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The number of real roots of an algebraic equation with real coefficients whose real roots are simple over an interval, the endpoints of which are not roots, is equal to the ...

Any linear combination of real spherical harmonics A_lP_l(costheta)+sum_(m=1)^l[A_l^mcos(mphi)+B_l^msin(mphi)]P_l^m(costheta) for l fixed whose sum is not premultiplied by a ...

The external (internal) similarity point of two fixed circles is the point at which all the circles homogeneously (nonhomogeneously) tangent to the fixed circles have the ...

Lachlan's term for a set of four lines, no three of which are concurrent.

Lachlan's term for a set of four points, no three of which are collinear.

A function which is not an algebraic function. In other words, a function which "transcends," i.e., cannot be expressed in terms of, algebra. Examples of transcendental ...

The triangle transformation principle gives rules for transforming equations involving an incircle to equations about excircles.

A tubular neighborhood of a submanifold N in M is an embedding of the normal bundle (nu_N) of N into M, i.e., f:nu_N->M, where the image of the zero section of the normal ...

Let a knot K be n-embeddable. Then its tunnel number is a knot invariant which is related to n.

The unlink, also called the trivial link, of n components consist of n disjoint circles in a plane (Rolfsen 1976, p. 65).