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  2. Volume of an n-ball - Wikipedia

    en.wikipedia.org/wiki/Volume_of_an_n-ball

    The volume of a n-ball is the Lebesgue measure of this ball, which generalizes to any dimension the usual volume of a ball in 3-dimensional space. The volume of a n -ball of radius R is where is the volume of the unit n -ball, the n -ball of radius 1. The real number can be expressed via a two-dimension recurrence relation.

  3. Square–cube law - Wikipedia

    en.wikipedia.org/wiki/Square–cube_law

    The square–cube law was first mentioned in Two New Sciences (1638). The square–cube law (or cube–square law) is a mathematical principle, applied in a variety of scientific fields, which describes the relationship between the volume and the surface area as a shape's size increases or decreases. It was first [dubious – discuss] described ...

  4. Surface-area-to-volume ratio - Wikipedia

    en.wikipedia.org/wiki/Surface-area-to-volume_ratio

    The surface-area-to-volume ratio has physical dimension inverse length (L −1) and is therefore expressed in units of inverse metre (m -1) or its prefixed unit multiples and submultiples. As an example, a cube with sides of length 1 cm will have a surface area of 6 cm 2 and a volume of 1 cm 3. The surface to volume ratio for this cube is thus.

  5. Divergence theorem - Wikipedia

    en.wikipedia.org/wiki/Divergence_theorem

    The volume rate of flow of liquid through a source or sink (with the flow through a sink given a negative sign) is equal to the divergence of the velocity field at the pipe mouth, so adding up (integrating) the divergence of the liquid throughout the volume enclosed by S equals the volume rate of flux through S. This is the divergence theorem.

  6. Volumetric flux - Wikipedia

    en.wikipedia.org/wiki/Volumetric_flux

    Volumetric flux. In fluid dynamics, the volumetric flux is the rate of volume flow across a unit area (m 3 ·s −1 ·m −2), and has dimensions of distance/time (volume/ (time*area)) - equivalent to mean velocity. The density of a particular property in a fluid's volume, multiplied with the volumetric flux of the fluid, thus defines the ...

  7. Dimensional weight - Wikipedia

    en.wikipedia.org/wiki/Dimensional_weight

    Dimensional weight, also known as volumetric weight, is a pricing technique for commercial freight transport (including courier and postal services), which uses an estimated weight that is calculated from the length, width and height of a package. The shipping fee is based upon the dimensional weight or the actual weight, whichever is greater.

  8. Volume element - Wikipedia

    en.wikipedia.org/wiki/Volume_element

    Volume element. In mathematics, a volume element provides a means for integrating a function with respect to volume in various coordinate systems such as spherical coordinates and cylindrical coordinates. Thus a volume element is an expression of the form where the are the coordinates, so that the volume of any set can be computed by For ...

  9. Lebesgue measure - Wikipedia

    en.wikipedia.org/wiki/Lebesgue_measure

    Lebesgue measure. In measure theory, a branch of mathematics, the Lebesgue measure, named after French mathematician Henri Lebesgue, is the standard way of assigning a measure to subsets of higher dimensional Euclidean n -spaces. For lower dimensions n = 1, 2, or 3, it coincides with the standard measure of length, area, or volume.

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