The basis for dimensional analysis. The theorem states that an equation for a physical system that can be written f(Q₁, Q₂,. . . , Q_m) = 0 can also be written as g(π₁, π₂,. . . , π_m − n) = 0 where Q_i are m dimensional parameters, numbers, and variables; π_i are m − n nondimensional quantities; and n is the number of fundamental dimensional units.