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A ruled surface M is a tangent developable of a curve y if M can be parameterized by x(u,v)=y(u)+vy^'(u). A tangent developable is a developable surface.

Let M be a regular surface with v_(p),w_(p) points in the tangent space M_(p) of M. Then the third fundamental form is given by III(v_(p),w_(p))=S(v_(p))·S(w_(p)), where S is ...

An oriented surface for which every point belongs to a Wiedersehen pair. Proof of the Blaschke conjecture established that the only Wiedersehen surfaces are the standard ...

The confluent hypergeometric function of the second kind gives the second linearly independent solution to the confluent hypergeometric differential equation. It is also ...

Attach a string to a point on a curve. Extend the string so that it is tangent to the curve at the point of attachment. Then wind the string up, keeping it always taut. The ...

The modified bessel function of the second kind is the function K_n(x) which is one of the solutions to the modified Bessel differential equation. The modified Bessel ...

The normal vector, often simply called the "normal," to a surface is a vector which is perpendicular to the surface at a given point. When normals are considered on closed ...

A primitive polynomial is a polynomial that generates all elements of an extension field from a base field. Primitive polynomials are also irreducible polynomials. For any ...

The problem of finding the curve down which a bead placed anywhere will fall to the bottom in the same amount of time. The solution is a cycloid, a fact first discovered and ...

A modified set of Chebyshev polynomials defined by a slightly different generating function. They arise in the development of four-dimensional spherical harmonics in angular ...