We study the linear fractional transformations in the Hecke group G() where is either root of x2 x 1 (the larger root being the “golden ratio” = 2 cos ? 5 .) Let g 2 G() and let z be a generic element of the upper half-plane. Exploiting the fact that 2 = + 1, we find that g(z) is a quotient of linear polynomials in z such that the coecients of z1 and z0 in the numerator and denominator of g(z) appear themselves to be linear polynomials in with coecients that are certain multiples of Fibonacci numbers. We make somewhat less detailed observations along similar lines about the functions in G(2 cos ? k ) for k greater than or equal to 5.
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机译：我们研究了HECKE组G（）中的线性分数变换，其中x2 x 1的根源（较大的根部是“金色比率”= 2 cos？5。）设g 2 g（），让z是通用的上半平面的元素。利用2 = + 1的事实，我们发现g（z）是z中线性多项式的商的商，使得G（z）中的分子和z0中的z1和z0的相位出现为具有线性多项式斐波纳契数的一定倍数的共识。我们沿着k（2 cos k）的相似线，k的相似线的详细观察略低于或等于5。
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