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If intersecting stable and unstable manifolds (separatrices) emanate from fixed points of different families, they are called heteroclinic points.

If R is a Noetherian ring, then S=R[X] is also a Noetherian ring.

A knot that secures a rope to a post, ring, another rope, etc., but does not keep its shape by itself.

The extremities of parallel radii of two circles are called homologous with respect to the similitude center collinear with them.

A linear transformation A:R^n->R^n is hyperbolic if none of its eigenvalues has modulus 1. This means that R^n can be written as a direct sum of two A-invariant subspaces E^s ...

The metric ds^2=(dx^2+dy^2)/((1-x^2-y^2)^2) for the Poincaré hyperbolic disk, which is a model for hyperbolic geometry. The hyperbolic metric is invariant under conformal ...

A catastrophe which can occur for three control factors and two behavior axes. The hyperbolic umbilic is the universal unfolding of the function germ f(x,y)=x^3+y^3. The ...

The hypocycloid x = a/(a-2b)[(a-b)cosphi-bcos((a-b)/bphi)] (1) y = a/(a-2b)[(a-b)sinphi+bsin((a-b)/bphi)] (2) has involute x = (a-2b)/a[(a-b)cosphi+bcos((a-b)/bphi)] (3) y = ...

When f:A->B is a ring homomorphism and b is an ideal in B, then f^(-1)(b) is an ideal in A, called the contraction of b and sometimes denoted b^c. The contraction of a prime ...

The incenter I is the center of the incircle for a polygon or insphere for a polyhedron (when they exist). The corresponding radius of the incircle or insphere is known as ...