The Rabbit Problem Revisited

The sequence obtained to solve this problem—the celebrated Fibonacci sequence 1, 1, 2, 3, 5, 8, 13, 21, ...—appears in a large number of natural phenomena (see [2], [6]) and has natural applications in computer science (see [1]). Here we reformulate the rabbit problem to recover two generalizations of the Fibonacci sequence presented elsewhere (see [7], [8]). Then, using a fixed-point technique, we present an elementary proof of the convergence of the sequences of ratios of two successive generalized Fibonacci numbers. The limits of these sequences will be called here generalized golden numbers. Finally, we reconsider electrical schemes to generate these ratios (see also [3]).