Journal for Geometry and Graphics 08 (2004), No. 1, 059--068
Copyright Heldermann Verlag 2004
The Manifold of Planes that Intersect Four Straight Lines in Points of a Circle
Hans-Peter Schroecker
Inst. of Discrete Mathematics and Geometry, University of Technology, Wiedner Hauptstr. 8-10/104, 1040 Wien, Austria
schroecker@dmg.tuwien.ac.at
Our topic is the manifold of planes that intersect four straight lines in three-dimensional euclidean space in points of a circle. The solution manifold is of class seven and contains 24 single lines, four double lines, a triple plane and four dual conics. We compute the solution manifold's equation, visualize it and discuss the special case of the four base lines being contained in a regulus.
Keywords: Circle in space, conic section in space.
MSC: 14N99; 51M04
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