Editing Dimensionless quantity (section)

== Buckingham {{pi}} theorem ==
{{main|Buckingham π theorem|l1=Buckingham {{pi}} theorem}}
{{Unreferenced section|date=April 2022}}
The Buckingham {{pi}} theorem<ref>{{ cite journal  | title=On Physically Similar Systems; Illustrations of the Use of Dimensional Equations | year=1914 | pages=345–376 | journal=Physical Review | doi=10.1103/physrev.4.345 | volume=4 | issue=4 | url=http://dx.doi.org/10.1103/PhysRev.4.345 | last1=Buckingham | first1= E. | bibcode=1914PhRv....4..345B }}
</ref> indicates that validity of the laws of physics does not depend on a specific unit system. A statement of this theorem is that any physical law can be expressed as an [[Identity (mathematics)|identity]] involving only dimensionless combinations (ratios or products) of the variables linked by the law (e.g., pressure and volume are linked by [[Boyle's law]] – they are inversely proportional). If the dimensionless combinations' values changed with the systems of units, then the equation would not be an identity, and Buckingham's theorem would not hold.

Another consequence of the theorem is that the [[Function (mathematics)|functional]] dependence between a certain number (say, ''n'') of [[variable (mathematics)|variables]] can be reduced by the number (say, ''k'') of [[independent variable|independent]] [[dimension]]s occurring in those variables to give a set of ''p'' = ''n'' − ''k'' independent, dimensionless [[quantity|quantities]]. For the purposes of the experimenter, different systems that share the same description by dimensionless [[quantity]] are equivalent.