We consider the following geometric optimization problem: find a maximum-area rectangle and a maximum-perimeter rectangle contained in a given convex polygon with n vertices. We give exact algorithms that solve these problems in time O(n). We also give (1 − ε)-approximation algorithms that take time O(ε−3/2 + ε−1/2 log n) for maximizing the area and O(ε−3 + ε−1 log n) for maximizing the perimeter.

The maximal area of a polygon with n = 2m edges and unit diameter is not known when m ≥ 5, nor is the maximal perimeter of a convex polygon with n = 2m edges and unit diameter known when m ≥ 4. We construct improved polygons in both problems, and show that the values we obtain cannot be improved for large n by more than c1/n in the area problem and c2/n in the perimeter problem, for certain con...

The objective of the present study was to assess the effect of diabetes on buccal mucosa by using cytomorphometry and to emphasize its relevance as an additional tool to aid in the evaluation of oral mucosal changes in diabetes mellitus. The study Group consisted of 100 subjects divided into 50 control subjects (Group C) and 50 Type II diabetic subjects (Group D). We analyzed and compared betwe...

Raw cane sugar is one of the most important product in the sugar industry and is the main raw material for the white sugar production. Morphological and physical properties of this product might influence the final white sugar. For instance, the behavior during centrifugation, transport and storage is related to the characteristics of these crystals. The object of this study was to determine th...

Given n points in the plane, we study three optimization problems of computing an empty pseudo-triangle: we consider minimizing the perimeter, maximizing the area, and minimizing the longest maximal concave chain. We consider two versions of the problem: First, we assume that the three convex vertices of the pseudotriangle are given. Let n denote the number of points that lie inside the convex ...

The relationship between numbers and other magnitudes has been extensively investigated in the scientific literature. Here, the objectives were to examine whether two continuous magnitudes, area and perimeter, are automatically processed and whether adults with developmental dyscalculia (DD) are deficient in their ability to automatically process one or both of these magnitudes. Fifty-seven stu...

Previous studies have suggested that the timing of puberty might have an impact on the adult skeleton. What composite of bone structure could be affected by the timing of puberty is unknown at present. In this study, we evaluated the relationship between age at menarche and bone cortex geometry at the distal radius. Using peripheral quantitative computed tomography, we determined total area of ...

Given a set of points in 2 or 3 dimensions, the problem of computing a geometric structure enclosing the point set while optimizing some criteria of the enclosing structure such as area, perimeter, surface area or volume has been widely studied in the literature [1, 2, 9, 7, 11, 16, 3, 5, 4, 6, 17, 14, 18]. In this paper, we are particularly interested in the 2 dimensional setting where the enc...