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A zonal harmonic is a spherical harmonic of the form P_l(costheta), i.e., one which reduces to a Legendre polynomial (Whittaker and Watson 1990, p. 302). These harmonics are ...

The chromatic invariant theta(G) of a connected graph G is the number of spanning trees of G that have internal activity 1 and external activity 0. For graphs other than the ...

A die (plural "dice") is a solid with markings on each of its faces. The faces are usually all the same shape, making Platonic solids and Archimedean duals the obvious ...

There are many formulas of pi of many types. Among others, these include series, products, geometric constructions, limits, special values, and pi iterations. pi is ...

Two fractions are said to be adjacent if their difference has a unit numerator. For example, 1/3 and 1/4 are adjacent since 1/3-1/4=1/12, but 1/2 and 1/5 are not since ...

A fundamental result of de Rham cohomology is that the kth de Rham cohomology vector space of a manifold M is canonically isomorphic to the Alexander-Spanier cohomology ...

An impossible hexnut modeled after the impossible torus. The figure above shows three impossible figures: the ambihelical hexnut in the lower left-hand corner, tribox in the ...

The point of concurrence of the four maltitudes of a cyclic quadrilateral. Let M_(AC) and M_(BD) be the midpoints of the diagonals of a cyclic quadrilateral ABCD, and let P ...

The area element for a surface with first fundamental form ds^2=Edu^2+2Fdudv+Gdv^2 is dA=sqrt(EG-F^2)du ^ dv, where du ^ dv is the wedge product.

A flow defined analogously to the axiom A diffeomorphism, except that instead of splitting the tangent bundle into two invariant sub-bundles, they are split into three (one ...