On Sharygin triangles with commensurable angles

Nikolai N. Osipov

Siberian Federal University, Krasnoyarsk, Russian Federation

Abstract: By a simple method we prove the following conjecture on Sharygin triangles: there is only one Sharygin triangle (up to similarity) whose angles are pairwise commensurable. Additionally, a similar result is proved on triangles with pairwise commensurable angles and two equal angle bisectors.

Keywords: Sharygin triangle, trigonometric diophantine equation.

UDC: 511.53

Received: 10.04.2025
Received in revised form: 21.05.2025
Accepted: 04.09.2025

Language: English