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In [[three-dimensional Euclidean space]], any [[rigid transformation|proper rigid transformation]], whether active or passive, can be represented as a [[screw displacement]], the composition of a [[translation (geometry)|translation]] along an axis and a [[rotation (mathematics)|rotation]] about that axis.
The terms ''active transformation'' and ''passive transformation'' were first introduced in 1957 by [[Valentine Bargmann]] for describing [[Lorentz transformations]] in [[special relativity]].<ref>{{cite journal |last=Bargmann |first=Valentine |title=Relativity |journal=Reviews of Modern Physics |volume=29 |number=2 |year=1957 |pages=161–174 |doi=10.1103/RevModPhys.29.161 |bibcode=1957RvMP...29..161B }}</ref>
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