Lisa Nicklasson: Geometric constructions and solutions of cubic equations

It is well known that, using ruler and compass, the angle can not be trisected in general, and the regular p-gon, where p is an odd prime, can be constructed if and only if p is a Fermat prime. Also, cubic equations can generally not be solved. But what happens if we allow angle trisection? Which p-gons can be constructed, and what cubic equations can be solved? These questions shall be answered, and we shall also see what can be constructed with a marked ruler, and what cubic equations can be solved using a parabola in addition to the classical tools.