On Sunday 10 June 2007 10:45, I wrote:
On Sunday 10 June 2007 02:11, George W. Hart wrote: ...
If you draw ABC properly within a tessellation of unit equilateral triangles, it is clear from the Pythagorean theorem that its edge length is sqrt[7]. See figure 5 of: http://www.georgehart.com/radiolaria/radiolaria.html
Very nice (and, completely irrelevantly, I like your ray-trace-olarian) but that only answers the question for p=1/3.
and then went on to observe that the construction generalizes. If I'd looked at the discussion in the vicinity of figure 5 and not merely at the pretty picture I'd have noticed that George does consider the general case (though not in the context of areas or side division), so he probably already knew how to generalize the proof. :-) -- g