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christianp / aperiodic-monotile

Smith, Myers, Kaplan and Goodman-Strauss's aperiodic monotile, in a variety of formats
Creative Commons Zero v1.0 Universal
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Replace the a and b sliders with a single slider #6

Open dkeenan7 opened 1 year ago

dkeenan7 commented 1 year ago

so we can traverse the continuum more easily. Call the value of the single slider x and have it vary from -1 to +1. Then a = (1+x)/(1-x) and b = 1/a. The detents will be at x = -1, √3-2, 0, 2-√3, 1.

dkeenan7 commented 1 year ago

OK. That was dumb. I think what I was going for was a = 1+x and b = 1-x.

dkeenan7 commented 1 year ago

OK. Finally figured how to go all the way from chevron - hat - equitortoise - turtle - comet with a single slider while preserving the scale. The slider θ goes from 0 to π/2 (or 0° to 90°) and we have a = sin(θ) and b = cos(θ). This keeps a²+b² constant. Chevron - hat - equitortoise - turtle - comet are 0° - 30° - 45° - 60° - 90°.