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Convergence of any pentagon that is inscribed in a circle to a perfect pentagon

Idan Tal
The applet demonstrates that for any pentagon inscribed in a circle, by dynamic process, its convergent to a perfect pentagon.. By connecting the midpoints of the arcs of a pentagon that is inscribed in a circle, we created new pentagon. The ruler allows the creation of a sequence of pentagons, the vertices of each of which are located at the middles of the arcs of the previous pentagon. For each pentagon, the values of the angles of the new pentagon obtained, and their standard deviations appear on the screen. The standard deviation indeed decreases monotonically, which suggests that the angles converge to 108°.