A generalized triangle group is a group that can be presented in the form G = 〈 x, y | x = y = w(x, y) = 1 〉 where p, q, r ≥ 2 and w(x, y) is an element of the free product 〈 x, y | x = y = 1 〉 involving both x and y. Rosenberger has conjectured that every generalized triangle group G satisfies the Tits alternative. It is known that the conjecture holds except possibly when the triple (p, q, r)...

(a) The medians intersect in a point interior to the triangle, called the centroid, which divides each of the medians in the ratio 2 : 1. (b) The medians form a new triangle, called the median triangle. (c) The area of the median triangle is 3/4 of the area of the given triangle in which the medians were constructed. (d) The median triangle of the median triangle is similar to the given triangl...

A new algorithm for mesh simplification with triangle constriction is presented in this paper. Constricting error defined by a combination of square volume error variation with constraint (SVEC), shape factor and normal constraint factor of triangle. Gauss curvature factor of each constricted triangle is used to distinguish strong feature triangle or nonstrong feature triangle. The triangle whi...

This paper presents a method, along with some optimizations, for computing whether or not two triangles intersect. The code, which is shown to be fast, can be used in, for example, collision detection algorithms.

We show that for percolation on any transitive graph, the triangle condition implies the open triangle condition.

The breeding biology of the Black Oystercatcher (Haemotopus bachmani) was studied on Triangle Island, British Columbia, Canada in 2003–2011. Breeding density at this remote site was relatively high, ranging from 2.23 to 3.72 pairs/km of shoreline in the 9 y. Most clutches were initiated in the last 2 wk of May, and the annual mean 1st clutch size ranged from 2.1 to 2.8 eggs/ nest, values simila...

In [1] we introduced the mixt-linear circles adjointly inscribed associated to a triangle, with emphasizes on some of their properties. Also, we’ve mentioned about mixt-linear circles adjointly ex-inscribed associated to a triangle. In this article we’ll show several basic properties of the mixt-linear circles adjointly exinscribed associate to a triangle. Definition 1 We define a mixt-linear c...