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Define the packing density eta of a packing of spheres to be the fraction of a volume filled by the spheres. In three dimensions, there are three periodic packings for ...

The inertial subranges of velocity power spectra for homogeneous turbulence exhibit a power law with exponent -5/3. This exponent (-5/3) is called the Kolmogorov constant by ...

Informally, self-similar objects with parameters N and s are described by a power law such as N=s^d, where d=(lnN)/(lns) is the "dimension" of the scaling law, known as the ...

An object is said to be self-similar if it looks "roughly" the same on any scale. Fractals are a particularly interesting class of self-similar objects. Self-similar objects ...

A polyhedron is said to be regular if its faces and vertex figures are regular (not necessarily convex) polygons (Coxeter 1973, p. 16). Using this definition, there are a ...

A general concept in category theory involving the globalization of topological or differential structures. The term derives from the Greek omicronlambdaomicronsigma (holos) ...

The stella octangula is a polyhedron compound composed of a tetrahedron and its dual (a second tetrahedron rotated 180 degrees with respect to the first). The stella ...

"The" trifolium is the three-lobed folium with b=a, i.e., the 3-petalled rose curve. It is also known as the paquerette de mélibée (Apéry 1987, p. 85), with paquerette being ...

The differential equation describing exponential growth is (dN)/(dt)=rN. (1) This can be integrated directly int_(N_0)^N(dN)/N=int_0^trdt (2) to give ln(N/(N_0))=rt, (3) ...

The Soicher graphs are three distance-regular graphs on 5346, 486, and 315 vertices, respectively. The first two are also distance-transitive but the third is not. The second ...