"HB" == Henry Baker <hbaker1@pipeline.com> writes:
HB> Where do the Marden ellipse foci go when the 3 vertices are collinear? HB> Suppose A,B,C are the 3 triangle vertices, with their opposite line segments a,b,c, respectively, as usual. HB> Suppose we go to the limit where a=b+c. As the triangle collapses, HB> the foci move further and further into the corners B,C. In the HB> limiting case, the foci are _at_ B,C. That was my intuition (or memory? I haven't really thought about such stuff much in the last 25 or so). But a simple poly with real (and therefore collinear) zeros such as 0=(x-1)*(x-2)*(x-3) seems to show otherwise. The roots of the 1st diff are bounded by 2+-sqrt(3)/3, and the root of the 2nd diff is 2, (as calculated and plotted by maxima). Or does this imply the that limit of an ellipse inscribed in a triangle is not the same as the limit of said triangle when the triangle is collapsed to a line segment? -JimC -- James Cloos <cloos@jhcloos.com> OpenPGP: 1024D/ED7DAEA6