GeoGebra Tutorial 28 – Animation and Hypocycloids

This is the 28th tutorial of the GeoGebra Intermediate Tutorial Series. If this is your first time to use GeoGebra, you might want to read the GeoGebra Essentials Series.

A hypocycloid is a special curve generated by the trace of a fixed point on a small circle that rolls within a larger circle. It is comparable to the cycloid but instead of the circle rolling along a line, it rolls within a circle.

In the tutorial below, menu commands, located in the menu bar, are in green bold text, and sub-menus are denoted by the > symbol. For example, Options>Labeling> New Points Only means, click the Options menu, choose Labeling from the list, then select New Points Only. The tool texts are colored orange. For example, New Point means the new point tool. Texts typed in the input box are colored blue.

Instructions

11 thoughts on “GeoGebra Tutorial 28 – Animation and Hypocycloids”

1. It has been a nice Easter Sunday becauase of your posts. May the Lord add more Days, Energy and Passion for Mathematics to the Writer

• Thank you very much Justus.

2. Thanks a lot for all three cycloid tutorials. They helped me a lot to pass the german Abitur 🙂

• You’re welcome Anon.

3. Very nice.
In step 6 and 13: Add Sliders n and m (going from 1 to 20). Instead of setting the Animation Speed to 3 and 9 put n/10 and m/10.
Now it is easy to adjust and make different Patterns – of course when adjusting n and m the Speed of the two different Rotations might not match up but it makes nice Patterns.
The reason I put n/10 and m/10 is that it slows down the Animation and this makes more points. Also I have made the trace piont size 1 to make the trace thinner.

4. Fun – This was down with plastic circles with teeth cut into the edge when I was a kid – and called spirograph.

As Karl says – slight adjustments give you all kinds of wonderful patterns. Anyone wanting the pattern you have shown as an example needs to set animation for q = 3 (and for p it is 1).

Also in both p & q the “animation repeat” needs to be set to “+> increasing”.
On my version (an old version Geogebra 3) is defaults to ” oscillating” which is not so good.

5. As always, nice stuff. You could add a link to the file you made on GeoGebraTube for people to see it directly, too, or to use the Construction Navigator.

• Thanks John. Yes, I’m planning to do that once I finish updating all the tutorials.