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## Monday, December 7, 2015

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