Let z be any complex number whose real and imaginary parts are not both rational. Set z_0 = floor(Re(z)) + i*floor(Im(z)) (the lower left corner of the integer grid square that z lies in). Thereafter set z_(n+1) = floor(Re(1/z_n)) + i*floor(Im(1/z_n)) Then z_0, z_1, ..., z_n, ... in Z[i] form a series of Gaussian integers representing z, generalizing continued fraction expansions of irrational real numbers. * Have such things been studied? * For almost all real numbers x, the geometric mean of all the "digits"* gm(x) = lim (K_0 K_1 ... K_n)^(1/n) n —> oo of the cfe of x is equal to the same number. What about the corresponding geometric mean of the Gaussian integers gm(z) = (z_0 z_1 ... z_n)^(1/n) ??? —Dan ————— * Should we call them "tigids"?