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2. Surface area - Wikipedia

   en.wikipedia.org/wiki/Surface_area

   A sphere of radius r has surface area 4πr 2.. The surface area (symbol A) of a solid object is a measure of the total area that the surface of the object occupies. [1] The mathematical definition of surface area in the presence of curved surfaces is considerably more involved than the definition of arc length of one-dimensional curves, or of the surface area for polyhedra (i.e., objects with ...

3. Pappus's centroid theorem - Wikipedia

   en.wikipedia.org/wiki/Pappus's_centroid_theorem

   The theorem applied to an open cylinder, cone and a sphere to obtain their surface areas. The centroids are at a distance a (in red) from the axis of rotation.. In mathematics, Pappus's centroid theorem (also known as the Guldinus theorem, Pappus–Guldinus theorem or Pappus's theorem) is either of two related theorems dealing with the surface areas and volumes of surfaces and solids of ...

4. On the Sphere and Cylinder - Wikipedia

   en.wikipedia.org/wiki/On_the_Sphere_and_Cylinder

   In his work, Archimedes showed that the surface area of a cylinder is equal to: = + = (+). and that the volume of the same is: =. [3] On the sphere, he showed that the surface area is four times the area of its great circle. In modern terms, this means that the surface area is equal to:

5. Shoelace formula - Wikipedia

   en.wikipedia.org/wiki/Shoelace_formula

   Shoelace scheme for determining the area of a polygon with point coordinates (,),..., (,). The shoelace formula, also known as Gauss's area formula and the surveyor's formula, [1] is a mathematical algorithm to determine the area of a simple polygon whose vertices are described by their Cartesian coordinates in the plane. [2]

6. Area density - Wikipedia

   en.wikipedia.org/wiki/Area_density

   A special type of area density is called column density (also columnar mass density or simply column density), denoted ρ A or σ.It is the mass of substance per unit area integrated along a path; [1] It is obtained integrating volumetric density over a column: [2] =.

7. Sphere - Wikipedia

   en.wikipedia.org/wiki/Sphere

   The sphere has the smallest surface area of all surfaces that enclose a given volume, and it encloses the largest volume among all closed surfaces with a given surface area. [11] The sphere therefore appears in nature: for example, bubbles and small water drops are roughly spherical because the surface tension locally minimizes surface area.

8. 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.

9. Locus (mathematics) - Wikipedia

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

   Each curve in this example is a locus defined as the conchoid of the point P and the line l.In this example, P is 8 cm from l. In geometry, a locus (plural: loci) (Latin word for "place", "location") is a set of all points (commonly, a line, a line segment, a curve or a surface), whose location satisfies or is determined by one or more specified conditions.