Hi Vladimir,

I agree with your conclusions on the deltoid. I think I needed that week's vacation.

With respect to a question I put to Golland: Do we lose any generality if we only look at an equilateral triangle?

Here are my thoughts. For any three non-collinear points in Euclidean 3-space it seems that we can find a plane (and if one plane, then an infinite number) such that the projections of the points on the plane would be the vertices of a equilateral triangle. Therefore, given a non-equilateral triangle and point we project the problem to an equilateral triangle and a point. Solve that problem and reverse the projection to solve the original problem (since the ratios of areas are invariant under a projection). What do you think?

Bractals