A Note on Transversals in Hyperbolic Planes

Knüppel (J Geom 105:13–20, 2014) shows that in a hyperbolic plane an asymptotic n-gon does not admit a transversal line when n is odd. If n is even then there exist n-gons which admit a transversal line. Recently Struve (J Geom 103:333–346, 2012) showed that in hyperbolic geometry an order structure can be introduced purely in terms of the calculus of reflections. Following this approach we give a short proof of the above mentioned theorem which provides new insights into the underlying foundations of the theorem.