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2. Pentomino - Wikipedia

   en.wikipedia.org/wiki/Pentomino

   When rotations and reflections are not considered to be distinct shapes, there are 12 different free pentominoes. When reflections are considered distinct, there are 18 one-sided pentominoes. When rotations are also considered distinct, there are 63 fixed pentominoes. Pentomino tiling puzzles and games are popular in recreational mathematics. [1]

3. 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.

4. Rotation (mathematics) - Wikipedia

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

   The rotation group is a Lie group of rotations about a fixed point. This (common) fixed point or center is called the center of rotation and is usually identified with the origin. The rotation group is a point stabilizer in a broader group of (orientation-preserving) motions. For a particular rotation: The axis of rotation is a line of its ...

5. Domino (mathematics) - Wikipedia

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

   Dominos can tile the plane in a countably infinite number of ways. The number of tilings of a 2×n rectangle with dominoes is , the nth Fibonacci number. [5]Domino tilings figure in several celebrated problems, including the Aztec diamond problem in which large diamond-shaped regions have a number of tilings equal to a power of two, [6] with most tilings appearing random within a central ...

6. 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 .

7. Givens rotation - Wikipedia

   en.wikipedia.org/wiki/Givens_rotation

   As rotations are applied just in the opposite order of the Euler angles table of rotations, this table is the same but swapping indexes 1 and 3 in the angles associated with the corresponding entry. An entry like zxy means to apply first the y rotation, then x, and finally z, in the basis axes.