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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.
A real life example spherical polyhedron is the football, being a spherical tiling of the truncated Icosahedron. This beach ball would be a hosohedron with 6 spherical lune faces, if the 2 white caps on the ends were removed.
This sphere was a fused quartz gyroscope for the Gravity Probe B experiment, and differs in shape from a perfect sphere by no more than 40 atoms (less than 10 nm) of thickness. It was announced on 1 July 2008 that Australian scientists had created even more nearly perfect spheres, accurate to 0.3 nm, as part of an international hunt to find a ...
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.
Sphere eversion using Thurston's corrugations; see the video's Wikimedia Commons page for a description of the video's contents Thurston 's corrugations: this is a topological method and generic; it takes a homotopy and perturbs it so that it becomes a regular homotopy.
An example can be found in the model of a buckminsterfullerene, a truncated icosahedron-shaped geodesic dome allotrope of elemental carbon discovered in 1985. [17] In other engineering and science applications, its shape was also the configuration of the lenses used for focusing the explosive shock waves of the detonators in both the gadget and ...
Other examples have been built in Europe. In 2012, an aluminium and glass dome was used as a dome cover to an eco home in Norway [14] and in 2013 a glass and wood clad dome home was built in Austria. [15] In Chile, examples of geodesic domes are being readily adopted for hotel accommodations either as tented style geodesic domes or glass ...
So for example, both Orion and the Big Dipper are visible during at least part of the year. Making stellar observations from a representative set of points across Earth, combined with knowing the shortest on-the-ground distance between any two given points, makes an approximate sphere the only possible shape for Earth.