If E is any ellipse inscribed in a convex quadrilateral, D – , then we prove that Area (E) Area(D – ) π 4 , and equality holds if and only if D – is a parallelogram and E is tangent to the sides of D – at the midpoints. We also prove that the foci of the unique ellipse of maximal area inscribed in a parallelogram, D – , lie on the orthogonal least squares line for the vertices of D – . This doe...

We show that any convex region which contains a unit segment, an equilateral triangle of sides 1 2 , and a square of side 1 3 always has area at least 0.227498. Using grid-search algorithm, we attempt to find a configuration of these three objects with minimal convex hull area. Consequently, we improve a lower bound for Moser’s worm problem from 0.2194 to 0.227498.

For any convex n-gon P we consider the polygons obtained dropping a vertex or an edge of P . The area distance of P to such (n − 1)-gons, divided by the area of P , is an affinely invariant functional on n-gons whose maximizers coincide with the affinely regular polygons. We provide a complete proof of this result. We extend these area functionals to planar convex bodies and we present connecti...

\ due. Several existing algorithms are available for solving the convex problem (6). We refer to a recent paper by Boyd and Yang [4. Sect. ;] discussing the details, including the advantages and disadvantages, of [hese numerical algorithms. AS a result. if W(a) is convex (which is alwavs the case when m < 3; see [51, for example), cl (~)(=c( (a)) could be computed with any of these algorithms. ...

In a convex grid drawing of a plane graph, every edge is drawn as a straight-line segment without any edge-intersection, every vertex is located at a grid point, and every facial cycle is drawn as a convex polygon. A plane graph G has a convex drawing if and only if G is internally triconnected. It has been known that an internally triconnected plane graph G of n vertices has a convex grid draw...

In this paper,  fuzzy convergence theory in the framework of $L$-convex spaces is introduced. Firstly, the concept of $L$-convex remote-neighborhood spaces is introduced and it is shown that the  resulting category is isomorphic to that of $L$-convex spaces. Secondly, by means of $L$-convex ideals, the notion of $L$-convergence spaces is introduced and it is proved that the  category of $L$-con...

Low efficiency of interference calculation has become the bottleneck that restricts further development of the performance of evolutionary algorithm for the polygon layout. To solve the problem, in this paper, we propose an algorithm of calculating overlapping area between two irregular polygons. For this algorithm, at first, two irregular polygons are respectively decomposed into the minimum n...

in this paper, the concept of fuzzy convex subgroup (resp. fuzzy convex lattice-ordered subgroup) of an ordered group (resp. lattice-ordered group) is introduced and some properties, characterizations and related results are given. also, the fuzzy convex subgroup (resp. fuzzy convex lattice-ordered subgroup) generated by a fuzzy subgroup (resp. fuzzy subsemigroup) is characterized. furthermore,...

Abstract. The area distance to a convex plane curve is an important concept in computer vision. In this paper we describe a strong link between area distances and improper affine spheres. This link makes possible a better understanding of both theories. The concepts of the theory of affine spheres lead to a new definition of an area distance on the outer part of a convex plane arc. Also, based ...