Circular division equation
A circle division equation is an equation of form
The solutions in the area of complex numbers correspond to the corners of a regular polygon (polygon) with n corners. This correspondence in the sense of a circle division gave its name to the circle division equations.
Geometric meaning
The regular n corner can be constructed with the exclusive use of compasses and rulers if and only if the real and imaginary parts of the solutions of the n th circle division equation can be represented by rational numbers and nested square roots . The first result of this connection systematically examined by Carl Friedrich Gauß was the discovery that the regular seventeenth- corner can be constructed with compasses and ruler .
Algebraic background
The Galois group of a circular equation is always Abelian and therefore solvable with roots . Generated from their solutions body called cyclotomic fields .