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我们的青年对数学深切地感兴趣。在数学小组的组员中很多这样的学生,他们的兴趣远远地超出教学大纲的范围。常常听到涉及高次方程解法的问题,特别是关于它们的根的计算问题。这是当然的,因为在解决很多初等数学问题时,需要解高次方程,特别是三次和四次代数方程。在教师面前就摆着这样一个任务:给出初等的为学生所易于了解的关于三次和四次方程的根的近似计算方法。在高等代数教程中所叙述的方法(“弦和切线”方法,拉格莹日方法和其他方法),是难于理解而且在实际应用中也是笨重的。
Our youth are deeply interested in mathematics. Many of these students in the math team’s group are far more interested than the syllabus. Frequently, problems involving solutions to higher-order equations are heard, especially with respect to the calculation of their roots. This is of course because when solving many elementary mathematics problems, it is necessary to solve higher order equations, especially the cubic and fourth order algebraic equations. In front of the teacher there is such a task: to give elementary students an easy way to understand the approximate calculation of the roots of the third and fourth equations. The methods described in the Advanced Algebra Tutorial (the “chord and tangent” method, the Lagerfeld method, and other methods) are difficult to understand and are also cumbersome in practical applications.