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The Lyons group is the sporadic group Ly of order |Ly| = 51765179004000000 (1) = 2^8·3^7·5^6·7·11·31·37·67. (2) It is implemented in the Wolfram Language as LyonsGroupLy[].

The Maclaurin-Bézout theorem says that two curves of degree n intersect in n^2 points, so two cubics intersect in nine points. This means that n(n+3)/2 points do not always ...

The nth-order Menger sponge graph is the connectivity graph of cubes in the nth iteration of the Menger sponge fractal. The first two iterations are shown above. The n-Menger ...

A set-like object in which order is ignored, but multiplicity is explicitly significant. Therefore, multisets {1,2,3} and {2,1,3} are equivalent, but {1,1,2,3} and {1,2,3} ...

A nonuniform rational B-spline curve defined by C(t)=(sum_(i=0)^(n)N_(i,p)(t)w_iP_i)/(sum_(i=0)^(n)N_(i,p)(t)w_i), where p is the order, N_(i,p) are the B-spline basis ...

The O'Nan group is the sporadic group O'N of order |O'N| = 460815505920 (1) = 2^9·3^4·5·7^3·11·19·31. (2) It is implemented in the Wolfram Language as ONanGroupON[].

Let (A,<=) and (B,<=) be well ordered sets with ordinal numbers alpha and beta. Then alpha<beta iff A is order isomorphic to an initial segment of B (Dauben 1990, p. 199). ...

For a system of n first-order ordinary differential equations (or more generally, Pfaffian forms), the 2n-dimensional space consisting of the possible values of ...

The derivative identity d/(dx)[f(x)g(x)] = lim_(h->0)(f(x+h)g(x+h)-f(x)g(x))/h (1) = (2) = lim_(h->0)[f(x+h)(g(x+h)-g(x))/h+g(x)(f(x+h)-f(x))/h] (3) = f(x)g^'(x)+g(x)f^'(x), ...

A diagram used in the solution of ordinary differential equations of the form (dw)/(dz)=(g(z,w))/(h(z,q)) which vanish when z=0, where g(0,0)=h(0,0)=0 (Ince 1956, pp. 298 and ...