On the (m+1)-terminal resistive-network problem

It is shown that any (m+1)-terminal positive resistive network forms an mth order metric space Sm, whose characteristic is completely defined by the main theorem stated in this work. A metric transformation transforms Sm into the mth-order distance space Dm, which is congruently imbeddable in m-dimensional Euclidean space Em. As a consequence, any (m+1)-terminal positive resistive network may be considered to form an mth-order simplex or geometrical figure Pm in Em. This figure was shown to have all its first- and higher-order angles acute and was called hyperacute-angled. As a consequence, problems on resistive networks, particularly on resistive n-ports, are equivalent to geometric problems on acute-angled simplexes imbeddable in multidimensional Euclidean space. All the arsenal of knowledge, acquired over many years, which we posses on Euclidean spaces may therefore be utilised in the solution of the resistive n-port problem.