A comparison of three types of scale invariance

Magnetic interactions and the method of images: a wealth of educational suggestions

“…(ii) proposes a dimensionless and scale-invariant formalization of physical problems, giving (in a simple, classical context) a significant example of an issue widely stressed in the literature [9][10][11][12][13];…”

“…In this regard, it is worth highlighting that scale-invariant expressions would be used whenever possible in mathematical equations describing properties of physical systems. In fact, scale invariance has largely been recognized as a key property of wide classes of physical phenomena [9][10][11][12][13] and its introduction has represented a significant turn in modern physics and, more generally, in natural sciences [19]. This concept is well known in the physics of fundamental interactions and in statistical physics [9,10,19], while examples from classical physics are less common.…”

“…The treatment given here is more general, systematic and teaching-oriented than other previous works on this theme [5][6][7][8]. Furthermore, we propose a dimensionless formalization of the physical problem under study, that has great educational potential, since it highlights (in a simple, classical context) the importance of getting scale-independent information on a physical system whenever possible (an issue widely stressed in the literature [9][10][11][12][13]). Moreover, the discussion of the proposed modelling of the system provides an opportunity to emphasize some crucial aspects of idealization procedures, often used in the description of a physical system.…”