Limacon with inner loop

Continuing my push to use Geogebra to introduce younger students to "fancy math", here is a plot similar to my last two blog entries. Although the shape is determined by the relative speeds of Jack and Jill, just as in the previous two postings, this one was shifted a bit to the right just so that the origin is more centered.

The original file is here.

I will not be posting here for a couple of weeks as a different project will intervene. Merry Christmas!

5-Leafed Rose the simple way

Here is an extension of yesterday's post, where I have adjusted the graph to get 5 leafs instead of 3.
This file can be found here.
Below is a bit of mathematics that I would have discussed in a class. with the goal of graphing in parametric mode on a graphic calculator. For students not yet up to that, I would adapt this so that they can experiment with different rotational speeds, reverse directions, etc., and would not include the pre-plotted graph.

 \[\begin{array}{c} A = ( - .75,0)\\ Jack = ( - .75 + \cos ( - 2t),0 + \sin ( - 2t))\\ C = (.75,0)\\ Jill = (.75 + \cos (3t),0 + \sin (3t))\\ {\rm{red}}\,{\rm{point = }}\frac{{Jack + Jill}}{2}\\ {\rm{red}}\,{\rm{point = }}\frac{{\left( {\cos ( - 2t) + \cos (3t),\sin ( - 2t) + \sin (3t)} \right)}}{2} \end{array}\]

Going in Circles Can be Fun!!

A major push of mine is using dynamic geometry such as GeoGebra to introduce younger students to more interesting mathematical concepts.
Here, based on knowledge of circles, rotations, and midpoints, a student can learn something about 3-leafed roses. The file can be found here.

I would love to see how to do this in Desmos, or how to make it web-friendly in Nspire.

Matrix Transformations in GeoGebra

GeoGebra provides a great avenue for traveling through the world of matrix transformations of the plane. Here is just a little example. Imagine if our teachers could compile a folder full of such sample, ready to pull out and share at a moments notice.

This one can be obtained  here. I hope it helps somebody somewhere.