 # Circular Hole Drilled in a Cylinder

Initializing live version Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

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

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

## Snapshots   ## Details

Consider a cylinder of radius with axis parallel to the axis. Its parametric equations are , , ,

where and are parameters.

Consider another cylinder, of radius with axis at a distance from the axis and where is the angle between the axis of the drill and the vertical. Its parametric equations are , , ,

where and are parameters.

The intersection curve of the two surfaces can be obtained by solving the system of three equations for three of the four parameters .

Solving for , , and gives the parametric equations for the intersection curve with parameter : , , The two parts of the equation represent the upper and lower half of the intersection curve.

## Permanent Citation

Erik Mahieu

 Feedback (field required) Email (field required) Name Occupation Organization Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback. Send