Constructions of squaring the circle, doubling the cube and angle trisection

The constructions of three classical Greek problems (squaring the circle, doubling the cube and angle trisection) using only a ruler and a compass are considered unsolvable. The aim of this article is to explain the original methods of construction of the above-mentioned problems, which is something new in geometry. For the construction of squaring the circle and doubling the cube the Thales' theorem of proportional lengths has been used, whereas the angle trisection relies on a rotation of the unit circle in the Cartesian coordinate system and the axioms of angle measurement. The constructions are not related to the precise drawing figures in practice, but the intention is to find a theoretical solution, by using a ruler and a compass, under the assumption that the above-mentioned instruments are perfectly precise.