From circles to ellipses?

Many people seem to think of circles as simple things and ellipses as "oh, that's math and I was no good at it...".

Here is a bit of a perspective on that created in GeoGebra.

If you know nothing of ellipses beyond "oval", start by just using the control buttons at the top. If you are comfortable with ellipses, but a bit of a skeptic, experiment with the sliders as well. If you really want to know what is happening, download the complete file here.

Regardless of where you stand, GeoGebra does give a great dynamic approach to mathematics.

math is an exploration!

Any study worthy of its name involves decoding and analyzing and learning from the work of others. A high school trig student has all the math skills needed to create a file like this. A lower grade student might be encouraged to learn about sines and cosines due to their "hidden" use here.

At worst: it's a a neat design! (find the file here.)