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A root of a polynomial P(z) is a number z_i such that P(z_i)=0. The fundamental theorem of algebra states that a polynomial P(z) of degree n has n roots, some of which may be ...

The delta function is a generalized function that can be defined as the limit of a class of delta sequences. The delta function is sometimes called "Dirac's delta function" ...

A surface of revolution is a surface generated by rotating a two-dimensional curve about an axis. The resulting surface therefore always has azimuthal symmetry. Examples of ...

When a measure lambda is absolutely continuous with respect to a positive measure mu, then it can be written as lambda(E)=int_Efdmu. By analogy with the first fundamental ...

A (finite, circular) conical surface is a ruled surface created by fixing one end of a line segment at a point (known as the vertex or apex of the cone) and sweeping the ...

A hyperboloid is a quadratic surface which may be one- or two-sheeted. The one-sheeted hyperboloid is a surface of revolution obtained by rotating a hyperbola about the ...

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.

For a curve with first fundamental form ds^2=Edu^2+2Fdudv+Gdv^2, (1) the Gaussian curvature is K=(M_1-M_2)/((EG-F^2)^2), (2) where M_1 = |-1/2E_(vv)+F_(uv)-1/2G_(uu) 1/2E_u ...

Also known as the first fundamental form, ds^2=g_(ab)dx^adx^b. In the principal axis frame for three dimensions, ds^2=g_(11)(dx^1)^2+g_(22)(dx^2)^2+g_(33)(dx^3)^2. At ...

An elliptic function with no poles in a fundamental cell is a constant.