Hyperboloid . Surface created by rotating a hyperbola around one of its axes of symmetry. Rotation around the conjugate axis produces a hyperboloid of a leaf. Rotation around the transverse axis creates a two-bladed hyperboloid.
Summary
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- 1 Definition
- 1 Hyperboloid of a leaf
- 2 Two-leaf hyperboloid
- 2 Applications
- 3 Sources
Definition
The Hyperboloid is the surface of revolution generated by the rotation of a hyperbola about one of its two axes of symmetry. These surfaces are of two kinds: one and two sheets
Hyperboloid of a leaf
It is the surface that is generated by sliding an inclined segment on two horizontal circles and is expressed in a Cartesian coordinate system using the formula:
The parameters a, b, c are the semi-axes of the hyperboloid of a leaf. If we section the figure by planes parallel to the XOY, the sections are similar ellipses. The ellipse determined by the XOY plane is the smallest of all possible and is called a throat ellipse.
Two-leaf hyperboloid
It is the surface that in a Cartesian coordinate system is determined by the equation:
When the negative sign precedes any of the other two terms, the hyperboloid is on the coordinate axis it affects.
