- Steve Phelps
It turns out that I needed to learn how to construct Malfatti Circles in order to construct the next Points of Intersection. Play through the construction below. There are a few lines that are hidden.
Italian mathematician Giovanni Malfatti (1731–1807) posed the following problem in 1803: Given a triangle, find three non-overlapping circles inside it such that the sum of their areas is maximal. Malfatti and many other mathematicians thought that the solution is given by the three circles each of which is tangent to the other two and also to two sides of the triangle. Malfatti computed the radii of these circles, and they are now known as Malfatti's circles. Later it became clear that Malfatti's conjecture was not true. It was proved in 1969 that the Malfatti circles never give a solution to Malfatti's problem! So far as is known, the Malfatti problem hasn't been solved yet in the general case.