Equidissections of polygons
نویسندگان
چکیده
منابع مشابه
Constructing equidissections for certain classes of trapezoids
We investigate equidissections of a trapezoid T (a), where the ratio of the lengths of two parallel sides is a. (An equidissection is a dissection into triangles of equal areas.) An integer n is in the spectrum S T (a) if T (a) admits an equidissection into n triangles. Suppose a is algebraic of degree 2 or 3, with each conjugate over Q having positive real part. We show that if n is large enou...
متن کاملArithmetic of 3−valent graphs and equidissections of flat surfaces
Our main object of study is a 3−valent graph with a vector function on its edges. The function assignes to an edge a pair of 2−adic integer numbers and satisfies additional condition: the sum of its values on three edges, terminating in the same vertex, is equal to 0. For each vertex of the graph three vectors corresponding to these edges generate a lattice over the ring of 2−adic integers. In ...
متن کاملConvexity of Sub-polygons of Convex Polygons
A convex polygon is defined as a sequence (V0, . . . , Vn−1) of points on a plane such that the union of the edges [V0, V1], . . . , [Vn−2, Vn−1], [Vn−1, V0] coincides with the boundary of the convex hull of the set of vertices {V0, . . . , Vn−1}. It is proved that all sub-polygons of any convex polygon with distinct vertices are convex. It is also proved that, if all sub-(n − 1)-gons of an n-g...
متن کاملDissections of Polygons into Convex Polygons
In the paper we present purely combinatorial conditions that allow us to recognize the topological equivalence (or non-equivalence) of two given dissections. Using a computer program based on this result, we are able to generate a set which contains all topologically non-equivalent dissections of a p0-gon into convex pi-gons, i = 1, ..., n, where n, p0, ..., pn are integers such that n ≥ 2, pi ...
متن کاملGuarding Fat Polygons and Triangulating Guarded Polygons
In this paper we study three related problems: (i) Given a fat polygon P , we show how to find a set G of points in P such that every point on the boundary of P sees at least one point of G. The set G is said to guard the boundary of P and its cardinality depends on the shape parameters of P . Fat polygons are often used to model more realistic inputs. (ii) Given k points that guard the boundar...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1990
ISSN: 0012-365X
DOI: 10.1016/0012-365x(90)90384-t