@article{2f8b437402ab4268b033be4b7d393c54,
title = "Billiards in ellipses revisited",
abstract = "We prove some recent experimental observations of Dan Reznik concerning periodic billiard orbits in ellipses. For example, the sum of cosines of the angles of a periodic billiard polygon remains constant in the 1-parameter family of such polygons (that exist due to the Poncelet porism). In our proofs, we use geometric and complex analytic methods.",
author = "Arseniy Akopyan and Richard Schwartz and Serge Tabachnikov",
note = "Funding Information: AA was supported by European Research Council (ERC) under the European Union{\textquoteright}s Horizon 2020 research and innovation programme (Grant Agreement No. 78818 Alpha). RS is supported by NSF Grant DMS-1807320. ST was supported by NSF Grants DMS-1510055, DMS-2005444, and SFB/TRR 191. Publisher Copyright: {\textcopyright} 2020, Springer Nature Switzerland AG.",
year = "2020",
doi = "10.1007/s40879-020-00426-9",
language = "English (US)",
journal = "European Journal of Mathematics",
issn = "2199-675X",
publisher = "Springer International Publishing AG",
}