This is a finite piece of Dini’s surface, which has constant negative Gaussian curvature. The same shape, extended indefinitely, can embed an infinitely long strip of the hyperbolic plane, with a geodesic G as one boundary and a hypercycle (a curve a fixed distance from G) as the other. The geodesic is mapped to the central axis of Dini’s surface, while the hypercycle is mapped to the outer helix.
@gregeganSF These feature in the answer to this mathoverflow question as to whether one may isometrically embed arbitrarily large hyperbolic disks in Euclidean 3-space. https://mathoverflow.net/a/3708/1345
@Ianagol@gregeganSF Mass produce? Or just on a small scale? I hear that making new mass-production pasta machines is hard, in part because of the sanitary requirements on food prep machines.
@henryseg@gregeganSF I’m even just thinking theoretically, how would constant negative gauss curvature pasta be designed? Most pasta is rolled from flat sheets, so is approximately intrinsically Euclidean aside from stretching.
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