I am studying the construction of Knopp's Osgodd curve. Specifically, start for instance from the triangle with vertices $(-1,0), (0,1), (1,0)$ and, at the $j$-th step, divide each triangle into two smaller ones with equal area by removing a wedge whose area equals $(r/j)^2$ of the given triangle, for $r\in (0,1)$ fixed.
The question is: How can be proven that the diameters of the triangles tend to zero?