configurations when mutual distances are used as coordinates.
Keywords
Cite
@article{arxiv.1709.06473,
title = {Planarity conditions and four-body central configurations equations with angles as coordinates},
author = {Manuele Santoprete},
journal= {arXiv preprint arXiv:1709.06473},
year = {2020}
}