منابع مشابه
Conical Existence of Closed Curves on Convex Polyhedra
Let C be a simple, closed, directed curve on the surface of a convex polyhedron P. We identify several classes of curves C that “live on a cone,” in the sense that C and a neighborhood to one side may be isometrically embedded on the surface of a cone Λ, with the apex a of Λ enclosed inside (the image of) C; we also prove that each point of C is “visible to” a. In particular, we obtain that the...
متن کاملOn Algebraic Curves over Real Closed Fields. I
In this paper we are concerned with the absolute theory of a smooth irreducible complete algebraic curve X defined over a real closed field K. Our theory is purely algebraic. It may be of interest even in the case that K is the field R of real numbers, since as far as I know there does not exist a purely algebraic theory of curves over R in the literature. Let F denote the field K(X) of rationa...
متن کاملSource Unfoldings of Convex Polyhedra via Certain Closed Curves
We extend the notion of a source unfolding of a convex polyhedron P to be based on a closed polygonal curve Q in a particular class rather than based on a point. The class requires that Q “lives on a cone” to both sides; it includes simple, closed quasigeodesics. Cutting a particular subset of the cut locus of Q (in P) leads to a non-overlapping unfolding of the polyhedron. This gives a new gen...
متن کاملConvex drawings of intersecting families of simple closed curves
A FISC or family of intersecting simple closed curves is a collection of simple closed curves in the plane with the properties that there is some open region common to the interiors of all the curves, and that every two curves intersect in nitely many points. Let F be a FISC. Intersections of the curves represent the vertices of a plane graph, G(F), whose edges are the curve arcs between vertic...
متن کاملSome Geometric Properties of Closed Space Curves and Convex Bodies
The main results of the paper are as follows. 1. On each smooth closed oriented curve in Rn, there exist two points the oriented tangents at which form an angle greater than π/2 + sin−1 1 n−1 . 2. If n is odd, then an (n+1)-gon with equal sides and lying in a hyperplane can be inscribed in each smooth closed Jordan curve in Rn. In particular, a rhombus can be inscribed in each closed curve in R...
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ژورنال
عنوان ژورنال: Časopis pro pěstování matematiky a fysiky
سال: 1920
ISSN: 1802-114X
DOI: 10.21136/cpmf.1920.121749