Circular Hole Drilled in a Sphere

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

Contributed by: Erik Mahieu (March 2014)
Open content licensed under CC BY-NC-SA


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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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