Sadly, technological progress has relegated our early (and usually laboriously crafted) efforts to museum exhibits --- compare the demo at https://en.wikipedia.org/wiki/Dandelin_spheres WFL On 11/11/18, Bill Gosper <billgosper@gmail.com> wrote:

Eons ago, trying to prove that locus-of-constant-difference is a conic section, I reinvented Dandelin spheres, with a possibly simpler proof that does not refer to their centers nor radii. gosper.org/hyperb.GIF uses instead the lemma that all tangents to a sphere from a point are equally long. The drawing probably needs stereo vision to be convincing. I'm not sure I realized at the time that the spheres could be unequal. —rwg _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun