Quien dijo que el crochet era cosas de abuelas?

Crocheting the Hyperbolic Plane

updated version is published in

Mathematical Intelligencer, Vol. 23, No. 2, pp. 17-28, Spring 2001.

David W. Henderson

Department of Mathematics, Cornell University, Ithaca, NY, USA, dwh2@cornell.edu

Daina Taimiða

Department of Mathematics, Cornell University, dtaimina@math.cornell.edu

For God's sake, please give it up. Fear it no less than the sensual passion, because it, too, may take up all your time and deprive you of your health, peace of mind and happiness in life.

 Wolfgang Bolyai urging his son János Bolyai to give up work on hyperbolic geometry.

In June of 1997, Daina was in a workshop watching the leader of the workshop, David, helping the participants study ideas of hyperbolic geometry using a paper and tape surface in much the same way that one can study ideas of spherical geometry by using the surface of a physical ball. David's hyperbolic plane was then so tattered and fragile that he was afraid to handle it much. Daina immediately began to think: "There must be some way to make a durable model." David made his first paper hyperbolic plane in the summer of 1978 while on canoe trip on the lakes of Maine using the scissors on his Swiss Army knife. He had just learned how to do the construction from William Thurston at a workshop at Bates College. This crude paper surface was used in the David's geometry classes and workshops (becoming more and more tattered) until 1986 when some high school teachers in a summer program that David was leading collaborated on a new larger paper and tape hyperbolic surface. This second paper and tape hyperbolic surface (used in classes and workshops for the next 11 years) was the one that Daina witnessed in use. Daina experimented with knitting (but the result was not rigid enough) and then settled on crocheting. She perfected her technique during the workshop and crocheted her first small hyperbolic plane and then while camping in the forests of Pennsylvania, she crocheted more and we started exploring its uses. In this paper we will share how to crochet a hyperbolic plane (and make related paper versions). We will share how we have used it to increase our own understanding of hyperbolic geometry. (Where does the formula pr² fit in hyperbolic geometry?) We will finish by proving that, in fact, it is an isometric model of the hyperbolic plane.

Si aun siguen animadas aqui les dejo este patron:

Comments

[Book Report]

After read blog topic's related post now I feel my research is almost completed. happy to see that.Thanks to share this brilliant matter.

[puntoyseguido]

jajaja, no creas que a mi tambien me asusto un poco.
La ventaja es que nosotras ya sabemos hacerlo!! :).
Por cierto, tus bolsitos estan geniales, me gusta muchisimo el colorido tan alegre.
Felicidades artistaza.

[Marida]

Me ha asustado un poco, no se si la asociación integrales-ganchillo me ayuda o me espanta. jeje

[lola]

Te has currado la busqueda, he? :-) es total, la caña.Feliz Año Nuevo