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  2. Plate trick - Wikipedia

    en.wikipedia.org/wiki/Plate_trick

    In mathematics and physics, the plate trick, also known as Dirac's string trick (after Paul Dirac, who introduced and popularized it), [1] [2] the belt trick, or the Balinese cup trick (it appears in the Balinese candle dance), is any of several demonstrations of the idea that rotating an object with strings attached to it by 360 degrees does not return the system to its original state, while ...

  3. Orientation entanglement - Wikipedia

    en.wikipedia.org/wiki/Orientation_entanglement

    In fact, the coffee cup is inextricably entangled. There is no way to untwist the bands without rotating the cup. However, consider what happens instead when the cup is rotated, not through just one 360° turn, but two 360° turns for a total rotation of 720°. Then if the cup is lowered to the floor, the two rubber bands coil around each other ...

  4. Rotational symmetry - Wikipedia

    en.wikipedia.org/wiki/Rotational_symmetry

    A rotocenter is the fixed, or invariant, point of a rotation. [3] There are two rotocenters per primitive cell. Together with double translational symmetry the rotation groups are the following wallpaper groups, with axes per primitive cell: p2 (2222): 4×2-fold; rotation group of a parallelogrammic, rectangular, and rhombic lattice.

  5. Angular displacement - Wikipedia

    en.wikipedia.org/wiki/Angular_displacement

    Figure 1: Euler's rotation theorem. A great circle transforms to another great circle under rotations, leaving always a diameter of the sphere in its original position. Figure 2: A rotation represented by an Euler axis and angle. In three dimensions, angular displacement is an entity with a direction and a magnitude.

  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. Right-hand rule - Wikipedia

    en.wikipedia.org/wiki/Right-hand_rule

    In mathematics and physics, the right-hand rule is a convention and a mnemonic, utilized to define the orientation of axes in three-dimensional space and to determine the direction of the cross product of two vectors, as well as to establish the direction of the force on a current-carrying conductor in a magnetic field.

  8. Rotation - Wikipedia

    en.wikipedia.org/wiki/Rotation

    A sphere rotating (spinning) about an axis. 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.

  9. 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.