The goal of this study was to characterise how third-grade primary school students understand the concept polygon as well relationships between polygons. Following a teaching experiment, answered questionnaire on recognition polygons and polygons, providing information about understood an example class. Dimensional deconstruction shapes (Duval, 2017) Statistical Implicative Analysis (Gras, Suzu...

[2] B. Bhattacharya and R. Benkoczi. On computing the optimal bridge between two convex polygons. [7] H. Edelsbrunner. Computing the extreme distances between two convex polygons. Linear-time algorithms for visibility and shortest path problems inside triangulated simple polygons.

Suppose there is a collection of n simple polygons in the plane, none of which overlap each other. The polygons are interlocked if no subset can be separated arbitrarily far from the rest. It is natural to ask the characterization of the subsets that makes the set of interlocked polygons free (not interlocked). This abstracts the essence of a kind of sliding block puzzle. We show that any monot...

We develop a valuation theory for generalized polygons similar to the existing theory for dense near polygons. This valuation theory has applications for the study and classification of generalized polygons that have full subpolygons as subgeometries.

We consider the problem of randomly generating simple polygons on a given set of points. This problem is of considerable importance in the practical evaluation of algorithms that operate on polygons, where it is necessary to check the correctness and to determine the actual CPU-consumption of an algorithm experimentally. We rst present an approach by O'Rourke and Virmani (1991). Next, we discus...

We present three diierent methods for nding solutions to the 2D translation-only containment problem: nd translations for k polygons that place them inside a given polygonal container without overlap. Both the container and the polygons to be placed in it may be nonconvex. First, we provide several exact algorithms that improve results for k = 2 or k = 3. In particular, we give an algorithm for...

Using results for the distribution of perimeters of random polygons arising from random lines in a plane, we obtain new analytic approximations to the distributions of areas and local line densities for random polygons and compute various limiting properties of random polygons. Using simulation, we show that the lengths of adjacent sides of polygons generated by random line processes in the pla...

A continuous nested sequence of similar triangles converging to the Brocard point of a given triangle is investigated. All these triangles have the same Brocard point. For polygons, the Brocard point need not exist, but there is always a limit object for an analogously defined nested sequence of inner polygons. This limit object is a Brocard point if and only if the inner polygons are all simil...

A continuous nested sequence of similar triangles converging to the Brocard point of a given triangle is investigated. All these triangles have the same Brocard point. For polygons, the Brocard point need not exist, but there is always a limit object for an analogously defined nested sequence of inner polygons. This limit object is a Brocard point if and only if the inner polygons are all simil...