Circular Hole Drilled in a Sphere

This Demonstration explores the shape of the difference between a sphere and a right circular cylinder.

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DETAILS

Consider a cylinder of radius , with axis at a distance from the axis. Its parametric equations are
,
,
,
where and are parameters.
The parametric equation of a sphere with radius is
,
,
,
where and are parameters.
The intersection curve of the two surfaces comes from solving the system of three equations
for three of the four parameters . In this Demonstration, solving for , , and gives the parametric equations for the intersection curve with parameter (the curve consists of four parts, depending on the sign inside the equations for and ).
For parts 1 and 2,
,
,
.
For parts 3 and 4,
,
,
.
Here
,
,
and
.
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