Abstract
In this paper metric properties of central quadrics and cones in n-dimensional Euclidean space are discussed. Basic statements on the system of confocal regular quadrics are proved, and some interesting analogues of famous three-dimensional theorems are given for higher dimension, such as the Apollonian theorem on pedal curves. We also investigate systems of focal cones, and in particular we determine the common lines of focal cones in any dimension. As further applications of our approach and of our formulas we give a detailed description of the construction of Chasles on conjugate diameters, and the wire model of Staude is also given.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
