Bill G. writes: << Some find it counterintuitive that slicing a cone gives an ellipse and not an oval. What about slicing a paraboloid of rotation? More generally how can eliminating a quadratic mumbloid vs a linear (planar) equation yield anything but a quadratic (conic)?

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What happens when a plane passes through both sheets of a hyperboloid (of two sheets) in R^3, but contains the vertex of only one sheet? (Naively it's hard to believe the intersection has the symmetry of a hyperbola.) ------------------------------------------------------------------------------------------- But to escalate the question a bit, what happens when two quadratic surfaces in R^3 intersect? It appears that all kinds of bizarre space curves are possible (that I never learned about in school). --Dan