What Is a Paraboloid?

A paraboloid is a surface obtained by rotating a parabola 180 °. A mathematical parabola is a set of points on the same plane whose distance from a fixed point (focus) is equal to the distance from a fixed line (quasi-line).

Parabolic is quadratic

In the headlights,

When a = b , the surface is called a rotating parabola , which can be defined by

The parametric equation of an elliptic paraboloid is:

Gaussian curvature:

The average curvature is:

They are all positive numbers, the largest at the vertex, the smaller the distance from the vertex, and the closer to zero.

The parabolic equation of the hyperbolic paraboloid is:

Gaussian curvature:

The average curvature is: