
Journal for Geometry and Graphics 08 (2004), No. 1, 059068 Copyright Heldermann Verlag 2004 The Manifold of Planes that Intersect Four Straight Lines in Points of a Circle HansPeter Schroecker Inst. of Discrete Mathematics and Geometry, University of Technology, Wiedner Hauptstr. 810/104, 1040 Wien, Austria schroecker@dmg.tuwien.ac.at Our topic is the manifold of planes that intersect four straight lines in threedimensional 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 [ Fulltextpdf (318 KB)] for subscribers only. 