A chord approach for an alternative ruler and compasses construction of the 17-side regular polygon (Q1337114)

It is well known that a 17-sided regular polygon can be constructed with ruler and compasses [see, for example, \textit{H. S. M. Coxeter}, Introduction to geometry (1961; Zbl 0095.345), p. 27]. In the present paper the author considers some relationships among certain functions of the lengths of chords of the polygon, which lead to equations whose roots can be found by using only rational operations and the extraction of square roots. This gives a direct ruler and compasses construction of the regular 17-gon.