Regular polygons and their constructions

Geometrijskim konstrukcijama pravilnih mnogokuta pomoću jednobridnog ravnala i šestara bavili su se još antički grčki matematičari. Glavno pitanje koje se javilo bilo je mogu li se svi pravilni mnogokuti konstruirati. Odgovor na to pitanje prvi je dao Carl Friedrich Gauss u svom djelu Disquisitiones Arithmeticae. On je dokazao konstruktibilnost pravilnog sedamnaesterokuta, a potom je i razvio teoriju koja mu je omogućila da formulira dovoljan uvjet za konstruktibilnost pravilnih mnogokuta. Njegov je dokaz s nužnošću upotpunio Pierre Wantzel. U radu je opisan dokaz Gauss - Wantzelovog teorema, a potom i nekoliko konstrukcija pravilnih mnogokuta koji se mogu konstruirati jednobridnim ravnalom i šestarom te nekoliko približnih konstrukcija.The ancient Greek mathematicians were already engaged in the geometric constructions of the regular polygons with compass and straightedge. The main question that was being asked was that if it was possible to construct all of the regular polygons. The answer to that question was first given by Carl Frierdrich Gauss in his Disquisitiones Arithmeticae.He proved the constructability of the regular heptadecagon, and later developed theory which allowed him to formulate a sufficient condition for the constructability of the regular polygons. Pierre Wantzel completed his proof with necessity. This thesis describes the proof of the Gauss - Wantzel theorem, construction of several regular polygons that can be constructed with compass and straightedge and several approximate constructions