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  2. Circumference - Wikipedia

    en.wikipedia.org/wiki/Circumference

    The circumference is the arc length of the circle, as if it were opened up and straightened out to a line segment. [1] More generally, the perimeter is the curve length around any closed figure. Circumference may also refer to the circle itself, that is, the locus corresponding to the edge of a disk. The circumference of a sphere is the ...

  3. n-sphere - Wikipedia

    en.wikipedia.org/wiki/N-sphere

    In mathematics, an n-sphere or hypersphere is an ⁠ ⁠-dimensional generalization of the ⁠ ⁠-dimensional circle and ⁠ ⁠-dimensional sphere to any non-negative integer ⁠ ⁠. The circle is considered 1-dimensional, and the sphere 2-dimensional, because the surfaces themselves are 1- and 2-dimensional respectively, not because they ...

  4. Great-circle distance - Wikipedia

    en.wikipedia.org/wiki/Great-circle_distance

    A diagram illustrating great-circle distance (drawn in red) between two points on a sphere, P and Q. Two antipodal points, u and v are also shown. The great-circle distance, orthodromic distance, or spherical distance is the distance between two points on a sphere, measured along the great-circle arc between them. This arc is the shortest path ...

  5. Spherical cap - Wikipedia

    en.wikipedia.org/wiki/Spherical_cap

    For example, assuming the Earth is a sphere of radius 6371 km, the surface area of the arctic (north of the Arctic Circle, at latitude 66.56° as of August 2016 [7]) is 2π ⋅ 6371 2 | sin 90° − sin 66.56° | = 21.04 million km 2 (8.12 million sq mi), or 0.5 ⋅ | sin 90° − sin 66.56° | = 4.125% of the total surface area of the Earth.

  6. Earth's circumference - Wikipedia

    en.wikipedia.org/wiki/Earth's_circumference

    Earth's circumference is the distance around Earth. Measured around the equator, it is 40,075.017 km (24,901.461 mi). Measured passing through the poles, the circumference is 40,007.863 km (24,859.734 mi). [1] Treating the Earth as a sphere, its circumference would be its single most important measurement. [2]

  7. Spherical geometry - Wikipedia

    en.wikipedia.org/wiki/Spherical_geometry

    Any two points that are not antipodal points determine a unique great circle. There is a natural unit of angle measurement (based on a revolution), a natural unit of length (based on the circumference of a great circle) and a natural unit of area (based on the area of the sphere).

  8. Spherical coordinate system - Wikipedia

    en.wikipedia.org/wiki/Spherical_coordinate_system

    For example, one sphere that is described in Cartesian coordinates with the equation x 2 + y 2 + z 2 = c 2 can be described in spherical coordinates by the simple equation r = c. (In this system—shown here in the mathematics convention—the sphere is adapted as a unit sphere, where the radius is set to unity and then can generally be ignored ...

  9. Sphere - Wikipedia

    en.wikipedia.org/wiki/Sphere

    A sphere (from Greek σφαῖρα, sphaîra) [1] is a geometrical object that is a three-dimensional analogue to a two-dimensional circle.Formally, a sphere is the set of points that are all at the same distance r from a given point in three-dimensional space. [2]