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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 Brocard circle, also known as the seven-point circle, is the circle having the line segment connecting the circumcenter O and symmedian point K of a triangle DeltaABC as ...

A cubic curve invented by Diocles in about 180 BC in connection with his attempt to duplicate the cube by geometrical methods. The name "cissoid" first appears in the work of ...

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

The (circular) helicoid is the minimal surface having a (circular) helix as its boundary. It is the only ruled minimal surface other than the plane (Catalan 1842, do Carmo ...

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 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 ...

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 ...