A hyperbolic plane is a mathematical object that consists of a surface of constant negative curvature—the opposite of a sphere, which has constant positive curvature. The geometry most of us learn in high school, known as Euclidean Geometry, holds that the hyperbolic plane does not and cannot exist. Although the history of mathematics goes back millennia, it’s been less than two centuries since mathematicians have come to believe that the hyperbolic plane is a possible, not an impossible, object in non-Euclidean geometry.
A crocheted hyperbolic plane is a model of a hyperbolic plane that is made by crocheting, using yarn and a crochet hook. Mathematician Daina Taimina was the first person to make a model of a hyperbolic plane using crochet, improving on the fragile paper models that a few mathematicians had previously made. Crocheted hyperbolic planes are significant because they demand that we reconsider accepted dualisms such as mathematics/art, abstract/tangible, artificial/natural, serious/frivolous, and rational/affective.