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An unlabeled transitive digraph with n nodes is called a "topology." The numbers of distinct topologies on n=1, 2, ... nodes are 1, 3, 9, 33, 139, 718, 4535, ... (OEIS ...

In many cases, the Hausdorff dimension correctly describes the correction term for a resonator with fractal perimeter in Lorentz's conjecture. However, in general, the proper ...

The number of equivalent hyperspheres in n dimensions which can touch an equivalent hypersphere without any intersections, also sometimes called the Newton number, contact ...

The n-hypersphere (often simply called the n-sphere) is a generalization of the circle (called by geometers the 2-sphere) and usual sphere (called by geometers the 3-sphere) ...

The radical line, also called the radical axis, is the locus of points of equal circle power with respect to two nonconcentric circles. By the chordal theorem, it is ...

In general, the external similitude center of two circles C_1=C(x_1,r_1) and C_2=C(x_2,r_2) with centers given in Cartesian coordinates is given by ...

Bezdek and Kuperberg (1991) have constructed packings of identical ellipsoids of densities arbitrarily close to ((24sqrt(2)-6sqrt(3)-2pi)pi)/(72)=0.753355... (OEIS A093824), ...

Not concentric.

The complex lattice Lambda_6^omega corresponding to real lattice K_(12) having the densest hypersphere packing (kissing number) in twelve dimensions. The associated ...

In 1611, Kepler proposed that close packing (either cubic or hexagonal close packing, both of which have maximum densities of pi/(3sqrt(2)) approx 74.048%) is the densest ...