Quadric Sections of Four-Dimensional Cones

  • Michal ZambojEmail author
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 809)


Graphic constructions of real three-dimensional quadrics as cuts of four-dimensional cones with three-dimensional spaces are described. All the constructions are presented on interactive models in GeoGebra 5 with use of descriptive geometry methods, which are based on a visualization technique of double orthogonal projection of the four-dimensional space onto two perpendicular three-dimensional spaces. We visualize a four-dimensional cone, its cutting 3-space and the section simultaneously in one figure. For detailed reasoning and verifications, the constructions are also supported analytically.


Four-dimensional geometry Quadric Conic sections Monge’s projection Descriptive geometry 



The work was supported by the grant SVV No. 260454. I also wish to thank Lukáš Krump (Charles University) for proof-reading, and the ICGG committee for suggesting valuable reference [1].


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Faculty of Mathematics and PhysicsCharles UniversityPrague 8Czech Republic

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