Two Celebrated Classical Problems in Geometric Constructions

The main topic of this paper is about two celebrated classical problems in geometric constructions where the only allowed instruments are compass and ruler with no scale. Two such problems are (1) trisecting an angle, and (2) doubling the cube. In addition, we also study about the construction of 7-gon and 10-gon.

conic sections

The curves known as conic sections, the ellipse, hyperbola, and parabola, were investigated intensely in Greek mathematics. The most famous work on the subject was the Conics, in eight books by Apollonius of Perga, but conics were also studied earlier by Euclid and Archimedes, among others. Conic sections were important not only for purely mathematical endeavors such as the problem of doubling the cube, but also in other scientific matters such as burning mirrors and sundials. How the ancient theory of conics is to be understood also played a role in the general development of the historiography of Greek mathematics.