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2. Rotation (mathematics) - Wikipedia

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

   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. Rotation can have a sign (as in the sign of an angle): a clockwise rotation is a negative magnitude so a counterclockwise turn ...

3. Rotations in 4-dimensional Euclidean space - Wikipedia

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

   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 is the special orthogonal group of order 4. In this article rotation means rotational displacement. For the sake of uniqueness, rotation angles are assumed to be in the segment [0, π] except ...

4. Four-dimensional space - Wikipedia

   en.wikipedia.org/wiki/Four-dimensional_space

   Mathematically, a four-dimensional space is a space that needs four parameters to specify a point in it. For example, a general point might have position vector a, equal to. This can be written in terms of the four standard basis vectors (e1, e2, e3, e4), given by. so the general vector a is. Vectors add, subtract and scale as in three ...

5. Orientation (geometry) - Wikipedia

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

   Orientation (geometry) Changing orientation of a rigid body is the same as rotating the axes of a reference frame attached to it. In geometry, the orientation, attitude, bearing, direction, or angular position of an object – such as a line, plane or rigid body – is part of the description of how it is placed in the space it occupies. [1]

6. 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. The algebra Cl (V) is the quotient of the tensor algebra ...

7. Rotation - Wikipedia

   en.wikipedia.org/wiki/Rotation

   Rotation or rotational motion is the circular movement of an object around a central line, known as an axis of rotation. A plane figure can rotate in either a clockwise or counterclockwise sense around a perpendicular axis intersecting anywhere inside or outside the figure at a center of rotation. A solid figure has an infinite number of ...