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在解题教学中,笔者发现一些数学问题的比值是一个定值,且这个定值恰好是黄金分割比。下面展示两个与黄金分割比有关的定值问题。1源于反比例函数的黄金分割比反比例函数问题是中考必考题,当反比例函数与正方形结合,则会得到一些结论。题1(2015年凉山州中考数学第11题)以正方形ABCD两条对角线的交点O为坐标原点,建立如图1所示的平面直角坐标系,双曲线y=3/x(x>0)经过点D,则正方形ABCD的面积是()。
In the problem-solving teaching, I found that the ratio of some mathematical problems is a fixed value, and this setting is exactly the golden ratio. Here are two valuation issues related to the golden ratio. 1 from the inverse proportion function of the golden ratio of the inverse proportion function is the exam questions, when the inverse proportion function and the square, you will get some conclusions. Problem 1 (2015 Liangshan Prefecture entrance exam math 11) to the square ABCD two diagonal intersection O as the origin of coordinates, as shown in Figure 1 to establish a rectangular system of rectangular coordinates, hyperbolic y = 3 / x (x> 0) passes through point D, then the area of square ABCD is ().