2
votes
3answers
264 views

Mid point with set square?

Is it possible to construct the midpoint of a segment in the hyperbolic plane using the set square only? With the set square one can draw the line through the given two points and drop the ...
5
votes
2answers
416 views

Bolyai's construction

Here is Bolyai's construction (in Klein model), which I learned recently from answer of Will Jagy to this question. It is a Compass-and-straightedge construction of asymptotically parallel line in ...
6
votes
2answers
698 views

Is there a ruler and compass construction of the common perpendicular of two geodesics in H^3?

Assume we have two geodesics in the Poincaré ball model of $\mathbb{H}^3$, viewed as arcs intersecting the boundary of and contained in the Euclidean unit sphere in $\mathbb{R}^3$. Is there a ruler ...