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  2. Rotation formalisms in three dimensions - Wikipedia

    en.wikipedia.org/wiki/Rotation_formalisms_in...

    Rotation formalisms are focused on proper (orientation-preserving) motions of the Euclidean space with one fixed point, that a rotation refers to.Although physical motions with a fixed point are an important case (such as ones described in the center-of-mass frame, or motions of a joint), this approach creates a knowledge about all motions.

  3. Spherical coordinate system - Wikipedia

    en.wikipedia.org/wiki/Spherical_coordinate_system

    The azimuth angle θ appears to equal positive 90°, as rotated counterclockwise from the azimuth-reference x–axis; and the inclination φ appears to equal 30°, as rotated from the zenith–axis. (Note the 'full' rotation, or inclination, from the zenith–axis to the y–axis is 90°).

  4. Rotation matrix - Wikipedia

    en.wikipedia.org/wiki/Rotation_matrix

    Noting that any identity matrix is a rotation matrix, and that matrix multiplication is associative, we may summarize all these properties by saying that the n × n rotation matrices form a group, which for n > 2 is non-abelian, called a special orthogonal group, and denoted by SO(n), SO(n,R), SO n, or SO n (R), the group of n × n rotation ...

  5. Rotational symmetry - Wikipedia

    en.wikipedia.org/wiki/Rotational_symmetry

    An object's degree of rotational symmetry is the number of distinct orientations in which it looks exactly the same for each rotation. Certain geometric objects are partially symmetrical when rotated at certain angles such as squares rotated 90°, however the only geometric objects that are fully rotationally symmetric at any angle are spheres ...

  6. 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 ...

  7. 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 .

  8. The 90-10 Rule is a Better Way to Trim Your Nails - AOL

    www.aol.com/lifestyle/90-10-rule-better-way...

    I once read an interview where Kim Kardashian mentioned that she always makes time for a manicure because even if everything else is in disarray, there’s something about having well-groomed ...

  9. File:90 degree rotations expressed in radian measure.svg

    en.wikipedia.org/wiki/File:90_degree_rotations...

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