Numerous mathematics problems are solved with the help of polynomials. Polinomial equation is an equation of form P (x) = 0 where “P” is a polynomial function of any order and “x” is unknown.
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The experience of most people with polynomial equations does not go much further from high school algebra and square formula. However, these numerical puzzles remain a fundamental component of all activities, from the calculation of planetary orbits to computer programming.
Although the resolution of lower-order polynomials, in which “X” in an equation is raised to the fourth power, it is often a simple task, things are complicated once we begin to see five or higher powers, reports the popular science publication.
For centuries, mathematicians have accepted this as a simple challenge of their work, but not Norman Wildberger. According to his new approaches presented in “The American Mathmatical Monthly”, there is a much simpler approach to high -order polynomials. All you have to do is get rid of annoying notions like irrational numbers.
Mathematicians have developed approximate solutions, but these require the integration of concepts such as irrational numbers in the classical formula.
To calculate such an irrational number, “would need an infinite amount of work and a larger hard disk than the universe“Explained Wildberger, a mathematician at the University of New South Wales Sydney in Australia.
This infinite number of possibilities is the fundamental problem, according to Wildberger.
“I don’t believe in irrational numbers“He said.
Instead, its approach is based on mathematical functions such as assembly, multiplication and square. Wildberger recently addressed this challenge by calling on specific polynomial variants called “series of powers“, Which possess infinite terms within the powers of” X “. To test this, he and computer scientist Dean Rubine used “A famous cubic equation used by Wallis in the seventeenth century to demonstrate Newton’s method”.
And mathematician Wildberger says the solution “worked wonderfully”.
The new approach could improve computer programs
The same is true for Catalan numbers. These also appear in the natural world, in areas such as biology, where they are used to analyze the possible folding models of RNA molecules.
“Catalan numbers are understood as intimately related to square equation“Explained Wildberger, who added:”Our innovation is the idea that if we want to solve higher equations, we should look for higher analogies of Catalan numbers”.
Wildberger believes that the new approach to higher power polynomials could soon lead to computer programs capable of solving equations without the need for radicals. It could also contribute to the improvement of algorithms in a variety of fields.
“This is a dramatic review of a basic chapter in algebra“Wildberger said.
