Hyperbolic Crochet

"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." -Henderson & Taimina, 2001.

Where to Find Us:

University of Texas - Pan American, Mathematics and General Classrooms Building, Room 2.326

Hyperbolic Garden

Picture of Garden in Lab
The garden is currently at IMAS for Spring 2014. Here are some pictures of the garden at IMAS.



Community Outreach:

Community Outreach

Check out our photo gallery of completed pieces here!

Project Materials:

1 Crochet Hook: Size: H (is good to start)
1 bunch (skein) of yarn

Approximate Cost: $3. If supplies are needed, EAGL may be able to provide them. Please contact Dr. Lawton for information.

Making Your Own Hyperbolic Crochet:

To Begin Weaving your Hyperbolic Crochet please see our Learning to Hyperbolic Crochet page.
The following page provides the user with detailed instructions and videos on how to create a Hyperbolic Crochet.

Submitting Your Finished Crochet:

Once finished, a volunteer has the option to either keep it home or donate it. We ask that you donate
your hyperbolic crochet to our growing collection. Visit our Submission page
for more information on how to contribute.

It is our hope that once we gather enough donations that we will be able to create an exhibit in South Texas,like this, promoting math and art.

Project Members:

Fall 2012:
Jesus Chavez, UTPA student (Lab Assistant)
Sarah Jane Schwartz, UTPA student (Lab Assistant)
Sarah Silva, UTPA student (volunteer)
Mayra Balderas, UTPA student (volunteer)

Spring 2012:
Jesus Chavez, UTPA student (Lab Assistant)
Alberto Lopez, UTPA student (Lab Assistant)
Sarah Jane Schwartz, UTPA student (volunteer)
Tessia Gonzalez, UTPA student (volunteer)
Rebekah Gomez, UTPA student (volunteer)
Michelle Gonzalez, UTPA student (volunteer)
Estrella Medina, UTPA student (volunteer)
Michelle Salazar, (volunteer)

Fall 2011:
Alberto Lopez, UTPA student (Lab Assistant)
Jesus Chavez, UTPA student (volunteer)
Baldermar Hernandez, UTPA student (volunteer)
April Marquez, UTPA student (volunteer)
Emily Sanchez, UTPA student (volunteer)
Camille Cuellar, UTPA student (volunteer)
Serena Oh, UTPA student (volunteer)
Sahira Chapa, UTPA student (volunteer)
Lohany Garcia, UTPA student (volunteer)
Beatriz Pardo, UTPA student (volunteer)
Marcella Soto, UTPA student (volunteer)
Sarah Schwartz, UTPA student (volunteer)
Mirta San Miguel, UTPA student (volunteer)
Denise Martinez, UTPA student (volunteer)
Roel Resendez, UTPA student (volunteer)
Baldemar Hernandez, UTPA student (volunteer)
Samantha Tmbnz, UTPA student (volunteer)
Magaly Garcia, UTPA student (volunteer)
Tessia Gonzalez, UTPA student (volunteer)
Betty A. Garcia, UTPA student (volunteer)
Yvette Galindo, UTPA student (volunteer)

Spring 2011:
Jesus "Jesse" Aguero, UTPA Junior: Computer Science.
Claudia Carranza, UTPA Senior: Mathematics.
Holly Kvapil, UTPA Senior: English.
Sandi Millford, UTPA Post-Bac Senior: Biology/Art.
Raul Rodriguez, UTPA Sophmore: Computer Engineering.
Dominic Fernandez, UTPA Junior: Computer Science.

Project Faculty Sponsors:

Dr. Sean Lawton, UTPA Assistant Professor: Department of Mathematics.

Source Materials:

My Crochet Teacher by Susan Bates, c 1987 Susan Bates, a division of Coats & Clark.
10*20*30 Minutes to Learn to Crochet by Leisure Arts, c 2000 Leisure Arts, Inc.
Experiencing Geometry, Euclidean and Non-Euclidean with History, 3rd Edition by David W. Henderson and Daina Taimina, c2005, 2001, 1996 Pearson Education Inc, ISBN: 0-13-143748-8.
Crocheting Adventures with Hyperbolic Planes by Daina Taimina, c2009 A K Peters, Ltd., ISBN: 978-1-56881-452-0
Foundations of Geometry by Venema, ISBN: 0-13-143700-3

Additional Links and Information about Hyperbolic Crochet

  1. TED Talks- Hyperbolic Crochet
  2. Hyperbolic Geometry in the Ocean
  3. Crocheting the Hyperbolic Plane by David W. Henderson and Daina Taimina
  4. Interview with Daina Taimina
  5. Crocheting Adventures with Hyperbolic Planes
  6. Daina Taimina's Website

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