Bezier for Young People

Bezier Curves are generally not confronted by k-12 students at all. Their equations can be complex, and in the absence of dynamic geometry, the topic in general can be mind boggling. Historically, algebra has been the driving force for graphing. With dynamic geometry, that can be reversed.

If you can mentally stomach (how's that phrase?) the idea of a point on a line steadily sliding from one location on that line to another location on that line, you've mastered the necessary skills. Visually, a point sliding from one place to another would look like this:

Being able to picture this is all you need to know. Here it is

Jack and Jill

Here is a short Geogebra example I put together as an example of how GeoGebra could be used to introduce young students to mathematics that they might never see unless they got into a precalculus class that included polar graphs.

Among the concepts used (but not named) are midpoint, rotation, rotational speed, and 3-leafed rose.
The only geometric term used is "circle".

Even so, the situation can be used as a springboard lots of questions.
 

Among those questions could be:

• What if they walked the same speed?
• What if Jill walked faster?
• What if they walked in the same direction around the circle?

Denying younger students the opportunity to ask these questions and explore their solutions is to do a disservice to those students.