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  2. Area - Wikipedia

    en.wikipedia.org/wiki/Area

    The formula for the surface area of a sphere is more difficult to derive: because a sphere has nonzero Gaussian curvature, it cannot be flattened out. The formula for the surface area of a sphere was first obtained by Archimedes in his work On the Sphere and Cylinder. The formula is: [6] A = 4πr 2 (sphere), where r is the radius of the sphere.

  3. Metric tensor - Wikipedia

    en.wikipedia.org/wiki/Metric_tensor

    In the mathematical field of differential geometry, a metric tensor (or simply metric) is an additional structure on a manifold M (such as a surface) that allows defining distances and angles, just as the inner product on a Euclidean space allows defining distances and angles there.

  4. Metric space - Wikipedia

    en.wikipedia.org/wiki/Metric_space

    An important area of study in finite metric spaces is the embedding of complex metric spaces into simpler ones while controlling the distortion of distances. This is particularly useful in computer science and discrete mathematics, where algorithms often perform more efficiently on simpler structures like tree metrics.

  5. Hectare - Wikipedia

    en.wikipedia.org/wiki/Hectare

    Image comparing the hectare (the small blue area at lower left) to other units. The entire yellow square is one square mile.. The hectare (/ ˈ h ɛ k t ɛər,-t ɑːr /; SI symbol: ha) is a non-SI metric unit of area equal to a square with 100-metre sides (1 hm 2), that is, 10,000 square metres (10,000 m 2), and is primarily used in the measurement of land.

  6. Basal area - Wikipedia

    en.wikipedia.org/wiki/Basal_area

    Basal area is the cross-sectional area of trees at breast height (1.3m or 4.5 ft above ground). It is a common way to describe stand density. In forest management, basal area usually refers to merchantable timber and is given on a per hectare or per acre basis. If one cut down all the merchantable trees on an acre at 4.5 feet (1.4 m) off the ...

  7. Circular mil - Wikipedia

    en.wikipedia.org/wiki/Circular_mil

    A circular mil is a unit of area, equal to the area of a circle with a diameter of one mil (one thousandth of an inch or 0.0254 mm). It is equal to π /4 square mils or approximately 5.067 × 10 −4 mm 2. It is a unit intended for referring to the area of a wire with a circular cross section.

  8. Riemannian manifold - Wikipedia

    en.wikipedia.org/wiki/Riemannian_manifold

    Formally, a Riemannian metric (or just a metric) on a smooth manifold is a choice of inner product for each tangent space of the manifold. A Riemannian manifold is a smooth manifold together with a Riemannian metric. The techniques of differential and integral calculus are used to pull geometric data out of the Riemannian metric. For example ...

  9. Area formula (geometric measure theory) - Wikipedia

    en.wikipedia.org/wiki/Area_formula_(geometric...

    In geometric measure theory the area formula relates the Hausdorff measure of the image of a Lipschitz map, while accounting for multiplicity, to the integral of the Jacobian of the map. It is one of the fundamental results of the field that has connections, for example, to rectifiability and Sard's theorem .