Lángi, Zsolt (2020) A solution to some problems of Conway and Guy on monostable polyhedra. BULLETIN OF THE LONDON MATHEMATICAL SOCIETY. ISSN 0024-6093 (In Press)
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Abstract
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.
| Item Type: | Article |
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| Subjects: | Q Science / természettudomány > QA Mathematics / matematika > QA73 Geometry / geometria |
| Depositing User: | Dr. Zsolt Lángi |
| Date Deposited: | 19 Sep 2021 12:59 |
| Last Modified: | 03 Apr 2023 07:21 |
| URI: | http://real.mtak.hu/id/eprint/129753 |
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