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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]
% of sphere Location Completed Removed Held record m ft Sphere: 157 515 71% Las Vegas, Nevada: 29 September 2023 – 29 September 2023 - current Avicii Arena (Globen) 110.40 362.2 77.2 % Stockholm, Sweden 19 February 1989 – 19 February 1989 – 29 September 2023 Kazakhstan Pavilion and Science Museum (Nur Alem) 80 262 ~100 % Astana, Kazakhstan
An arrangement in which the midpoint of all the spheres lie on a single straight line is called a sausage packing, as the convex hull has a sausage-like shape.An approximate example in real life is the packing of tennis balls in a tube, though the ends must be rounded for the tube to coincide with the actual convex hull.
The sum of the angles of a spherical triangle is not equal to 180°. A sphere is a curved surface, but locally the laws of the flat (planar) Euclidean geometry are good approximations. In a small triangle on the face of the earth, the sum of the angles is only slightly more than 180 degrees. A sphere with a spherical triangle on it.
The tectonic plates of the lithosphere on Earth Earth cutaway from center to surface, the lithosphere comprising the crust and lithospheric mantle (detail not to scale). A lithosphere (from Ancient Greek λίθος (líthos) 'rocky' and σφαίρα (sphaíra) 'sphere') is the rigid, [1] outermost rocky shell of a terrestrial planet or natural satellite.
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 ...
The great circle g (green) lies in a plane through the sphere's center O (black). The perpendicular line a (purple) through the center is called the axis of g, and its two intersections with the sphere, P and P ' (red), are the poles of g. Any great circle s (blue) through the poles is secondary to g. A great circle divides the sphere in two ...
More generally, every two great circles on a sphere are concentric with each other and with the sphere. [ 4 ] By Euler's theorem in geometry on the distance between the circumcenter and incenter of a triangle, two concentric circles (with that distance being zero) are the circumcircle and incircle of a triangle if and only if the radius of one ...