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The number of regions into which space can be divided by n mutually intersecting spheres is N=1/3n(n^2-3n+8), giving 2, 4, 8, 16, 30, 52, 84, ... (OEIS A046127) for n=1, 2, ...

A sequence of approximations a/b to sqrt(n) can be derived by factoring a^2-nb^2=+/-1 (1) (where -1 is possible only if -1 is a quadratic residue of n). Then ...

The Stammler circle is the circumcircle of the Stammler triangle. Unexpectedly, it has center at the circumcenter O (X_3) of the reference triangle and radius 2R (Ehrmann and ...

For a particular format in the IEEE 754-2008 framework, a subnormal number is a nonzero floating-point number with magnitude less than the magnitude of that formatÕs smallest ...

For a plane curve, the tangential angle phi is defined by rhodphi=ds, (1) where s is the arc length and rho is the radius of curvature. The tangential angle is therefore ...

An attractive compound of three regular tetrahedra can be obtained by taking three tetrahedra with a C_2 axes aligned along the z-axis and rotating them a sixth of a turn ...

Let f:R×R->R be a one-parameter family of C^2 maps satisfying f(0,mu)=0 (1) [(partialf)/(partialx)]_(mu=0,x=0)=0 (2) [(partial^2f)/(partialxpartialmu)]_(0,0)>0 (3) ...

The trigyrate rhombicosidodecahedron is a convex equilateral solid obtained by rotating three of the pentagonal cupolas of a small rhombicosidodecahedron by 1/10 of a turn ...

A trimagic cube is a magic cube that remains magic when all its numbers are both squared and cubed. Only two trimagic cubes are known. The first trimagic cube was found by C. ...

A characterization of normal spaces which states that a topological space X is normal iff, for any two nonempty closed disjoint subsets A, and B of X, there is a continuous ...