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A ruled surface M is a normal developable of a curve y if M can be parameterized by x(u,v)=y(u)+vN^^(u), where N is the normal vector (Gray 1993, pp. 352-354; first edition ...

A quadric is a quadratic surface. A surface of the form (x^2)/(a^2+theta)+(y^2)/(b^2+theta)+(z^2)/(c^2+theta)=1 is also called a quadric, and theta is said to be the ...

The period for a quasiperiodic trajectory to pass through the same point in a surface of section. If the rotation number is irrational, the trajectory will densely fill out a ...

One of the straight lines sweeping out a ruled surface. The rulings on a ruled surface are asymptotic curves.

The tritangent of a cubic surface is a plane which intersects the surface in three mutually intersecting lines. Each intersection of two lines is then a tangent point of the ...

Complex Analysis

There are nine possible types of isolated singularities on a cubic surface, eight of them rational double points. Each type of isolated singularity has an associated normal ...

The 27 real or imaginary lines which lie on the general cubic surface and the 45 triple tangent planes to the surface. All are related to the 28 bitangents of the general ...

The volume of a solid body is the amount of "space" it occupies. Volume has units of length cubed (i.e., cm^3, m^3, in^3, etc.) For example, the volume of a box (cuboid) of ...

This theorem states that, for a partial differential equation involving a time derivative of order n, the solution is uniquely determined if time derivatives up to order n-1 ...