Cone from a Rotating Line
- Susan Addington
A cone can be formed by rotating a line: Start with a circle c and a point C that's not in the plane of the circle. Make all lines that go through C and all the points on the circle. In this applet, move point B around the circle, and see the trace of the line BC as B goes around the circle. (To animate B, use the triangular "Play" button at the bottom of the left pane.) Drag the mouse or your finger in the right pane to get different views. Move the point C to get a different cone. Then delete the traces from the previous position by clicking the Clear traces button.
In some situations "cone" means a finite cone, with a circle as a base and ending at the vertex. In other situations (such as conic sections) an infinite cone is needed; it continues beyond both the circle and the vertex. To see the finite cone, check Show segment and uncheck Show line. Visit Mathematical Intentions at http://www.quadrivium.info for some history of conic sections. Troubleshooting: If you get an error message in the 3D window at right, here are some things to try:
- Try a different browser
- Research how to enable WebGL in your browser
- Download the applet file (see the three vertical dots in the upper right of this window) and open it in your own copy of GeoGebra. Download the GeoGebra software at https://www.geogebra.org/download.