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说起椭圆的定义,学生容易想到的是其第一定义,即平面内与两个定点的距离的和等于常数(大于两定点间的距离)的点的轨迹就叫做椭圆.其实椭圆还有其他的定义方法隐含在教材中.在人教A版高中数学教材选修2-1(以下简称教材)第二章《圆锥曲线与方程》第2.2节《椭圆》的教学中,笔者就带领学生深入研读教材,探索了椭圆的其他刻画方式.这里抛砖引玉,以飨读者.1椭圆的定义1.1第一定义教材中通过探究得出椭圆的第一定义,即:把
Speaking of the definition of an ellipse, students easily think of its first definition, that is, the trajectory of the point where the sum of the distances between the plane and the two fixed points equals a constant (greater than the distance between two fixed points) is called an ellipse. In fact, there are other ellipses and other The definition of the method is implicit in the teaching materials. In the teaching of the A version of the senior high school mathematics textbook elective 2-1 (hereinafter referred to as the teaching material) the second chapter “conical curve and equation” section 2.2 “ellipse” in the teaching, the author will lead the students in-depth Studying the teaching materials and exploring other ways of depicting the ellipse. Here to introduce the reader to the reader. 1 Definition of the ellipse 1.1 The first definition The first definition of the ellipse is found in the textbook.