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詹姆斯·利根在《Fhe Mathematics Feacher》1984年第5期上介绍了他所发现的二次曲线中的黄金比,其要点如下(可参看《数学通讯》1985年第1期): 1.如果椭圆的焦点在圆的直径的两端,那么当且仅当长轴与短轴成黄金比时(用φ表示黄金比,φ=(5~(2/1)+1)/2。下同),椭圆的面积与圆的面积相等.这样的椭圆叫做“黄金椭圆”。 2.在平面直角坐标系{O;i,j}中,设黄金椭圆的方程为x~2/a~2+y~2/b~2=1。这里a,b分别表示椭圆的长半轴与短半轴。
James Rygen introduced the gold ratio in the quadratic curve he found in “Fhe Mathematics Feacher”, Issue 5, 1984. The main points are as follows (see Mathematical Newsletter, Issue 1, 1985): 1. If elliptical The focus is at both ends of the diameter of the circle, then if and only if the long axis and the short axis are in the golden ratio (indicating the gold ratio with φ, φ=(5~(2/1)+1)/2. Same as below), The area of the ellipse is equal to the area of the circle. Such an ellipse is called a “golden ellipse”. 2. In the plane rectangular coordinate system {O;i,j}, let the equation of the gold ellipse be x~2/a~2+y~2/b~2=1. Here, a,b respectively represent the long half axis and the short half axis of the ellipse.