  The possibility of approximating a continuous function on a compact subset of
the real line by a feedforward single hidden layer neural network with a
sigmoidal activation function has been studied in many papers. Such networks
can approximate an arbitrary continuous function provided that an unlimited
number of neurons in a hidden layer is permitted. In this paper, we consider
constructive approximation on any finite interval of $\mathbb{R}$ by neural
networks with only one neuron in the hidden layer. We construct algorithmically
a smooth, sigmoidal, almost monotone activation function $\sigma$ providing
approximation to an arbitrary continuous function within any degree of
accuracy. This algorithm is implemented in a computer program, which computes
the value of $\sigma$ at any reasonable point of the real axis.
