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2. Rotor (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Rotor_(mathematics)

   In mathematics, a rotor in the geometric algebra of a vector space V is the same thing as an element of the spin group Spin(V).We define this group below. Let V be a vector space equipped with a positive definite quadratic form q, and let Cl(V) be the geometric algebra associated to V.

3. Rotations and reflections in two dimensions - Wikipedia

   en.wikipedia.org/wiki/Rotations_and_reflections...

   A rotation in the plane can be formed by composing a pair of reflections. First reflect a point P to its image P′ on the other side of line L 1. Then reflect P′ to its image P′′ on the other side of line L 2. If lines L 1 and L 2 make an angle θ with one another, then points P and P′′ will make an angle 2θ around point O, the ...

4. Rotation (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Rotation_(mathematics)

   Rotation of an object in two dimensions around a point O. 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, for example, the motion of a rigid body around a fixed point.

5. Rotation of axes in two dimensions - Wikipedia

   en.wikipedia.org/wiki/Rotation_of_axes_in_two...

   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 origin is kept fixed and the x′ and y′ axes are obtained by rotating the x and y axes counterclockwise through an angle .

6. Orientation (geometry) - Wikipedia

   en.wikipedia.org/wiki/Orientation_(geometry)

   The rotations were described by orthogonal matrices referred to as rotation matrices or direction cosine matrices. When used to represent an orientation, a rotation matrix is commonly called orientation matrix, or attitude matrix. The above-mentioned Euler vector is the eigenvector of a rotation matrix (a rotation matrix has a unique real ...

7. Rotations in 4-dimensional Euclidean space - Wikipedia

   en.wikipedia.org/wiki/Rotations_in_4-dimensional...

   Fig.1: simple rotations (black) and left and right isoclinic rotations (red and blue) Fig.2: a general rotation with angular displacements in a ratio of 1:5 Fig.3: a general rotation with angular displacements in a ratio of 5:1 All images are stereographic projections. Every rotation in 3D space has a fixed axis unchanged by rotation.