A solution to some problems of Conway and Guy on monostable polyhedra

Lángi, Zsolt ✉ [Lángi, Zsolt (Geometria), szerző] MTA-BME Szilárd testek morfodinamikája Kutatócs... (BME / ÉPK / SZTT)

Angol nyelvű Szakcikk (Folyóiratcikk) Tudományos
  • SJR Scopus - Mathematics (miscellaneous): Q1
Azonosítók
A convex polyhedron is called monostable if it can rest in stable position only on one of its faces. The aim of this paper is to investigate three questions of Conway, regarding monostable polyhedra, which first appeared in a 1969 paper of Goldberg and Guy. In this note, we answer two of these problems and make a conjecture about 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 convex polyhedron with only one stable and one unstable point.
Hivatkozás stílusok: IEEEACMAPAChicagoHarvardCSLMásolásNyomtatás
2025-02-12 17:28