Представлення кубічної ірраціональності за допомогою суми двох періодичних гіллястих ланцюгових дробів
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 algebrai...
Saved in:
| Date: | 2023 |
|---|---|
| Main Authors: | , , |
| Format: | Article |
| Language: | Ukrainian |
| Published: |
Інститут прикладних проблем механіки і математики ім. Я. С. Підстригача НАН України
2023
|
| Subjects: | |
| Online Access: | https://www.fmmit.lviv.ua/index.php/fmmit/article/view/345 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Physico-mathematical modeling and informational technologies |
| Download file: |  |
Institution
Physico-mathematical modeling and informational technologies| Summary: | 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. |
|---|---|
| DOI: | 10.15407/fmmit2023.38.135 |