Elliptic cones

Categories

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

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

Description

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

$\frac{x^2}{a^2} + \frac{y^2}{b^2} - \frac{z^2}{c^2} = 0$,

where for the models $a \neq b$. Such surfaces have two pieces intersecting in $(0,0,0)$. The model show only one piece

One of the models shows behaviour of lines of curvature on the surface. In particular, it is regular orthogonal net everywhere except the vertex. One family from the net goes along straight rulings of the cone.

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