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The basic quantities describing a sphere (meaning a 2-sphere, a 2-dimensional surface inside 3-dimensional space) will be denoted by the following variables r {\displaystyle r} is the radius, C = 2 π r {\displaystyle C=2\pi r} is the circumference (the length of any one of its great circles ),
In mathematics, the theory of finite sphere packing concerns the question of how a finite number of equally-sized spheres can be most efficiently packed. The question of packing finitely many spheres has only been investigated in detail in recent decades, with much of the groundwork being laid by László Fejes Tóth .
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.
Example model An artistic model created by Father Magnus Wenninger called Order in Chaos, representing a chiral subset of triangles of a 16-frequency icosahedral geodesic sphere, {3,5+} 16,0: A virtual copy showing icosahedral symmetry great circles. The 6-fold rotational symmetry is illusionary, not existing on the icosahedron itself.
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 ...
In geometry, a spherical polyhedron or spherical tiling is a tiling of the sphere in which the surface is divided or partitioned by great arcs into bounded regions called spherical polygons. A polyhedron whose vertices are equidistant from its center can be conveniently studied by projecting its edges onto the sphere to obtain a corresponding ...
In other words, all of its faces are the same size and shape (congruent) and all edges are the same length. The regular tetrahedron is the simplest convex deltahedron , a polyhedron in which all of its faces are equilateral triangles; there are seven other convex deltahedra.
Strictly speaking, the laser diffraction equivalent diameter is the diameter of a sphere yielding, on the same detector geometry, the same diffraction pattern as the particle. In the size regimen where the Fraunhofer approximation is valid, this diameter corresponds to the projected area diameter of the particle in random orientation. For ...