منابع مشابه
Euler's Polyhedron Formula
where V , E, and F are, respectively, the number of vertices, edges, and faces of p. The formula was first stated in print by Euler in 1758 [11]. The proof given here is based on Poincaré’s linear algebraic proof, stated in [17] (with a corrected proof in [18]), as adapted by Imre Lakatos in the latter’s Proofs and Refutations [15]. As is well known, Euler’s formula is not true for all polyhedr...
متن کاملA Formal Proof of Euler’s Polyhedron Formula
Euler’s polyhedron formula asserts for a polyhedron p that
متن کاملCharacterization of polyhedron monotonicity
The notion of polygon monotonicity has been well researched to be used as an important property for various geometric problems. This notion can be more extended for categorizing the boundary shapes of polyhedrons, but it has not been explored enough yet. This paper characterizes three types of polyhedron monotonicity: strong-, weak-, and directional-monotonicity: (Toussaint, 1985). We reexamine...
متن کاملThe Polyhedron-Hitting Problem
We consider polyhedral versions of Kannan and Lipton's Orbit Problem [14, 13] determining whether a target polyhedron V may be reached from a starting point x under repeated applications of a linear transformation A in an ambient vector space Q. In the context of program veri cation, very similar reachability questions were also considered and left open by Lee and Yannakakis in [15], and by Bra...
متن کاملOn the cut polyhedron
The cut polyhedron cut(G) of an undirected graph G = (V,E) is the dominant of the convex hull of all its nonempty edge cutsets. After examining various compact extended formulations for cut(G), we study some of its polyhedral properties. In particular, we characterize all the facets induced by inequalities with right-hand side at most 2. These include all the rank facets of the polyhedron.
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ژورنال
عنوان ژورنال: Formalized Mathematics
سال: 2008
ISSN: 1898-9934,1426-2630
DOI: 10.2478/v10037-008-0002-6