Take the Viviani curve intersection of a sphere and a cylinder. Analytically explain what happens to the intersection curve if you keep the radius of the sphere constant, fix one side of the cylinder at the origin, and change the radius of the cylinder. Especially, discuss the cases when the radius of the cylinder goes to 0 and ∞

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Take the Viviani curve intersection of a sphere and a cylinder. Analytically explain what happens to the intersection curve if you keep the radius of the sphere constant, fix one side of the cylinder at the origin, and change the radius of the cylinder. Especially, discuss the cases when the radius of the cylinder goes to 0 and   ∞

laure6237ma · Accepted Answer

Step 1If   r  =  0 ,   x  =  y  =  0 and   z  =  ±  RAnd if   r  →  ∞ , as   x  =                              x          2                +                  y          2                    r        ≤                    R        2            r        →  0 the curve tends to the circle   x  =  0  ,      y    2    +      z    2    =      R    2   .The projection of the intersection curve on the plane xz is inscribed on a parabola (one or two arcs).

Take the Viviani curve intersection of a sphere and a cylinder. Analytically explain what happens to

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