cp's OEIS Frontend

This constant d gives the imaginary part of -2*11*Z = c + d*i, where Z is the fixed point of a complex function w (of the loxodromic type) mapping vertices of golden triangles, starting with vertices (D_1, D_2, D_3), circumcribed by the unit circle with center at the origin, and D_1 = i (the complex unit), D_2 = (s - phi*i)/2 and D_3 = (-s - phi*i)/2. This function is w(z) = a*z + b, with a = (-1 + phi) * exp(-3*Pi*i/5) = -((2 - phi) + s*i)/2 and b = (1 - phi)*i, where s = sqrt(3 - phi) = A182007 (the length of the base (D2, D3) of the first triangle).

The real part c = (-1 + 3*phi)*s is given in A385445.

For details see A385445, and eqs.(5a,b) of the linked paper there.

This constant c gives sqrt(11)*rho_1, where rho_1 = length(Z, D_1), with the fixed point Z = -(A385445 + A385446*i)/(2*11) of the complex map w given in A385445 and D_1 = i.

See A385445 for details and the linked paper, eq. (7b).

This equals the ratio length(Z, D_1)/s, with the fixed point of a complex loxodromic map w mapping iteratively golden triangles, starting with the one inscribed in a circumcircle with center ot the origin of the complex plane, the top vertex D_1 = i (the complex unit) and the base D_2 = (s - phi*i)/2, D_3 = (-s - phi*i)/2, with s = A182007.

See A385445 for details and a linked paper.