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Let R be a ring. If phi:R->S is a ring homomorphism, then Ker(phi) is an ideal of R, phi(R) is a subring of S, and R/Ker(phi)=phi(R).

A fork of a tree T is a node of T which is the endpoint of two or more branches.

For any real alpha and beta such that beta>alpha, let p(alpha)!=0 and p(beta)!=0 be real polynomials of degree n, and v(x) denote the number of sign changes in the sequence ...

A closed curve associated with a knot which is displaced along the normal by a small amount. For a knot K parameterized as x^mu(s) for 0<=s<=L along the length of the knot by ...

If f^'(x) is continuous and the integral converges, int_0^infty(f(ax)-f(bx))/xdx=[f(0)-f(infty)]ln(b/a).

A non-Euclidean space with constant negative Gaussian curvature.

A triangle formed by the arcs of three geodesics on a smooth surface.

If the abstract simplicial complex S is isomorphic with the vertex scheme of the simplicial complex K, then K is said to be a geometric realization of S, and is uniquely ...

The dual of the great truncated cuboctahedron U_(20) and Wenninger dual W_(93).

The dual of the great stellated truncated dodecahedron U_(66) and Wenninger dual W_(104).