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  2. Argument (complex analysis) - Wikipedia

    en.wikipedia.org/wiki/Argument_(complex_analysis)

    Figure 1. This Argand diagram represents the complex number lying on a plane.For each point on the plane, arg is the function which returns the angle . In mathematics (particularly in complex analysis), the argument of a complex number z, denoted arg(z), is the angle between the positive real axis and the line joining the origin and z, represented as a point in the complex plane, shown as in ...

  3. Rotation matrix - Wikipedia

    en.wikipedia.org/wiki/Rotation_matrix

    where for every direction in the base space, S n, the fiber over it in the total space, SO(n + 1), is a copy of the fiber space, SO(n), namely the rotations that keep that direction fixed. Thus we can build an n × n rotation matrix by starting with a 2 × 2 matrix, aiming its fixed axis on S 2 (the ordinary sphere in three-dimensional space ...

  4. List of space groups - Wikipedia

    en.wikipedia.org/wiki/List_of_space_groups

    In Hermann–Mauguin notation, space groups are named by a symbol combining the point group identifier with the uppercase letters describing the lattice type. Translations within the lattice in the form of screw axes and glide planes are also noted, giving a complete crystallographic space group. These are the Bravais lattices in three dimensions:

  5. Orientability - Wikipedia

    en.wikipedia.org/wiki/Orientability

    A torus is an orientable surface The Möbius strip is a non-orientable surface. Note how the disk flips with every loop. The Roman surface is non-orientable.. In mathematics, orientability is a property of some topological spaces such as real vector spaces, Euclidean spaces, surfaces, and more generally manifolds that allows a consistent definition of "clockwise" and "anticlockwise". [1]

  6. Ambigram - Wikipedia

    en.wikipedia.org/wiki/Ambigram

    Animation of a half-turn ambigram of the word ambigram, with 180-degree rotational symmetry [1]. An ambigram is a calligraphic composition of glyphs (letters, numbers, symbols or other shapes) that can yield different meanings depending on the orientation of observation.

  7. Argument of periapsis - Wikipedia

    en.wikipedia.org/wiki/Argument_of_periapsis

    The argument of periapsis (also called argument of perifocus or argument of pericenter), symbolized as ω (), is one of the orbital elements of an orbiting body. . Parametrically, ω is the angle from the body's ascending node to its periapsis, measured in the dire

  8. Quaternions and spatial rotation - Wikipedia

    en.wikipedia.org/wiki/Quaternions_and_spatial...

    3D visualization of a sphere and a rotation about an Euler axis (^) by an angle of In 3-dimensional space, according to Euler's rotation theorem, any rotation or sequence of rotations of a rigid body or coordinate system about a fixed point is equivalent to a single rotation by a given angle about a fixed axis (called the Euler axis) that runs through the fixed point. [6]

  9. Rotation (mathematics) - Wikipedia

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

    If a rotation of Minkowski space is in a space-like plane, then this rotation is the same as a spatial rotation in Euclidean space. By contrast, a rotation in a plane spanned by a space-like dimension and a time-like dimension is a hyperbolic rotation , and if this plane contains the time axis of the reference frame, is called a "Lorentz boost".