Euler's rotation theorem is a result in geometry stating that any displacement of a rigid body in three dimensional space that leaves one point fixed is equivalent to a single rotation about some axis running through that fixed point. Leonhard Euler proved the result in 1775 using spherical geometry. Composing two such rotations yields another rotation, giving the set of rotations a group structure known as the rotation group, and in linear algebra terms a non identity rotation matrix has one eigenvalue equal to one, whose eigenvector marks the axis of rotation, with the other two eigenvalues either complex conjugates or both equal to minus one. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/
Facts
Classification
Statement Form Connections
Has Statement Form
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
In Branch
Source Euler's rotation theorem (Wikipedia)
Named After
Derived from the theorem's own name (unambiguous possessive-token match to exactly one live mathematician entity, w-bfill-g5-0924 browse backfill)
Proved By
Source Euler's rotation theorem (Wikipedia)
Sources
1. Euler's rotation theorem (Wikipedia)
Lead paragraph
who proved it in 1775 by means of spherical geometry
In Branch: Geometry, Lead sentence
In geometry, Euler's rotation theorem states that, in three-dimensional space, any displacement of a rigid body such that a point
View the SourceReader Challenges (0)
No disputes yet. Spotted an error or a better source? Open the first one.
Sign in to dispute this or suggest a correction.