Quilting the Klein Quartic

Aus de_evolutionary_art_org
Wechseln zu: Navigation, Suche


Elisabetta Matsumoto: Quilting the Klein Quartic. In: Bridges 2017, Pages 411–414.



The Klein Quartic curve contains the maximal number of symmetries a genus 3 surface can have: 84(g − 1) = 168. We create a fabric model of 24 regular heptagons that not only captures the platonic nature of the Klein Quartic, but it is flexible enough to be everted through any of its holes, thus illustrating 24 of the 168 symmetries, whilst rigid models can only display 12.

Extended Abstract


 author      = {Elisabetta Matsumoto},
 title       = {Quilting the Klein Quartic},
 pages       = {411--414},
 booktitle   = {Proceedings of Bridges 2017: Mathematics, Art, Music, Architecture, Education, Culture},
 year        = {2017},
 editor      = {David Swart, Carlo H. S\'equin, and Krist\'of Fenyvesi},
 isbn        = {978-1-938664-22-9},
 issn        = {1099-6702},
 publisher   = {Tessellations Publishing},
 address     = {Phoenix, Arizona},
 note        = {Available online at \url{http://archive.bridgesmathart.org/2017/bridges2017-411.pdf}}

Used References

[1] John Baez. Klein’s Quartic Curve. Available at http://math.ucr.edu/home/baez/klein.html., 2013.

[2] Greg Egan. Klein’s Quartic Curve. Available at http://www.gregegan.net/SCIENCE/KleinQuartic/ KleinQuartic.html., 2006.

[3] A. Hurwitz. U¨ ber algebraische Gebilde mit eindeutigen Transformationen in sich.

[4] Hermann Karcher and Mathias Weber. The Geometry of Klein’s Riemannian Manifold. In Silvio Levy, editor, The Eightfold Way: The Beauty of Kleins Quartic Curve, pages 9–49. Cambridge Univ. Press, 1999.

[5] Felix Klein. U¨ber die Transformationen siebenter Ordnung der elliptischen Funktionen. Math. Annalen, 14:428–471, 1879. (Translation into English by S. Levy [7].).

[6] J. Lehner and M. Newman. On Riemann surfaces with maximal automorphism groups. Glasgow Math. J., 8:102–112, 1967.

[7] Silvio Levy. The Eightfold Way: The Beauty of Kleins Quartic Curve. Cambridge Univ. Press, 1999.

[8] H. E. Rauch and J. Lewittes. The Riemann surface of Klein with 168 automorphisms. In R. C. Gunning, editor, Problems in Analysis, pages 297–308. Princeton Univ. Press, 1970.

[9] Carlo S´equin. Patterns on the Genus-3 Klein Quartic. In Proceedings of Bridges 2006: Mathematics, Music, Art, Architecture, Culture. Tessellations Publishing, 2006.

[10] Mike Stay. Klein’s Quartic Curve. Available at http://math.ucr.edu/~mike/klein/. Accessed on 26 Feb 2017 at 21:19:29.


Full Text


internal file

Sonstige Links