Elliptic paraboloids

Categories

• Curves
  • Types of curves on surfaces
    • Lines of curvature

• Surfaces
  • Quadrics (surfaces of order two)
    • Classification of surfaces of 2nd order

Description

Elliptic paraboloid is a 2nd order surface given in the standard Cartesian coordinates by the eqaution

$\frac{x^2}{a^2} + \frac{y^2}{b^2} = z$,

where for the models $a \neq b$. The models should be viewed upside-down.

One of the models shows behaviour of lines of curvature on the surface. In particular, this is everywhere regular orthogonal net.

Another model shows the cross-sections with planes parallel to $z=0$. These sections are ellipses.

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