Given a set S of n > 2 points in the plane (in general position), we show how to compute in O(n) time, a triangle T with maximum (or minimum) area enclosing S among all enclosing triangles with fixed perimeter P and one fixed angle ω. We show that a similar approach can be used to compute a triangle T with maximum (or minimum) perimeter enclosing S among all enclosing triangles with fixed area ...

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...

In this paper, we examine the tilings of a 2 × n “triangular strip” with triangles. These tilings have connections with Fibonacci numbers, Pell numbers, and other known sequences. We will derive several different recurrences, establish some properties of these numbers, and give a refined count for these tilings (i.e., by the number and type of triangles used) and establish several properties of...

An N-tiling of triangle ABC by triangle T is a way of writing ABC as a union of N triangles congruent to T , overlapping only at their boundaries. The triangle T is the “tile”. The tile may or may not be similar to ABC. This paper is the first of four papers, which together seek a complete characterization of the triples (ABC,N, T ) such that ABC can be N-tiled by T . In this paper, we consider...

In this paper we discuss a new algorithm that for any input quality constrained Delaunay triangulation with minimum interior angle greater than or equal to 30 , produces a quality nonobtuse boundary and/or interface Delaunay triangulation by the Delaunay insertion of a nite number of boundary and/or interface points. A boundary (interface) obtuse triangle is a triangle that has an obtuse angle ...