Dissections into equilateral triangles (Q1179939)

The paper shows that an equilateral triangle (and more generally any convex polygon) has no finite dissection into incongruents equilateral triangles. Moreover, the maximum number \(f(n)\) of distinct sizes of equilateral triangles in a dissection of an equilateral triangle into \(n\) parts is equal to \(cn-o(n)\) as \(n\to\infty\) for some constant \(c\geq 5/7\). As the author points out it would be interesting to determine the exact value of \(\lim f(n)/n\) for \(n\to\infty\), in particular to decide if it is less than 1.