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  2. Dilaton - Wikipedia

    en.wikipedia.org/wiki/Dilaton

    The dilaton made its first appearance in Kaluza–Klein theory, a five-dimensional theory that combined gravitation and electromagnetism. It appears in string theory . However, it has become central to the lower-dimensional many-bodied gravity problem [ 2 ] based on the field theoretic approach of Roman Jackiw .

  3. List of common coordinate transformations - Wikipedia

    en.wikipedia.org/wiki/List_of_common_coordinate...

    As φ has a range of 360° the same considerations as in polar (2 dimensional) coordinates apply whenever an arctangent of it is taken. θ has a range of 180°, running from 0° to 180°, and does not pose any problem when calculated from an arccosine, but beware for an arctangent.

  4. Rotation matrix - Wikipedia

    en.wikipedia.org/wiki/Rotation_matrix

    This has the convenient implication for 2 × 2 and 3 × 3 rotation matrices that the trace reveals the angle of rotation, θ, in the two-dimensional space (or subspace). For a 2 × 2 matrix the trace is 2 cos θ, and for a 3 × 3 matrix it is 1 + 2 cos θ. In the three-dimensional case, the subspace consists of all vectors perpendicular to the ...

  5. Polar coordinate system - Wikipedia

    en.wikipedia.org/wiki/Polar_coordinate_system

    Polar coordinates are two-dimensional and thus they can be used only where point positions lie on a single two-dimensional plane. They are most appropriate in any context where the phenomenon being considered is inherently tied to direction and length from a center point.

  6. Dilation (metric space) - Wikipedia

    en.wikipedia.org/wiki/Dilation_(metric_space)

    In Euclidean space, such a dilation is a similarity of the space. [2] Dilations change the size but not the shape of an object or figure. Every dilation of a Euclidean space that is not a congruence has a unique fixed point [3] that is called the center of dilation. [4] Some congruences have fixed points and others do not. [5]

  7. Spacetime diagram - Wikipedia

    en.wikipedia.org/wiki/Spacetime_diagram

    Fig 4–2. Relativistic time dilation, as depicted in a single Loedel spacetime diagram. Both observers consider the clock of the other as running slower. Relativistic time dilation refers to the fact that a clock (indicating its proper time in its rest frame) that moves relative to an observer is observed to run slower. The situation is ...

  8. Gaussian curvature - Wikipedia

    en.wikipedia.org/wiki/Gaussian_curvature

    The Gaussian curvature is the product of the two principal curvatures Κ = κ 1 κ 2. The sign of the Gaussian curvature can be used to characterise the surface. If both principal curvatures are of the same sign: κ 1 κ 2 > 0, then the Gaussian curvature is positive and the surface is said to have an elliptic point. At such points, the surface ...

  9. Strain-rate tensor - Wikipedia

    en.wikipedia.org/wiki/Strain-rate_tensor

    A two-dimensional flow that, at the highlighted point, has only a strain rate component, with no mean velocity or rotational component. In continuum mechanics, the strain-rate tensor or rate-of-strain tensor is a physical quantity that describes the rate of change of the strain (i.e., the relative deformation) of a material in the neighborhood of a certain point, at a certain moment of time.