It exhibits two distinct constructions both of which demonstrate that n^2 + 2 unit equilateral triangles are sufficient to cover an equilateral triangle of side n + ε. The obvious area argument shows that at least n^2 + 1 are required.
A small modification of the second figure can show that for any non-equilateral triangle, n^2 + 1 such triangles will cover a similar triangle of length ration 1 : n + ε; it remains (as of 2010, at least; see [1]) an open problem whether a construction of n^2 + 1 triangles exists in the equilateral case.
A small modification of the second figure can show that for any non-equilateral triangle, n^2 + 1 such triangles will cover a similar triangle of length ration 1 : n + ε; it remains (as of 2010, at least; see [1]) an open problem whether a construction of n^2 + 1 triangles exists in the equilateral case.
1. http://www.wfnmc.org/mc20101.pdf