Open AccessHow to solve third degree equations without moving to complex numbers
Author(s) -
Antoni Leon Dawidowicz
Publication year - 2020
Publication title -
annales universitates paedagogicae cracoviensis. studia ad didacticam mathematicae pertinentia
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.102
H-Index - 1
eISSN - 2450-341X
pISSN - 2080-9751
DOI - 10.24917/20809751.12.6
Subject(s) - degree (music) , mathematics , algebraic equation , algebraic number , theory of equations , algebraic solution , the renaissance , algebra over a field , pure mathematics , differential equation , mathematical analysis , differential algebraic equation , nonlinear system , ordinary differential equation , art , physics , quantum mechanics , acoustics , art history
During the Renaissance, the theory of algebraic equations developed in Europe. It is about finding a solution to the equation of the formanxn + . . . + a1x + a0 = 0,represented by coefficients subject to algebraic operations and roots of any degree. In the 16th century, algorithms for the third and fourth-degree equations appeared. Only in the nineteenth century, a similar algorithm for thehigher degree was proved impossible. In (Cardano, 1545) described an algorithm for solving third-degree equations. In the current version of this algorithm, one has to take roots of complex numbers that even Cardano didnot know.This work proposes an algorithm for solving third-degree algebraic equations using only algebraic operations on real numbers and elementary functions taught at High School.