Journal for Geometry and Graphics 29 (2025), No. 1, 033--042
Copyright by the authors licensed under CC BY SA 4.0
Center of the Ellipse at the Base of a Cone with a Constant Base Area
Yasuo Minami
College of Industrial Technology, Nihon University, Narashino, Japan
minami.yasuo@nihon-u.ac.jp
The locus of the center of the top surface in an inverted cone was considered geometrically when the cone was tilted. When the area of the ellipse on the top surface of the volume is constant, the locus of the center of the top surface is found to be part of an ellipsoid. The locus of the center of the ellipse is also shown for the case where the volume between the top surface and the cone is held constant and the length of the major axis of the top surface of the volume is constant. Here, the behavior of the center of the top surface of a right circular cone cut in a plane is applicable to describe the motion of conduction electrons in single-layer graphene, which is being tremendously studied recently in the field of physics, since the behavior of conduction electrons in single-layer graphene is described by a right circular cone (Dirac cone).
Keywords: ellipsoid cone, elliptic cone, center of ellipse.
MSC: 51N30; 51M25, 51M10.
[ Fulltext-pdf (443 KB)]