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The golden gnomon is the obtuse isosceles triangle whose ratio of side to base lengths is given by 1/phi=phi-1, where phi is the golden ratio. Such a triangle has angles of ...

A golden rhombohedron is a rhombohedron whose faces consist of congruent golden rhombi. Golden rhombohedra are therefore special cases of a trigonal trapezohedron as well as ...

tau is the ratio tau=omega_2/omega_1 of the two half-periods omega_1 and omega_2 of an elliptic function (Whittaker and Watson 1990, pp. 463 and 473) defined such that the ...

A triple (a,b,c) of positive integers satisfying a<b<c is said to be harmonic if 1/a+1/c=2/b. In particular, such a triple is harmonic if the reciprocals of its terms form an ...

A family of operators mapping each space M_k of modular forms onto itself. For a fixed integer k and any positive integer n, the Hecke operator T_n is defined on the set M_k ...

Let alpha_i and A_i be algebraic numbers such that the A_is differ from zero and the alpha_is differ from each other. Then the expression ...

The sequence defined by G(0)=0 and G(n)=n-G(G(n-1)). (1) The first few terms for n=1, 2, ... are 1, 1, 2, 3, 3, 4, 4, 5, 6, 6, 7, 8, 8, 9, 9, ... (OEIS A005206). This can be ...

Let b_1=1 and b_2=2 and for n>=3, let b_n be the least integer >b_(n-1) which can be expressed as the sum of two or more consecutive terms. The resulting sequence is 1, 2, 3, ...

Let R[z]>0, 0<=alpha,beta<=1, and Lambda(alpha,beta,z)=sum_(r=0)^infty[lambda((r+alpha)z-ibeta)+lambda((r+1-alpha)z+ibeta)], (1) where lambda(x) = -ln(1-e^(-2pix)) (2) = ...

The thinnest sequence which contains 1, and whenever it contains x, also contains 2x, 3x+2, and 6x+3: 1, 2, 4, 5, 8, 9, 10, 14, 15, 16, 17, ... (OEIS A005658).