I had an idea for visualizing the sum of angles in 2D polygons. My idea is that you have physical "pucks" on a display that can detect the positions of them.
The pucks are connected by drawing lines on the display and the angles is displayed. Also the sum of the angles is calculated and displayed along with the name of the polygon. On the sketch I show four pucks, but you should be able to use any number of them from three to at least nine.
The idea is to visualize that the sum of the angles is the same in polygons with the same number of sides and also to show the sum of the angles for different types of polygons.
Maybe one should add something the student should do, like calculating the sum of angles, or some other better idea...
Another use for this basic platform would be to explore optics. If one used a different set of pucks like "spotlight", "mirror", "prism", "lens" etc one could simulate optics and add labels and explanations on the display.
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