Let \(A, B, C\) be the vertices of a triangle with angles \(\alpha, \beta, \gamma\) at these. The \(n-1\) lines through \(A\) which together with the lines \(AB\) and \(AC\), divide the angle \(\alpha\) in \(n\) (greater than 1) equal parts are called the \(n\)-sectors of the triangle.
The author determines all triangles with the property that all three edges and all \(3(n-1)\) \(n\)-sectors have rational lengths. He shows that such triangles exist only if \(n = 2\) or 3.