[url=http://www.jstor.org/stable/2324301?seq=1#page_scan_tab_contents]Watkins and Zeitlin (1993)[/url] published a method to simply compute the minimal polynomial of cos(2π/[i]n[/i]), based on the [url=https://en.wikipedia.org/wiki/Chebyshev_polynomials#First_kind]Chebyshev polynomials of the first kind[/url]. By using their method GeoGebra is able to prove various properties of regular [i]n[/i]-gons since November 2017.
This collection demonstrates how useful this new feature is. As a further improvement of the Watkins-Zeitlin method, another software tool [url=ttps://github.com/kovzol/RegularNGons]RegularNGons[/url] can be used to automatically find interesting features of a regular polygon.