In 1978, Landsberg proposed an elegant way of obtaining the inequality between arithmetic and
geometric mean by using the first and second laws of thermodynamics. This result opened a debate on
the logic legitimacy of this procedure to obtain some mathematical truths. Although this discussion
can not be considered completed, the Landsberg approach has shown a great richness in obtaining many
algebraic inequalities. In the present article we apply the Landsberg method to some properties of
normed spaces trough a vector space of temperatures. In this way, the result that establishes the
equivalence between all p -norms in the space ##IMG##
[http://ej.iop.org/images/0143-0807/36/6/065021/ejp518814ieqn3.gif] {${{mathbb{R}}}^{n}$} and the
minimal constant that guaranties this fact are readily found. Geometrical surfaces stemming from
energy conservation are a consequence of this interpretation. In this manner, an application for
thermal equilibrium of n…