Representationofcubicirrationalityusingthesumoftwoperiodicbranche dchainfractions

Abstract

The paper creates such an algorithm that represents cubic irrationality using the sum
of two periodic branched chain fractions. The unity and convergence of these
fractions are proved. It is logically assumed that the irrationalities of higher orders
are directly related to the order of the algebraic equation. However, it is difficult to
propose such a simple procedure for constructing the corresponding irreducible
equation for the simple reason that there are no closed formulas for roots higher than
degree four. And the existing formulas for the 3rd and 4th orders are not very
suitable for constructing an equation that corresponds to the given irrationality.
Therefore, in the future, we will propose a simple way of constructing the
corresponding irreducible equation and perform the necessary research on its basis.