几何画板中椭圆的几种结构方法(国外英文资料).doc

几何画板中椭圆的几种构造方法(国外英文资料) Several methods of construction of ellipse in geometrical drawing board Chen xiaolong in wenzhou middle school In the course of teaching, I found that using geometric drawing boards can have many ways to construct an image of the ellipse. The first definition of the ellipse: the trajectory of the distance between the two points in the plane and F2, the sum of the distances between the two points, the value of 2a (2a | F1F2 |). Elliptical construction method one: (1) to make A circle with O, 2a to make A circle of radius, to take A little P in the circle, and to take A in the circle. (2) connect PO, PA, PA and PO to point M, connect MA; (3) define the point M as the tracking point, select the point P, and let the point P rotate at any point on the circle to get the path of the point M, which is the ellipse of the length of A for the long axis of the focal length of 2a. Reason: MP = MA in the diagram, so OM + MA = OM + MP = OP = the radius of the circle, which conforms to the first definition of the ellipse. Elliptic second definition: a fixed point M (x, y) and point (c, 0) and F it to straight line: the distance of the x = ratio is constant (a c 0), the point Ms trajectory is an ellipse. The point F is a focal point of the ellipse, and the line is the alignment of the focal point in the ellipse. The constant e = (0 e 1) is the eccentricity of the ellipse. Elliptical construction method two: (1) take points F and line L, (point F is not on L). Im going to make a line, and Im going to take a point P on the line; (2) to measure the length of the FP by using the F as the circle, measure the length of the FP, and take the parameter e = 0.8 (which can be changed to other positive Numbers less than 1), and calculate the FP/e; (3) the perpendicular line of line L at P dot, L at M, and M for the center of the circle, the circle of the radius of FP/e, and the perpendicular line of the perpendicular line, which is the parallel line of L of N, and t