Crocheting the Hyperbolic Plane

Even if we weren’t home­school­ing, I don’t think I could give up some of my HSing lists, because I’d miss out on things like this.

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 (1775–1856) to his son János, urg­ing him to give up work on non-Euclid­ean geometry

The crin­kled edges of a let­tuce leaf curve and expand in a shape that has per­plexed math­e­mati­cians for cen­turies. Those curves—an exam­ple of a high-lev­el geom­e­try con­cept called the hyper­bol­ic plane—were not even defined by geom­e­try the­o­rists until the 19th cen­tu­ry. And in the almost 200 years fol­low­ing, math­e­mati­cians strug­gled to find a way to mod­el the com­plex shape known as the geo­met­ric oppo­site of the sphere.

Then math­e­mati­cian Daina Taim­i­na picked up her cro­chet nee­dles and some syn­thet­ic yarn, and the prob­lem was solved. In 1997, Taim­i­na, of Cor­nell Uni­ver­si­ty, found a way to cro­chet her way into “hyper­bol­ic space.” Her woolen cre­ations, which resem­ble crenu­lat­ed flow­ers and hair scrunchies, became the first phys­i­cal mod­els of the hyper­bol­ic plane.

Taim­i­na and her hus­band, fel­low Cor­nell math­e­mati­cian David Hen­der­son, are the co-authors of Expe­ri­enc­ing Geom­e­try, a wide­ly used text­book on both Euclid­ean and non-Euclid­ean spaces. They talk to NPR’s Jac­ki Lyden about hyper­bol­ic geom­e­try and crochet.

Lis­ten to the NPR interview

Anoth­er inter­view

Their own site, with patterns

Cyn is Rick's wife, Katie's Mom, and Esther & Oliver's Mémé. She's also a professional geek, avid reader, fledgling coder, enthusiastic gamer (TTRPGs), occasional singer, and devoted stitcher.
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