We try to add to A Variant of the Malfatti Problem
As stated in the Wikipedia entry on Malfatti circles, it is an open problem to decide, given a number $n$ and any triangle, whether a greedy method gives an area-maximizing packing of n disks in that triangle.
Question: if, instead of total area, we want to maximize the sum of the perimeters of the $n$ disks being packed into any given triangle, will the same greedy approach of successively putting the largest possible circle into what remains of the triangle give an optimal answer? Basically, will the problem become easier to decide if we replace area by perimeter?
Speculation: If we move to non-Euclidean geometry, the greedy method that attempts to produce an optimal packing for a triangle is more likely to fail in hyperbolic geometry. In elliptic geometry since there appear to be more 'room' in the interior of a triangle than its corners, greedy has better chances of being correct.
