Description
BME Geometria Tanszék virtuális szemináriuma
Absztrakt:
A convex polyhedron is called monostable if it can rest in stable
position only on one of its faces. In this talk we investigate
three questions of Conway, regarding monostable polyhedra, from the open
problem book of Croft, Falconer and Guy (Unsolved Problems in Geometry,
Springer, New York, 1991), which first appeared in the literature in
a 1969 paper.
In this note we answer two of these problems and conjecture
an answer for the third one. The main tool of our proof is a general
theorem describing
approximations of smooth convex bodies by convex polyhedra in terms of their
static equilibrium points. As another application of this theorem, we prove the
existence of a `polyhedral Gomboc', that is, a convex polyhedron with only one
stable and one unstable point.