Circular hyperboloid of one sheet


Obtained by rotating a hyperbola around its conjugate (minor) axis,

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by rotating one line around another line when these lines are skew.

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This hyperboloid is doubly ruled surface - has two systems of ruling.

  • Through each point passes one ruling from each system.

  • All rulings in one system are skew lines.

  • Each ruling from one system intersects all rulings from the other system.

  • On the smallest circle of the hyperboloid lie the vertices of cross-section hyperbolas(intersections with planes that contain the axis).

  • Smallest circle contains those points of the rulings that are closest to the axis.

  • Orthogonal projections of the rulings to the plane of the smallest circle (or a plane parallel to that plane) are tangents of the smallest circle.

  • Tangent planes in the points on the smallest circle are parallel to the axis.

    Asymptotic cone of one-sheeted hyperboloid

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    Created by Sonja Gorjanc, translated by Helena Halas and Iva Kodrnja - 3DGeomTeh - Developing project of the University of Zagreb