“K”图给力,解题不忧——例谈“K”型图在数学解题中的应用

在数学问题的解决过程中，有意识地提炼一些典型的数学模型，可以有效地提高解题速度和准确率，“K”型图在几何题型中较为常见，本文浅谈该基本图形在解题中几种常见的应用．

巧用“K”型图,妙解数学题

在初中数学的学习过程中,利用数学的基本图形、基本模型解题已经成为现在数学教学必不可少的一部分.“K”型图就是其中的一种基本图形,文章着重阐述其在数学解题中的应用.

构造“K”型图,妙解等角问题

“K”型图是初中几何解题中重要的辅助图形,通过一道作业题的解法对比,总结等角问题中“K”型图的构造方法,指出以已知条件中的定长边作为直角边来构造“斜放”的直角是关键,从而简化计算,快速解决问题。

Comparative study on forming limit prediction of AA7075-T6 sheet with M−K model and Lou−Huh criterion

In order to effectively predict the fracture of AA7075-T6 sheet, the forming limit curves of AA7075-T6 high-strength sheet were drawn according to Morciniak Kuczyski (M K) model and Lou Huh criterion, respectively. The errors between the predicted values of the two theoretical prediction models and experimental values were calculated by error analysis. The forming limit curves were verified by the punch stretch test to evaluate the prediction accuracy of M K model and Lou Huh criterion. The error analysis results show that the mean error of Lou Huh criterion with the optimal parameters for all tensile specimens is 25.04%, while the mean error of M K model for all tensile specimens is 74.24%. The prediction accuracy of Lou Huh criterion in predicting the fracture of AA7075-T6 sheet is higher. The punch stretch test results show that the forming limit curve drawn by Lou Huh criterion can effectively predict the fracture of AA7075-T6 sheet, but the prediction accuracy of M K model is relatively poor.

领悟核心 拓展思维——以“构造‘K’型图解决问题”为例

"K"型图是初中几何中的重要模型,是解决直角问题的重要方式。立足典型性图形,通过各种方式的构造,把"K"型图的运用从直角外延到特殊角,拓宽其适用范围,得到构造"K"型图解决问题的一般步骤。

“一线三直角”应用的三种境界

对于初中平面几何问题,其解题过程就是对图形进行认识与剖析,通过归纳提炼出基本图形,建立几何模型,从而形成几何直观,发展学生数学建模等核心素养的过程。在众多基本图形中,"K"型图的应用非常广泛,对于其中的"一线三直角",其基本图形的应用有三种境界。