Meanings
- geometryA theorem which states that, in 3-dimensional space, any displacement of a rigid body such that some point on it remains fixed is equivalent to a single rotation about some axis that runs through said point.
2005, JSME International Journal: Mechanical systems, machine elements and manufacturing, Volume 48, Issue 4, Japan Society of Mechanical Engineers, page 501, According to Euler's rotation theorem, any finite rotation transformations may be described using only three angles defined as Euler angles.
2 more examples
Otherwise, this approach will be valid subject to the previous rotation of the axes according to Euler's Rotation Theorem.
2003, On the Move to Meaningful Internet Systems 2003: CoopIS, DOA, and ODBASE, Proceedings, page 136From Euler's rotation theorem we know that an arbitrary rotation in three dimensions can be parameterized by three independent variables called the Euler angles, each rotating around an orthogonal axis.
2006, Patricia J. Lee, Quantum Information Processing with Two Trapped Cadmium Ions, University of Michigan, page 40
Origin
Named after Swiss mathematician Leonhard Euler (1707–1783), who proved the theorem in 1775.
Full word history & related roots →Translations
German Satz vom Fußball
- Satz vom Fußballmathematical theorem
Portuguese Teorema de rotação de Euler
- Teorema de rotação de Eulermathematical theorem
Cite this entry
Euler's rotation theorem. (n.d.). In WatkinsX Dictionary. Retrieved November 5, 2026, from https://dictionary.watkinsx.com/word/Euler's%20rotation%20theorem
“Euler's rotation theorem.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/Euler's%20rotation%20theorem. Accessed November 5, 2026.
WatkinsX Dictionary, s.v. “Euler's rotation theorem,” accessed November 5, 2026, https://dictionary.watkinsx.com/word/Euler's%20rotation%20theorem.
Source: Euler's rotation theorem on Wiktionary, CC BY-SA 4.0.