Lines on a Cubic Surface

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The level sets of the cubic polynomial . When , the surface contains six affine lines. When , the surface contains 24 affine lines. For each line, one coordinate is constant, so the lines can be grouped into three sets of eight (shown in different colors) depending upon which coordinate plane the lines are parallel to.

Contributed by: Ryan Hoban (The Experimental Geometry Lab at the University of Maryland) (March 2011)
Based on work by: William Goldman
Open content licensed under CC BY-NC-SA


Snapshots


Details

Snapshot 1: , surface contains no affine lines

Snapshot 2: , surface contains six affine lines

Snapshot 3: , surface contains 24 affine lines

Snapshot 4: , the surface contains 24 affine lines. There are four Eckardt points where three of these lines simultaneously intersect.



Permanent Citation

Ryan Hoban (The Experimental Geometry Lab at the University of Maryland) "Lines on a Cubic Surface"
http://demonstrations.wolfram.com/LinesOnACubicSurface/
Wolfram Demonstrations Project
Published: March 7 2011

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