references.bib

### HISTORIC

@BOOK{poncelet1822,
    author = {J.-V. Poncelet},
    title = {Traité sur les propriétés projectives des figures},
    publisher = {Bachelier},
    address={Paris},
    year = {1822},
    url={https://gallica.bnf.fr/ark:/12148/bpt6k9608143v.texteImage}
}

@article{garcia2019-incenter,
    author = {Garcia, Ronaldo},
    title = {Elliptic Billiards and Ellipses Associated to the 3-Periodic Orbits},
    journal = {American Mathematical Monthly},
    volume={126},
    number={06},
    pages={491--504},
    Eprint ={doi:10.1080/00029890.2019.1593087},
    year = {2019}
}

@ARTICLE{griffiths1978,
author={Philipp Griffiths and Joseph Harris},
     TITLE = {On {C}ayley's explicit solution to {P}oncelet's porism},
   JOURNAL = {Enseign. Math. (2)},
  FJOURNAL = {L'Enseignement Math\'{e}matique. Revue Internationale. 2e S\'{e}rie},
    VOLUME = {24},
      YEAR = {1978},
    NUMBER = {1-2},
     PAGES = {31--40},
}

@article{jacobi1849,
	Author = {Jacobi, C. G. J.},
	Journal = {J. reine angew. Math.},
	Pages = {376--389},
	Title = {{\"U}ber die {A}nwendung der elliptischen {T}ranscendentten auf ein bekanntes {P}roblem der {E}lementargeometrie},
	doi = {10.1515/crll.1828.3.376},
	Volume = {3},
	Year = {1828}
}

@BOOK{jacobi1884,
 Title = {Vorlesungen \"uber {D}ynamik},
  Note = {Gehalten an der {U}niversit\"at zu {K}\"onigsberg im {W}intersemester 1842--1843},
  Publisher = {Druck \& Verlag von George Reimer},
  Address = {Berlin},
	Author = {Jacobi, C. G. J.},
	Editor = {Alfred Clebsch},
	Year = {1884},
	url={https://quod.lib.umich.edu/u/umhistmath/AAS8078.0001.001/5?rgn=full+text;view=pdf}
}
	
@ARTICLE{jacobi1837,
    author = {Jacobi, C. G. J.},
    title = {Zur {T}heorie der {V}ariations-{R}echnung und der {D}ifferential-{G}leichungen},
    journal = {J. reine angew. Math.},
    volume = {17},
    year = {1837},
    pages = {68--82},
    issn = {0075-4102},
    mrclass = {DML},
    mrnumber = {1578150},
    doi = {10.1515/crll.1837.17.68},
    url = {https://doi.org/10.1515/crll.1837.17.68},
}

@article{jacobi1839,
	Author = {Jacobi, C. G. J.},
	Journal = {J. reine angew. Math.},
	Keywords = {doi:10.1515/crll.1839.19.309},
	Pages = {309--313},
	Title = {Note von der geod\"atischen {L}inie auf einem {E}llipsoid und den verschiedenen {A}nwendungen einer merkw\"urdigen analytischen {S}ubstitution [The geodesic on an ellipsoid and various applications of a remarkable analytical substitution].},
	Volume = {19},
	Year = {1839},
	doi={doi:10.1515/crll.1839.19.309},
  notes={Letter to Bessel, Dec. 28, 1838. French translation (1841)}
}

@article{darboux1870,
   year={1870},
   author={Gaston Darboux},
   title={Sur les polygones inscrits et circonscrits à l'ellipso\"ide},
   journal={Bulletin de la Société {p}hilomatique de Paris},
   series={6e serie},
   volume={7},
   pages={92--95},
   url={https://www.biodiversitylibrary.org/item/98693#page/98/mode/1up}
}

@article{birkhoff1927,
	Author = {Birkhoff, G.},
	Da = {1927/12/01},
	Doi = {10.1007/BF02421325},
	Isbn = {1871-2509},
	Journal = {Acta Mathematica},
	Number = {1},
	Pages = {359--379},
	Title = {On the periodic motions of dynamical systems},
	Url = {https://doi.org/10.1007/BF02421325},
	Volume = {50},
	Year = {1927}
}

@ARTICLE{neumann1859,
  author={Neumann, C.},
  title={De problemate quodam mechanico, quod ad primam integralium ultraellipticorum classem revocatur},
  journal={J. reine angew. Math.},
  pages={46--63},
  year={1859},
  volume={56},
  doi = {10.1515/crll.1859.56.46}
}

### BOOKS

@BOOK{johnson29,
    author={Johnson, R. A.},
    title={Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle},
    year={1929},
    address={Boston, MA},
    publisher={Houghton Mifflin}
}

@BOOK{lockhart09,
  title={A Mathematician’s Lament},
  author={Paul Lockhart},
  publisher={Bellevue Library Press},
  year={2009},
  isbn={978-1934137178}
}

@BOOK{darboux1917,
    author = {Gaston Darboux},
    title ={Principes de géométrie analytique},
    publisher = {Gauthier-Villars},
    address = {Paris},
    year = {1917},
    url = {https://archive.org/details/principesdegom00darbuoft/page/n6},
}

@BOOK{birkhoff66,
  author = {Birkhoff, G. D.},
  address={Providence, RI},
  title = {Dynamical Systems},
  edition = {1966},
  year = {1927},
  url = {http://www.freeinfosociety.com/media/pdf/2219.pdf},
  zblnumber = {53.0732.01},
  series = {Colloqium Publications},
  volume = 9,
  publisher = {American Mathematical Society}
}

@ONLINE{sergei91,
    author = {Sergei Tabachnikov},
    title = {Geometry and Billiards},
    series = {Student Mathematical Library},
    volume = {30},
    publisher = {American Mathematical Society},
    address={Providence, RI},
    note={Mathematics Advanced Study Semesters, University Park, PA},
    year = {2005},
    url = {http://www.math.psu.edu/tabachni/Books/billiardsgeometry.pdf}
}

@BOOK{coxeter67,
    author = {Coxeter, H. S. M. and Greitzer, S. L.},
    title = {Geometry Revisited},
    series = {New Mathematical Library},
    volume = {19},
    publisher = {Random House, Inc.},
    address={New York},
    year = {1967},
    pages = {xiv+193},
    isbn = {[0-394-70919-5]},
    mrclass = {51-01},
    mrnumber = {3155265},
    zblnumber = {0166.16402},
}

@BOOK{kozlov91,
  title={Billiards: A Genetic Introduction to the Dynamics of Systems with Impacts},
  author={Kozlov, V. V. and Treshch{\"e}v, D. V.},
  isbn={9781470445010},
  series={Translations of mathematical monographs},
  url={https://books.google.com.br/books?id=b18buAEACAAJ},
  year={1991},
  publisher={American Mathematical Society},
  address={Providence, RI}
}

@BOOK{dragovic11,
  title={Poncelet Porisms and Beyond: Integrable Billiards, Hyperelliptic Jacobians and Pencils of Quadrics},
  author = {Vladimir Dragovi\'{c} and Milena Radnovi\'{c}},
  isbn={9783034800143},
  lccn={2011926874},
  series={Frontiers in Mathematics},
  url={https://books.google.com.br/books?id=QcOmDAEACAAJ},
  year={2011},
  publisher={Springer},
  address={Basel}
}

### ARTICLES

@article{akopyan12,
  journal={Journal of Classical Geometry},
  volume={1},
  year={2012},
  author={Arseniy Akopyan},
  title={Conjugation of lines with respect to a triangle},
  url={https://users.mccme.ru/akopyan/papers/conjugation_en.pdf},
  pages={23--31}
}

@article{schwartz07,
  author={Richard Schwartz},
  title={The Poncelet grid},
  journal={Adv. Geometry},
  volume={7},
  year={2007},
  pages={157--175}
}

@article{sergei07_grid,
  author = {Mark Levi and Sergei Tabachnikov},
  title = {The Poncelet Grid and Billiards in Ellipses},
  journal = {The American Mathematical Monthly},
  volume = {114},
  number = {10},
  pages = {895-908},
  year  = {2007},
  publisher = {Taylor & Francis},
  doi = {10.1080/00029890.2007.11920482},
  URL = {https://doi.org/10.1080/00029890.2007.11920482}
}

@article{sergei10_pentagram,
  title={The Pentagram Map: A Discrete Integrable System},
  author={Valentin Ovsienko and Richard Schwartz and Sergei Tabachnikov},
  journal={S. Commun. Math. Phys.},
  year={2010},
  volume={299},
  number={409},
  url={https://doi.org/10.1007/s00220-010-1075-y}
}

@article{dekov05,
  author={Sara Grozdev and Deko Dekov},
  title={A Survey of Mathematics Discovered by Computers},
  journal={International Journal of Computer Discovered Mathematics (IJCDM)},
  issn={2367-7775},
  month={november},
  year={2015},
  volume={0},
  number={0},
  pages={3--20},
  url={https://www.journal-1.eu/2015/01/Grozdev-Dekov-A-Survey-pp.3-20.pdf}
}

@article{igor17,
  title={Synthetic foundations of cevian geometry, {III}: The generalized orthocenter},
  author={Igor Minevich and Patrick Morton},
  year={2017},
  journal={Journal of Geometry},
  volume={108},
  pages={437--455},
  doi={10.1007/s00022-016-0350-2},
  url={https://arxiv.org/pdf/1506.06253.pdf}
}

@ARTICLE{connes07,
  title={A Property of Parallelograms Inscribed in Ellipses},
  author={Alain Connes and Don Zagier},
  journal={The American Mathematical Monthly},
  volume={114},
  number={10},
  year={2007},
  pages={909--914},
  publisher={Mathematical Association of America},
  url={https://people.mpim-bonn.mpg.de/zagier/files/amm/114/fulltext.pdf}
}

@ARTICLE{dragovic88,
    author = {Vladimir Dragovi\'{c} and Milena Radnovi\'{c}},
    title = {Caustics of {P}oncelet polygons and classical extremal polynomials},
    journal = {Regul. Chaotic Dyn.},
    fjournal = {Regular and Chaotic Dynamics. International Scientific Journal},
    volume = {24},
    year = {2019},
    number = {1},
    pages = {1--35},
    issn = {1560-3547},
    mrclass = {37D50 (14H70 26C05 41A10 70H06)},
    mrnumber = {3908388},
    doi = {10.1134/S1560354719010015},
    url = {https://doi.org/10.1134/S1560354719010015},
}

@ARTICLE{sergei2016-com,
    author = {Richard Schwartz and Sergei Tabachnikov},
    title = {Centers of mass of {P}oncelet polygons, 200 years after},
    journal = {Math. Intelligencer},
    fjournal = {The Mathematical Intelligencer},
    volume = {38},
    year = {2016},
    number = {2},
    pages = {29--34},
    issn = {0343-6993},
    mrclass = {51M15 (01A55 51M25)},
    mrnumber = {3507116},
    mrreviewer = {Victor V. Pambuccian},
    doi = {10.1007/s00283-016-9622-9},
    url = {http://www.math.psu.edu/tabachni/prints/Poncelet5.pdf},
    zblnumber = {1351.01013},
}

@article{sergei2016proj,
  title={Projective configuration theorems: old wine into new wineskins},
  author={Sergei Tabachnikov},
  journal={arXiv preprint arXiv:1607.04758},
  year={2016}
}

@article{fierobe2019,
    author = {Fierobe, Corentin},
    title = {On the circumcenters of triangular orbits in elliptic billiard},
    year = {2021},
    url = {arxiv.org/pdf/1807.11903.pdf},
    note={to appear},
    journal={Journal of Dynamical and Control Systems}
    }
}

@article{sergei2014-circumcenter-of-mass,
author={Sergei Tabachnikov and Emmanuel Tsukerman},
title={Circumcenter of Mass and Generalized Euler Line},
journal={Discrete Comput. Geom.},
volume={51},
pages={815-–836},
year={2014},
doi={10.1007/s00454-014-9597-2}
}


@ARTICLE{olga14,
    author = {Romaskevich, Olga},
    title = {On the incenters of triangular orbits on elliptic billiards},
    journal = {Enseign. Math.},
    fjournal = {L'Enseignement Math\'{e}matique},
    volume = {60},
    year = {2014},
    number = {3-4},
    pages = {247--255},
    issn = {0013-8584},
    mrclass = {37D50 (14H50)},
    mrnumber = {3342645},
    mrreviewer = {Mohammad Soufi},
    doi = {10.4171/LEM/60-3/4-2},
    url = {https://pdfs.semanticscholar.org/e0a4/4c62befebf56472cda62589dacbc404f8710.pdf},
    zblnumber = {1371.37073},
}

@ARTICLE{alexey14,
    author = {Glutsyuk, Alexey},
    title = {On odd-periodic orbits in complex planar billiards},
    journal = {J. Dyn. Control Syst.},
    fjournal = {Journal of Dynamical and Control Systems},
    volume = {20},
    year = {2014},
    number = {3},
    pages = {293--306},
    issn = {1079-2724},
    mrclass = {37C25 (37F05)},
    mrnumber = {3224419},
    doi = {10.1007/s10883-014-9236-5},
    url = {https://doi.org/10.1007/s10883-014-9236-5},
    arxiv = {1309.1849},
    zblnumber = {1333.37009},
}

@ARTICLE{centina15,
    author = {del Centina, Andrea},
    title = {Poncelet's Porism: a long story of renewed discoveries I},
    year = {2016},
    journal = {Arch. Hist. Exact Sci.},
    fjournal = {Archive for History of Exact Sciences},
    volume = {70},
    number = {2},
    pages = {1--122},
    issn = {0003-9519},
    mrclass = {01A60 (51M04 51N35)},
    doi = {10.1007/s00407-015-0163-y},
    url = {https://doi.org/10.1007/s00407-015-0163-y},
    zblnumber = {1333.01015},
}

@ARTICLE{grozdev17,
    author={Sava Grozdev and Hiroshi Okumura and Deko Dekov},
    title={Computer Discovered Mathematics: Triangles homothetic with the Orthic     triangle},
    journal={Int. J. of Comp. Disc. Mathematics (IJCDM)},
    fjournal={International Journal of Computer Discovered Mathematics (IJCDM)},
    issn={2367-7775},
    volume={2},
    year={2017},
    pages={46--54},
    mrclass={51-04 (68T01 68T99)},
    url={http://www.journal-1.eu/2017/Grozdev-Okumura-Dekov-Orthic-triangles-pp.46-54.pdf}
}

@ARTICLE{garcia2019-monthly,
    author = {Garcia, Ronaldo},
    title = {Elliptic Billiards and Ellipses Associated to the 3-Periodic Orbits},
    journal = {American Mathematical Monthly},
    volume={126},
    number={06},
    pages={491--504},
    url={https://doi.org/10.1080/00029890.2019.1593087},
    year = {2019}
}

@ONLINE{reznik2019-intelligencer,
author={Reznik, Dan and Garcia, Ronaldo and Koiller, Jair},
journal={Math Intelligencer},
day={12},
month={12},
year={2019},
url={https://arxiv.org/abs/1911.01515},
publisher={Springer US},
issn={1866-7414}
}

@unpublished{garcia2020-ellipses,
Author = {Ronaldo Garcia and Dan Reznik and Jair Koiller},
Title = {Loci of 3-periodics in an Elliptic Billiard: why so many ellipses?},
Year = {2020},
howpublished = {arXiv:2001.08041},
url={https://arxiv.org/abs/2001.08041}
}

@unpublished{garcia2020-properties,
Author = {Ronaldo Garcia and Dan Reznik and Jair Koiller},
Title = {New Properties of Triangular Orbits in Elliptic Billiards},
Year = {2020},
Eprint = {arXiv:2001.08054},
url={https://arxiv.org/abs/2001.08054}
}

@MISC{helman19,
  author       = {Mark Helman},
  howpublished = {Private Communication},
  day          = {4},
  month        = {August},
  year         = {2019},
  address      = {Houston, TX},
  comment      = {Proofs of the ellipticity of X(7),X(142),X(144),X(57),X(63)},
  institution  = {Rice University}
}

### ONLINE

@ONLINE{himmelstrand12,
  title={A Survey of Dynamical Billiards},
  author={Markus Himmelstrand and Victor Wilén and Maria Saprykina},
  publisher={Department of Mathematics, Royal Institute of Technology (KTH)},
  url={https://pdfs.semanticscholar.org/3d98/090d1023f48be37d534682ad989a89cb0042.pdf},
  year={2012}
}

@ONLINE{richardson10,
    author = {Richardson, Bill},
    title = {I was just looking for an example},
    year = {2010},
    url = {http://www.math.wichita.edu/~richardson/Orthic-story/orthic-triangle-complete.html},
    institution = {Wichita State University},
}

@online{etc,
    author = {Kimberling, C.},
    title = {Encyclopedia of Triangle Centers},
    year = {2019},
    url = {https://faculty.evansville.edu/ck6/encyclopedia/ETC.html},
}

@online{etc-bicentric,
    author = {Kimberling, C.},
    title = {Bicentric Pairs of Points},
    howpublished={Encyclopedia of Triangle Centers},
    year = {2020},
    url = {https://faculty.evansville.edu/ck6/encyclopedia/BicentricPairs.html},
}


@ONLINE{wp_geodesics,
   title={Geodesics on an ellipsoid},
   author={Wikipedia},
   year={2019},
   url={https://en.wikipedia.org/wiki/Geodesics_on_an_ellipsoid#Geodesics_on_a_triaxial_ellipsoid}
}

@ONLINE{mw,
    author = {Weisstein, E.},
    title = {Mathworld},
    journal = {MathWorld--A Wolfram Web Resource},
    url = {http://mathworld.wolfram.com},
    year = {2019}
}

@ONLINE{mw-envelope,
    author = {Weisstein, E.},
    title = {Envelope of a Curve},
    journal = {MathWorld--A Wolfram Web Resource},
    url = {http://mathworld.wolfram.com/Envelope.html},
    year = {2019}
}

@ONLINE{mw_orthic,
    author = {Weisstein, E.},
    title = {Orthic Triangle},
    journal = {MathWorld--A Wolfram Web Resource},
    url = {http://mathworld.wolfram.com/OrthicTriangle.html},
    year = {2019}
}

@misc{mathematica-v10,
  author = {Stephen Wolfram},
  title = {Mathematica, Version 10.0},
  Address = {Champaign, IL},
  year={2019}
}

@book{odehnal2015-conics,
    AUTHOR = {Glaeser, Georg and Stachel, Hellmuth and Odehnal, Boris},
     TITLE = {The universe of conics},
      NOTE = {From the ancient Greeks to 21st century developments},
 PUBLISHER = {Springer Spektrum, Berlin},
      YEAR = {2016},
      ISBN = {978-3-662-45449-7; 978-3-662-45450-3},
   MRCLASS = {14-03 (14H45 51N20 51N35)},
  MRNUMBER = {3494965},
MRREVIEWER = {Roberto Mu\~{n}oz},
       DOI = {10.1007/978-3-662-45450-3},
       URL = {https://doi.org/10.1007/978-3-662-45450-3},
}

@book{akopyan2007,
author={A. V. Akopyan and A. A. Zaslavsky},
title={Geometry of Conics},
published={Amer. Math. Soc.}, address={Providence, RI},
year={2007},
note={Russian 2nd edition},
url={https://bit.ly/32n7t3t}
}

@online{dykstra2006-loci,
title={Orbiting Vertex: Follow That Triangle Center!},
author={Justin Dykstra and Clinton Peterson and Ashley Rall and Erika Shadduck},
year={2006},
url={bit.ly/2JaWMK9}
}

@article{odehnal2011-poristic,
    AUTHOR = {Odehnal, Boris},
     TITLE = {Poristic loci of triangle centers},
   JOURNAL = {J. Geom. Graph.},
  FJOURNAL = {Journal for Geometry and Graphics},
    VOLUME = {15},
      YEAR = {2011},
    NUMBER = {1},
     PAGES = {45--67},
     url={https://www.geometrie.tuwien.ac.at/odehnal/pltc.pdf}
}

@ARTICLE{pamfilos2020-euler,
title={Triangles Sharing their Euler Circle and Circumcircle},
author={Paris Pamfilos},
journal={International Journal of Geometry},
volume={9},
number={1},
pages={5--24},
year={2020},
url={ijgeometry.com/wp-content/uploads/2020/03/1.-5-24.pdf}
}

@article{georgiev2012-poncelet,
author={Vladimir Georgiev and Veneta Nedyalkova},
title={Poncelet’s porism and periodic triangles in ellipse},
year={2012},
journal={Dynamat},
url={www.dynamat.oriw.eu/upload_pdf/20121022_153833__0.pdf}
}