Bart De Bruyn, On a Problem Regarding the $n$-Sectors of a
Forum Geometricorum, 5 (2005) 47--52.
Abstract: Let Delta be a triangle with vertices A, B, C and angles alpha,
beta, gamma. The n-1 lines through A which, together with the lines AB and
AC, divide the angle alpha in n >= 2 equal parts are called the n-sectors
of Delta. In this paper we determine all triangles with the property
that all three edges and all 3(n-1) n-sectors have rational lengths.
We show that such triangles exist only if n = 2, 3.
[ps file][pdf file]
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