Mathematical modeling takes very different forms.
In engineering, physics and computer science the subjects are often so tightly related to their models that we can speak about simulations. On the other hand, in humanities and economy the models are much more freely related to their subject and we should often speak about analogies.
But these high level analogies present us with problems of a deeper understanding. We illustrate this on comparison of two very simple (mathematical) forms: triangle and rectangle. Quite suprisingly this relates to some of the key paradigma of modern mathematics.