A Note on Angle Construction

Many interesting facts in angle construction stem from a study of algebraic equations. An ideal place of beginning involves a fundamental theorem from the theory of equations. This theorem reads, If a cubic equation with integral coefficients has no rational roots, then none of its roots can be constructed with the Euclidean instruments. Proofs of this theorem appear in various textbooks. Notable among these references is the work of W. V. Lovitt entitled Elementary Theory of Equations (chapter 14).