Skip to main content
SpringerLink
Log in

Centers of Mass of Poncelet Polygons, 200 Years After

  • Mathematical Gems and Curiosities
  • Sergei Tabachnikov, Editor
  • Published:
The Mathematical Intelligencer Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. W. Barth, Th. Bauer. Poncelet theorems. Exposition. Math. 14 (1996), 125–144.

  2. H. J. M. Bos, C. Kers, F. Oort, D. W. Raven. Poncelet’s closure theorem. Exposition. Math. 5 (1987), 289–364.

  3. I. Dolgachev. Classical algebraic geometry. A modern view. Cambridge U. Press, Cambridge, 2012.

  4. V. Dragović, M. Radnović. Poncelet porisms and beyond. Integrable billiards, hyperelliptic Jacobians and pencils of quadrics. Birkhäuser/Springer Basel AG, Basel, 2011.

  5. V. Dragović, M. Radnović. Bicentennial of the great Poncelet theorem (1813–2013): current advances. Bull. Amer. Math. Soc. 51 (2014), 373–445.

  6. L. Flatto. Poncelet’s theorem. Amer. Math. Soc., Providence, RI, 2009.

  7. M. Gardner. Mathematical Games. Six sensational discoveries that somehow or another have escaped public attention, Scientific American, (1975), 126–130.

  8. Ph. Griffiths, J. Harris. On Cayley’s explicit solution to Poncelet’s porism. Enseign. Math. 24 (1978), no. 1-2, 31–40.

  9. W. M’Clelland. A treatise on the geometry of the circle and some extensions to conic sections by the method of reciprocation. Macmillan and Co., London and New York, 1891.

  10. O. Romaskevich. On the incenters of triangular orbits on elliptic billiards. Enseign. Math. 60 (2014), 247–255.

  11. R. Schwartz, S. Tabachnikov. Elementary surprises in projective geometry. Math. Intelligencer 32 (2010) no. 3, 31–34.

  12. A. Shen. Poncelet Theorem Revisited. Math. Intelligencer 20 (1998) no. 4, 30–32.

  13. A. Skutin. On rotation of an isogonal point. J. Classical Geom. 2 (2013), 66–67.

  14. M. Weill. Sur les polygones inscrits et circonscrits à la fois à deux cercles. Journ. de Liouville 4 (1878), 265–304.

  15. A. Zaslavsky, G. Chelnokov. Poncelet theorem in Euclidean and algebraic geometry (in Russian). Matemat. Obrazovanie (2001), no. 4 (19), 49–64.

  16. A. Zaslavsky, D. Kosov, M. Muzafarov. Trajectories of remarkable points of the Poncelet triangle (in Russian). Kvant (2003), no. 2, 22–25.

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Brown University, Providence, RI, 02912, USA

    Richard Schwartz

  2. Department of Mathematics, Penn State University, University Park, PA, 16802, USA

    Sergei Tabachnikov

Authors
  1. Richard Schwartz
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sergei Tabachnikov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sergei Tabachnikov.

Additional information

This column is a place for those bits of contagious mathematics that travel from person to person in the community, because they are so elegant, surprising, or appealing that one has an urge to pass them on. Contributions are most welcome.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Schwartz, R., Tabachnikov, S. Centers of Mass of Poncelet Polygons, 200 Years After. Math Intelligencer 38, 29–34 (2016). https://doi.org/10.1007/s00283-016-9622-9

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00283-016-9622-9

Keywords

Search

Navigation