Malfatti's Packing Problem
You can use this applet to compare the efficiency of the Malfatti Packing (of 3 circles of possibly different size into a given triangle) against Lob-Richmond's 'Greedy' algorithm
Historical background, courtesy of Wikipedia:
In 1803, Malfatti posed the problem of how best to cut 3 circles out of a given triangle in order to maximise the total area of the circles, motivated by thinking about cutting circular columns from a triangular prism. He conjectured that the best way to do this was for each circle to touch 2 sides of the triangle. This seemed to make good sense, until in 1930, Lob and Richmond noticed that Malfatti was plainly wrong for an extremely thin isosceles triangle (you can see using the applet). Amusingly, it turns out, in fact, that Malfatti was never correct; that is to say that there is no triangle in the set of all triangles for which Malfatti's method is more efficient than Lob-Richmond's method!
How to use the applet: Move points A, B and C around.