Confocal Quadrics

Boris Odehnal (), Hellmuth Stachel () and Georg Glaeser ()
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Boris Odehnal: University of Applied Arts Vienna, Department of Geometry
Hellmuth Stachel: Vienna University of Technology, Institute of Discrete Mathematics and Geometry
Georg Glaeser: University of Applied Arts Vienna, Department of Geometry

Chapter Chapter 7 in The Universe of Quadrics, 2020, pp 279-325 from Springer

Abstract: Abstract The picture shows an elliptic paraboloid with its curvature lines. These lines are the curves of intersection with confocal elliptic and hyperbolic paraboloids, and therefore, in general of degree four. Families of quadrics which intersect the planes of symmetry along confocal conics are called confocal. They belong to a range, i.e., a dual pencil. It is interesting to see that confocal quadrics are connected with various geometric problems, and often the famous theorem of Ivory plays a central role.

Date: 2020
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DOI: 10.1007/978-3-662-61053-4_7

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