Talk:Special case

Circle as special case of ellipse

I changed the reference "all circles are ellipses" to "all squares are rectangles." The reason for this is that, under the formal definition of an ellipse, circles are not, in fact, ellipses. In particular, an ellipse is "the set of all points in a plane the sum of whose distance to two fixed points, called the foci, is constant." In fact, circles do not have foci, and the formal definition of a circle is "the set of all points in a plane equidistant from a fixed point, called the center."

It is questionable:

In geometry, an ellipse (from Greek ἔλλειψις elleipsis, a "falling short") is a plane curve that results from the intersection of a cone by a plane in a way that produces a closed curve. Circles are special cases of ellipses, obtained when the cutting plane is orthogonal to the cone's axis.

VladimirReshetnikov (talk) 21:54, 10 February 2012 (UTC)

I agree that the definition regarding a plane's intersection with a cone is one definition of an ellipse, with the orthogonal case being a circle. However, I teach math at a college and notice that most of the algebra textbooks use the "foci" definition of an ellipse, not the "plane intersection" definition. I'm not sure which definition is better. There may be scholarly materials that would shed light on this, but I haven't researched the available literature. In any event, I switched the article to the rectangle/square concept because this seems non-controversial. — Preceding unsigned comment added by Pgordon2 (talk • contribs) 20:51, 12 February 2012 (UTC)

Yes, the circle is a special case of the ellipse, even if you use the "foci" definition of an ellipse. In the case of the circle, the two foci coincide at the same point. Duoduoduo (talk) 16:40, 6 June 2013 (UTC)