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    Heya, most questions im ok with, but i think the spanish is a bit for a barrier to me for this one

    Could anyone give me a transation? that would be awesome

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    3.18 – In \mathbb{R}^3, we consider a straight line r, a half-plane \pi whose boundary is the line L, and a shape \mathbb{F} contained in the half-plane \pi. The shape of revolution of \mathbb{F} around L consists of the shape obtained by performing on \mathbb{F} all rotations of an arbitrary angle \theta around the same axis L.

    Considering the axis r=OZ as line of revolution, show that:

    (a) the shape of revolution of a line parallel to L is a cylinder.

    (b) the shape of revolution of a line secant to L is a cone.

    (c) the shape of revolution of the half-parabola which cuts the axis L perpendicularly at its vertex is a paraboloid.

    (d) the shape of revolution of the half-ellipse which touches L perpendicularly is an ellipsoid.

    (e) the shape of revolution of the half-branch of the hyperbola which touches r perpendicularly is one leaf of an elliptic hyperboloid (of two leaves).

    (f) the shape of revolution of a branch of the hyperbola with axis perpendicular to L is an hyperboloid of one leaf.
 
 
 
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Updated: January 28, 2015
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