How to Create a 3D Surface of Revolution by Rotating ANY 2D Figure about ANY LINE
- Author:
- Tim Brzezinski
- Topic:
- Geometry, Solids or 3D Shapes
In GeoGebra 3D, it is possible to form a surface of revolution by ROTATING ANY 2D FIGURE about ANY LINE (and not just the x- and y-axes). These objects DO NOT NEED to even be located with the (gray) xy-plane either.
What we need to do first is use GeoGebra's CURVE command, as illustrated in the silent video (2:19) below this resource.
Note the CURVE we defined in the video results in a line segment with starting endpoint C and final endpoint D. Yet we could have defined any of the components of this CURVE using ANY FUNCTION with respect to t (and not just linear).
The possibilities are endless!
Slide the "n" slider. Move any of the 4 LARGE BLUE POINTS anywhere you'd like at any time. What kinds of 3D surfaces can we create here?
How the resource above was made (in 2:19) - Silent Demo
Here's a much simpler means to use the CURVE command (start at 1:56). Thank you to Bernat Ancochea for pointing this out to me.
TO EXPLORE IN AUGMENTED REALITY:
1) Open up GeoGebra 3D app on your device.
2) Go to MENU (upper left corner).
Go to OPEN. Under Search, type measmzyn.
(Note these are the last 8 digits of this URL for this resource).
3) Find the slider named n.
You can move any of the 4 large points anywhere you'd like at any time.