Rotation in mathematics is a concept originating in geometry. Any rotation is a motion of a certain space that preserves at least one point. It can describe...

In geometry, there exist various rotation formalisms to express a rotation in three dimensions as a mathematical transformation. In physics, this concept...

Rotation operator may refer to: An operator that specifies a rotation (mathematics) Three-dimensional rotation operator Rot (operator) aka Curl, a differential...

In the theory of three-dimensional rotation, Rodrigues' rotation formula, named after Olinde Rodrigues, is an efficient algorithm for rotating a vector...

In mathematics, the rotation number is an invariant of homeomorphisms of the circle. It was first defined by Henri Poincaré in 1885, in relation to the...

known as versors, provide a convenient mathematical notation for representing spatial orientations and rotations of elements in three dimensional space...

In mathematics, a rotation of axes in two dimensions is a mapping from an xy-Cartesian coordinate system to an x′y′-Cartesian coordinate system in which...

The coin rotation paradox is the counter-intuitive mathematical fact that, when one coin is rolled without slipping around the rim of another coin of equal...

may also refer to: Rotation (anatomy) Rotation (mathematics) Rotation (medicine), medical student training Rotation (physics), ratio between a given angle...

Mathematically, a rotation is a rigid body movement which, unlike a translation, keeps at least one point fixed. This definition applies to rotations...

In linear algebra, a rotation matrix is a transformation matrix that is used to perform a rotation in Euclidean space. For example, using the convention...

rotation around a fixed axis of a rigid body are mathematically much simpler than those for free rotation of a rigid body; they are entirely analogous to...

In mathematics and physics, vector is a term that refers to quantities that cannot be expressed by a single number (a scalar), or to elements of some...

numerical linear algebra, a Givens rotation is a rotation in the plane spanned by two coordinates axes. Givens rotations are named after Wallace Givens,...

In discrete mathematics, tree rotation is an operation on a binary tree that changes the structure without interfering with the order of the elements....

In mathematics, the group of rotations about a fixed point in four-dimensional Euclidean space is denoted SO(4). The name comes from the fact that it...

two rotations results in another rotation, every rotation has a unique inverse rotation, and the identity map satisfies the definition of a rotation. Owing...

composition of rotations (i.e. chained rotations). The geometrical definition demonstrates that three consecutive elemental rotations (rotations about the...

Earth's rotation or Earth's spin is the rotation of planet Earth around its own axis, as well as changes in the orientation of the rotation axis in space...

to a reflection. The statements above can be expressed more mathematically. Let a rotation about the origin O by an angle θ be denoted as Rot(θ). Let a...

In mathematics, a matrix (pl.: matrices) is a rectangular array or table of numbers or other mathematical objects with elements or entries arranged in...

infinitesimal rotation matrix or differential rotation matrix is a matrix representing an infinitely small rotation. While a rotation matrix is an orthogonal...

In mathematics, a group is a set with an operation that combines any two elements of the set to produce a third element within the same set and the following...

mathematics, a function defined on an inner product space is said to have rotational invariance if its value does not change when arbitrary rotations...

binary aspects of mathematical or scientific objects, such as odd and even (sign of a permutation), sense of orientation or rotation (cw/ccw), one sided...

Pure mathematics is the study of mathematical concepts independently of any application outside mathematics. These concepts may originate in real-world...

may be continuous (such as rotation of a circle) or discrete (e.g., reflection of a bilaterally symmetric figure, or rotation of a regular polygon). Continuous...

In geometry, an improper rotation (also called rotation-reflection, rotoreflection, rotary reflection, or rotoinversion) is an isometry in Euclidean space...

In mathematics, a reflection (also spelled reflexion) is a mapping from a Euclidean space to itself that is an isometry with a hyperplane as the set of...

Optical rotation, also known as polarization rotation or circular birefringence, is the rotation of the orientation of the plane of polarization about...