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  2. Cantilever method - Wikipedia

    en.wikipedia.org/wiki/Cantilever_method

    The cantilever method is an approximate method for calculating shear forces and moments developed in beams and columns of a frame or structure due to lateral loads. The applied lateral loads typically include wind loads and earthquake loads, which must be taken into consideration while designing buildings.

  3. Arc length - Wikipedia

    en.wikipedia.org/wiki/Arc_length

    Thus the length of a curve is a non-negative real number. Usually no curves are considered which are partly spacelike and partly timelike. In theory of relativity, arc length of timelike curves (world lines) is the proper time elapsed along the world line, and arc length of a spacelike curve the proper distance along the curve.

  4. Euler–Bernoulli beam theory - Wikipedia

    en.wikipedia.org/wiki/Euler–Bernoulli_beam_theory

    The curve () describes the deflection of the beam in the direction at some position (recall that the beam is modeled as a one-dimensional object). q {\displaystyle q} is a distributed load, in other words a force per unit length (analogous to pressure being a force per area); it may be a function of x {\displaystyle x} , w {\displaystyle w ...

  5. Curvature - Wikipedia

    en.wikipedia.org/wiki/Curvature

    In mathematics, curvature is any of several strongly related concepts in geometry that intuitively measure the amount by which a curve deviates from being a straight line or by which a surface deviates from being a plane. If a curve or surface is contained in a larger space, curvature can be defined extrinsically relative to the ambient space.

  6. Crofton formula - Wikipedia

    en.wikipedia.org/wiki/Crofton_formula

    Since a convex curve intersects almost every line either twice or not at all, the unoriented Crofton formula for convex curves can be stated without numerical factors: the measure of the set of straight lines which intersect a convex curve is equal to its length. The same formula (with the same multiplicative constants) apply for hyperbolic ...

  7. Differentiable curve - Wikipedia

    en.wikipedia.org/wiki/Differentiable_curve

    Any regular curve may be parametrized by the arc length (the natural parametrization). From the point of view of a theoretical point particle on the curve that does not know anything about the ambient space, all curves would appear the same. Different space curves are only distinguished by how they bend and twist.

  8. Ribbon (mathematics) - Wikipedia

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

    In differential geometry, a ribbon (or strip) is the combination of a smooth space curve and its corresponding normal vector.More formally, a ribbon denoted by (,) includes a curve given by a three-dimensional vector (), depending continuously on the curve arc-length (), and a unit vector () perpendicular to () at each point. [1]

  9. List of formulae involving π - Wikipedia

    en.wikipedia.org/wiki/List_of_formulae_involving_π

    More formulas of this nature can be given, as explained by Ramanujan's theory of elliptic functions to alternative bases. Perhaps the most notable hypergeometric inversions are the following two examples, involving the Ramanujan tau function τ {\displaystyle \tau } and the Fourier coefficients j {\displaystyle \mathrm {j} } of the J-invariant ...

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