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  2. 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 .

  3. Polar coordinate system - Wikipedia

    en.wikipedia.org/wiki/Polar_coordinate_system

    In green, the point with radial coordinate 3 and angular coordinate 60 degrees or (3, 60°). In blue, the point (4, 210°). In mathematics, the polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction.

  4. Examples of groups - Wikipedia

    en.wikipedia.org/wiki/Examples_of_groups

    Let's investigate our square's symmetry group some more. Right now, we have the elements a, b and e, but we can easily form more: for instance a ∘ a, also written as a 2, is a 180° degree turn. a 3 is a 270° clockwise rotation (or a 90° counter-clockwise rotation). We also see that b 2 = e and also a 4 = e.

  5. Axis–angle representation - Wikipedia

    en.wikipedia.org/wiki/Axis–angle_representation

    The angle θ and axis unit vector e define a rotation, concisely represented by the rotation vector θe.. In mathematics, the axis–angle representation parameterizes a rotation in a three-dimensional Euclidean space by two quantities: a unit vector e indicating the direction of an axis of rotation, and an angle of rotation θ describing the magnitude and sense (e.g., clockwise) of the ...

  6. 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.

  7. Coordinate system - Wikipedia

    en.wikipedia.org/wiki/Coordinate_system

    It assigns three numbers (known as coordinates) to every point in Euclidean space: radial distance r, polar angle θ , and azimuthal angle φ . The symbol ρ ( rho ) is often used instead of r . In geometry , a coordinate system is a system that uses one or more numbers , or coordinates , to uniquely determine the position of the points or ...

  8. Rotations and reflections in two dimensions - Wikipedia

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

    An xy-Cartesian coordinate system rotated through an angle to an x′y′-Cartesian coordinate system 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 ...

  9. Retrograde and prograde motion - Wikipedia

    en.wikipedia.org/wiki/Retrograde_and_prograde_motion

    An object with an axial tilt up to 90 degrees is rotating in the same direction as its primary. An object with an axial tilt of exactly 90 degrees, has a perpendicular rotation that is neither prograde nor retrograde. An object with an axial tilt between 90 degrees and 180 degrees is rotating in the opposite direction to its orbital direction.