Abstract:In this note we announce some results that will appear in [6] on the minimization of the functional F(Γ) =´Γ k + ds, where Γ is a network of three curves with xed equal angles at the two junctions. The informal description of the results is accompanied by a partial review of the theory of elasticae and a di use discussion about the onset of interesting variants of the original problem passing from curves to networks. The considered energy functional F is given by the elastic energy and a term that penalize the total length of the network. We will show that penalizing the length is tantamount to x it. The paper is concluded with the explicit computation of the penalized elastic energy of the " Figure Eight", namely the unique closed elastica with self-intersections (see Figure 1).