Tuesday, April 8, 2014

Is an ellipse really a conic?

I don't think so. Consider that an ellipse is supposed to have equal eccentricity on each end -- it's not supposed to be shaped like a cross section of an egg.

But now consider that a cone has a varying radius from it's base to its vertex. At the vertex of a cone, the peak of the cone, the radius is zero, at its base, the radius of the cone is however large you want to make it.

The ellipse is (supposedly) the result of cutting the cone at a SLANT. This means the radius of the cone is different at one end of the ellipse than the other. This means that the only way to have a true ellipse is to have a section of a cylinder, not of a cone. Nevertheless, they persist in calling it a "conic". Is there something I overlooked?

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