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文[1]给出了“黄金”数列,即q=(5~(1/2)-1)/2的正项等比数列有如下的性质:(1)a_n=a_(n+1)+ a_(n+2);(2)1/a_n=1/(a_(n-1))+1/(a_(n-2))(n≥3).文[2]利用顶角为36°的等腰三角形构造了一个几何模型说明这两条性质.过程详见文献[2],本文不赘叙.
[1] gives the “golden” sequence, that is, q = (5 ~ (1/2) -1)/2 positive items with the following properties: (1) a_n = a_(n + 1) + a_(n+2);(2)1/a_n=1/(a_(n-1))+1/(a_(n-2))(n≥3). [2]Using the top An isosceles triangle with an angle of 36° constructs a geometric model illustrating these two properties. The procedure is described in the literature [2].