12 Facts About Hyperbolic paraboloid

In geometry, a Hyperbolic paraboloid is a quadric surface that has exactly one axis of symmetry and no center of symmetry.

The term "Hyperbolic paraboloid" is derived from parabola, which refers to a conic section that has a similar property of symmetry.

Every plane section of a Hyperbolic paraboloid by a plane parallel to the axis of symmetry is a parabola.

The paraboloid is hyperbolic if every other plane section is either a hyperbola, or two crossing lines .

The Hyperbolic paraboloid is elliptic if every other nonempty plane section is either an ellipse, or a single point .

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The paraboloid is hyperbolic if the factors are real; elliptic if the factors are complex conjugate.

An elliptic Hyperbolic paraboloid is shaped like an oval cup and has a maximum or minimum point when its axis is vertical.

Hyperbolic paraboloid is a doubly ruled surface shaped like a saddle.

Any paraboloid is a translation surface, as it can be generated by a moving parabola directed by a second parabola.

Therefore, the shape of a circular Hyperbolic paraboloid is widely used in astronomy for parabolic reflectors and parabolic antennas.

Hyperbolic paraboloid is a doubly ruled surface: it contains two families of mutually skew lines.

Hyperbolic paraboloid is a saddle surface, as its Gauss curvature is negative at every point.