3 papers
math.GM2026
A Hypotenuse-Angle Axiomatization of the Hilbert Plane
Roberto Volpe
We show that, in $\MG^{-}$ --- $\MG$, the Hilbert plane, deprived of the Side-Angle-Side axiom --- a hypotenuse-angle criterion for right triangles, together with the existence of…
math.HO2026
On the Reconstruction of SAS from Other Triangle Congruence Criteria, Part II: Eliminating the Pons Asinorum
Roberto Volpe
In the first part of this work we showed that, within a Hilbert plane deprived of the Side-Angle-Side axiom, the Side-Angle-Angle criterion, together with a ray correspondence prin…
math.HO2026
On the Reconstruction of SAS from Other Triangle Congruence Criteria
Roberto Volpe
Starting from a Hilbert plane and removing the Side-Angle-Side (SAS) congruence axiom, we investigate to what extent SAS can be recovered synthetically from the remaining classical…