I've been studying Ring Theory, and there is a marvellous chapter about Constructible Numbers and Euclidean Geometry (LEQUAIN, Y et al. Elementos de Álgebra) and I began wondering: What about the Hyperbolic Geometry?
I studied the Hyperbolic Plane in three ways: Without models, Half-Plane Poincaré Model and Disk Poincaré Model. But I'm not sure about this question: What are the analogue in the hyperbolic plane for euclidean non-graduated ruler and compass that can make the Constructible Numbers?
Any help would be appreciated! Thanks!
A length $t$ in the hyperbolic plane can be constructed if and only if $\sinh t$ is a length that can be constructed in the Euclidean plane. The constructible angles in the hyperbolic plane are exactly the same as those in the Euclidean plane.
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