So the artists could draw in the half-plane model, and then use a computer to convert to the circle model.)ĮDIT: For example, figure 1 of this paper shows a tessellation by square like shapes of the hyperbolic plane, displayed in the half-plane model. Let kids create a tessellation pattern by cutting one shape from the side of the square.
Drawing in a half-plane model appears to be much simpler than in a circle model. Step 1: Cut out a square from the tag board (or poster board).
(It's interesting, because if so, this presents a much easier way to replicate Escher's work. Go do a simple image search, MC Escher tessellation, images. Trying to wrap my head around how those little people could go up and down the stairs forever. My question is, as interpreted as half-plane models, would these correspond to tessellations of the hyperbolic plane? (It would also be interesting to see them changed into other models of the hyperbolic, such as the Poincaré disk model.) I could stare at his works for hours on end. The second piece would also need to be extended downwards, but since the lizards are shrinking exponentially, they would converge to a line, it appears. But it is not too hard to imagine extending the artwork left, up, and right into the whole half-plane. Note that these pieces do not contain the whole half-plane, of course. These look suspiciously like Poincaré half-plane models of the hyperbolic plane (there are pieces of artwork by Escher specifically based on the hyperbolic plane).
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