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Here there is a choice between separating the spheres into regions of close-packed equal spheres, or combining the multiple sizes of spheres into a compound or interstitial packing. When many sizes of spheres (or a distribution) are available, the problem quickly becomes intractable, but some studies of binary hard spheres (two sizes) are ...
Figure 3 Shown here is a modified form of the cannonball stack wherein three extra spheres have been added to show all eight spheres in the top three tiers of the FCC lattice diagramed in Figure 1. Figure 4 Shown here are all eleven spheres of the HCP lattice illustrated in Figure 1. The difference between this stack and the top three tiers of ...
A Klerksdorp sphere. It is 3 to 4 centimetres (1.2 to 1.6 in) in maximum diameter and 2.5 centimetres (0.98 in) in thickness. Klerksdorp spheres are small objects, often spherical to disc-shaped, that have been collected by miners and rockhounds from 3-billion-year-old pyrophyllite deposits mined by Wonderstone Ltd., near Ottosdal, South Africa.
If f(x, y, z) = 0 and g(x, y, z) = 0 are the equations of two distinct spheres then (,,) + (,,) = is also the equation of a sphere for arbitrary values of the parameters s and t. The set of all spheres satisfying this equation is called a pencil of spheres determined by the original two spheres. In this definition a sphere is allowed to be a ...
István Lénárt demonstrating a number of Lénárt spheres. A Lénárt sphere is an educational manipulative and writing surface for exploring spherical geometry, invented by Hungarian István Lénárt as a modern replacement for a spherical blackboard.
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.
Cenosphere formed from coal combustion, magnified 400×. A cenosphere or kenosphere is a lightweight, inert, hollow sphere made largely of silica and alumina [1] and filled with air or inert gas, typically produced as a coal combustion byproduct at thermal power plants.
Smale's original proof was indirect: he identified (regular homotopy) classes of immersions of spheres with a homotopy group of the Stiefel manifold. Since the homotopy group that corresponds to immersions of S 2 {\displaystyle S^{2}} in R 3 {\displaystyle \mathbb {R} ^{3}} vanishes, the standard embedding and the inside-out one must be regular ...
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