Showing papers on "Regular polygon published in 1978"
TL;DR: This paper derives a clipping algorithm and discusses both two- and three-dimensional implementations of the algorithm which finds the proper intersection of a line with any convex planar, polygon or spacial polyhedron.
142 citations
TL;DR: A method is presented for decomposing polygons into convex sets based upon a Delaunay tessellation of the polygon and implemented as a divide-and-conquer technique.
Abstract: A method is presented for decomposing polygons into convex sets. The method is based upon a Delaunay tessellation of the polygon. It is implemented as a divide-and-conquer technique.
89 citations
TL;DR: It is shown that this is a serious problem in the sense that these complications will occur for most population densities and a simple apportionment method is suggested.
Abstract: (1978). Convex Polygons That Cannot Tile the Plane. The American Mathematical Monthly: Vol. 85, No. 10, pp. 785-792.
25 citations
13 citations
01 Jan 1978
TL;DR: In this paper, Herz and Kaapke used Besicovitch's results to solve the problem of maximizing the ratio of area A to perimeter P of a convex polygonal set S for the case S is a triangle.
Abstract: Of all sets lying within a given convex plane set S, which one gives the greatest ratio of area A to perimeter P? This was posed to one of us by E. Bombieri for the case when S is a square. He asserted that T. Bang used an easy upper bound on A/P in an elementary proof of the Prime Number Theorem. After solving this problem from scratch, we learned from M. Silver that Besicovitch (1) had solved a closely related problem, which we call Besicovitch's problem and which will be discussed shortly. Later, we found that the problem of maximizing A/P had occurred to Garvin (4, 5) and that he solved the problem when S is a triangle. Garvin inspired DeMar (2) to consider and solve Besicovitch's problem for the triangle and for polygons. DeMar found that Steiner (8, p. 166) had solved Besicovitch's problem for triangles, but Steiner was only interested in subsets which touched all sides of a polygon (8, p. 168). More recently, J. Wills has referred us to Herz and Kaapke (6) who use Besicovitch's results to solve our problem of maximizing A/P for polygons circumscribed about a circle.
12 citations
6 citations
01 Sep 1978
TL;DR: A procedure is given for computing the bivariate normal probability over an angular region or a convex polygon which is implemented into a Fortran IV computer program designed to yield 3,6, or 9 decimal digits of accuracy.
Abstract: : A procedure is given for computing the bivariate normal probability over an angular region or a convex polygon. The procedure is implemented into a Fortran IV computer program which is designed to yield 3,6, or 9 decimal digits of accuracy. Comparisons with two other published methods, for the same achievable accuracy, show our program to be much faster.
4 citations
TL;DR: In this article, how to construct a regular polygon is described. But it is not a regular polygons construction, it is a regular linear polygon construction, and it is difficult to construct.
Abstract: (1978). How to Construct a Regular Polygon. The American Mathematical Monthly: Vol. 85, No. 3, pp. 186-188.
2 citations
TL;DR: In this article, it was shown that convex polyhedra in R3, each face of which is equiangular or composed of such, constitute four infinite series (prism, antiprism, and two types of truncated antiprisms); outside of this series, there are only a finite number of types.
Abstract: Depending on the type, considering only the topological structure of the network of faces, and the angles of corresponding faces at corresponding vertices, convex polyhedra in R3, each face of which is equiangular or composed of such, constitute four infinite series (prism, antiprism, and two types of truncated antiprisms); outside of this series, there are only a finite number of types.
TL;DR: In case S is simply connected, then S is a union of σ ( m ) or fewer convex sets, where σ(m) = [(m − N )(m − 3 2 ) + 3 2 ] .