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向量在立体几何中的应用
摘要
作为现代数学的重要标志之一的向量已进入了中学数学教学,为用代数方法研究几何问题提供了强有力的工具,,几何占有很重要的地位,有些几何问题用常规方法去解决往往比较复杂,运用向量作行与数的转化,,它能将平面几何许多问题代数化、程序化从而得到有效的解决,:证明与计算,用空间向量解决立体几何中的这些问题,其独到之处,在于用向量来处理空间问题,淡化了传统方法的有“形”到“形”的推理过程,使解题变得程序化.
关键词:向量;立体几何;证明;计算;运用
ABSTRACT
As one of the important signs of modern mathematics the vector has entered middle school mathematics teaching, using algebraic method research geometry problems provides powerful tools, promoted the high school of the geometry of algebra. And in the high school mathematics system, geometric occupies a very important position, some geometry problems with conventional method to solve tend to plex, using vector for the number of rows and transformation, makes the process is greatly simplified. Vector method was used the plane geometry, it will be when the plane geometry many problems algebra effectively, programmed to solve, reflected in mathematics, the bination of Numbers and forms. Three-dimensional geometry often involved the two big problems: proof and calculation, with space vector solve three-dimensional geometry in these problems, its unique, is using vector to deal with the problem of space, fade the traditional methods are "form" to "form" reasoning process, causes the problem-solving e programmed.
Keywords:Vector; solid geometry; proof; calculation; use
目录
摘要 Ⅰ
ABSTRACT Ⅰ
1 向量方法在研究几何问题中的作用 1
2 向量方法解决证明问题的直接应用 2
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3 向量方法解决度量问题的直接应用 10
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4 向量方法解决证明与计算问题有关的综合应用 14
5 向量在立体几何中应用的教学反思 21
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参考文献 23
1 向量方法在研究几何问题中的作用
向量是高中数学新增加的内容,在作用上它取代了以往复数在高中数学教材中的地位,但从目前的使用情况来看,,而向量却有平面向量和空间向量之分,这一点在与几何(尤其是立体几何)的联系上表现得更