"DA" == Dan Asimov <dasimov@earthlink.net> writes:
DA> My point is that the ellipses for c > 0 DA> do not approach the line segment [-1,1]. DA> They approach the line segment [-sqrt(⅓), sqrt(⅓)]. My question, based on Henry's first post on the theorem, can be summarized as: What do they approach? Is it [-1,1]? And why? Clearly not. My resulting hypothesis is: if one looks at the ellipse geometrically, via the pins and string method of drawing one, is it perhaps the case that the string's length remains constant as the triangle/ellipse collapse? Which would be the case if the minor radius goes to zero without any change to the major radius. Looking at http://en.wikipedia.org/wiki/Conic_Section, the details are quite a bit different that what was presented when I last studied. Directrix, latus rectum and 'linear eccentricity', as opposed to eccentricity are all new to me. Given the above ellipse, might the directrices be the lines yi+1 and yi-1, y \in R? -JimC -- James Cloos <cloos@jhcloos.com> OpenPGP: 1024D/ED7DAEA6