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The book is on the use of crochet to make physical surfaces with the geometry of the hyperbolic plane. The full hyperbolic plane cannot be embedded smoothly into three-dimensional space, but pieces of it can. Past researchers had made models of these surfaces out of paper, but Taimiņa's work is the first work to do so using textile arts. [1]
Hyperbolic crochet [ edit ] While attending a geometry workshop at Cornell University about teaching geometry for university professors in 1997, Taimiņa was presented with a fragile paper model of a hyperbolic plane, made by the professor in charge of the workshop, David Henderson (designed by geometer William Thurston . [ 4 ] )
The pseudosphere and its relation to three other models of hyperbolic geometry. The half pseudosphere of curvature −1 is covered by the interior of a horocycle.In the Poincaré half-plane model one convenient choice is the portion of the half-plane with y ≥ 1. [7]
Of these, the tractoid (or pseudosphere) is the best known; using the tractoid as a model of the hyperbolic plane is analogous to using a cone or cylinder as a model of the Euclidean plane. However, the entire hyperbolic plane cannot be embedded into Euclidean space in this way, and various other models are more convenient for abstractly ...
The metric of the model on the half-plane, { , >}, is: = + ()where s measures the length along a (possibly curved) line. The straight lines in the hyperbolic plane (geodesics for this metric tensor, i.e., curves which minimize the distance) are represented in this model by circular arcs perpendicular to the x-axis (half-circles whose centers are on the x-axis) and straight vertical rays ...
Move over, Wordle, Connections and Mini Crossword—there's a new NYT word game in town! The New York Times' recent game, "Strands," is becoming more and more popular as another daily activity ...
Studied by Eugenio Beltrami in 1868, [2] as a surface of constant negative Gaussian curvature, the pseudosphere is a local model of hyperbolic geometry. The idea was carried further by Kasner and Newman in their book Mathematics and the Imagination , where they show a toy train dragging a pocket watch to generate the tractrix.
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