This is a response to Dan Meyer's [url=http://blog.mrmeyer.com/?p=16767]"Discrete Functions Gone Wild!"[/url]
He expands the function [math]f(n)={(n−2) \cdot 180^{\circ} \over n}[/math] to the rational numbers, to which I demonstrate with the applet [url=http://www.geogebratube.org/student/m33865]http://www.geogebratube.org/student/m33865[/url]
But then [url=http://blog.mrmeyer.com/?p=16747#comment-766303]Danny asks[/url] if we not only alter angle measure but also side length?
This is one way to do so where we actually get closed shapes.
For this applet, each angle has measure [math]{(n−2) \cdot 180^{\circ} \over n}[/math]; if [math]n = 5 {1 \over 3}[/math], the side lengths are 1, 1, 1, 1, 1, and [math]{1 \over 3}[/math] and repeating.
