DOI: 10.68381/jca18032 ISSN: 0944-6532
Only Solid Spheres Admit a False Axis of Revolution
Jesús Jerónimo-Castro, Luis Montejano, Efrén Morales-Amaya
Let
K\subset \mathbb{R}^{3}
K
⊂
R
3
be a convex body. A point
p_{0}
p
0
is a point of revolution for
K
K
if every section of
K
K
through
p_{0}
p
0
has an axis of symmetry that passes through
p_{0}
p
0
. In particular, every point that lies in an axis of revolution is a point of revolution. A line
L\subset \mathbb{R}^3
L
⊂
R
3
is a false axis of revolution, if every point of
L
L
is a point of revolution for
K
K
but
L
L
is not an axis of revolution. The purpose of this paper is to prove that only solid spheres admit a false axis of revolution