Armed only with a triangle and a dream, Marion Walter, a professor of mathematics at the University of Oregon, embarked on a quest for mathematical enlightenment. She battled rough angles and contemplated numerous strategies to find answers. In the end, Walter discovered characteristics of a triangle when each of its sides is trisected. Okay, Walter’s “quest” was not that exciting or epic, but ...

Triangle algebras are equationally defined structures that are equivalent with certain residuated lattices on a set of intervals, which are called interval-valued residuated lattices (IVRLs). Triangle algebras have been used to construct Triangle Logic (TL), a formal fuzzy logic that is sound and complete w.r.t. the class of IVRLs. In this paper, we prove that the so-called pseudo-prelinear tri...

The triangle-free process begins with an empty graph on n vertices and iteratively adds edges chosen uniformly at random subject to the constraint that no triangle is formed. We determine the asymptotic number of edges in the maximal triangle-free graph at which the triangle-free process terminates. We also bound the independence number of this graph, which gives an improved lower bound on the ...

In computational geometry, packing problems ask whether a set of rigid pieces can be placed inside a target region such that no two pieces overlap. The triangle packing problem is a packing problem that involves triangular pieces, and it is crucial for algorithm design in many areas, including origami design, cutting industries, and warehousing. Previous works in packing algorithms have conject...

An overview of the ‘triangle’ method for estimating soil surface wetness and evapotranspiration fraction from satellite imagery is presented here. The method is insensitive to initial atmospheric and surface conditions, net radiation and atmospheric correction, yet can yield accuracies comparable to other methods. We describe the method first from the standpoint of the how the triangle is obser...

Newly hatched chicks will spontaneously peck at conspicuous objects in their field of view, and soon learn to distinguish between edible food particles and unpleasant tasting objects. To examine whether the selective pecking is based on the ability to memorize shapes, we analyzed pecking behavior of 1- to 2-days-old quail chicks (Coturnix japonica) by using ball- and triangle-shaped beads both ...

Species invasion is a complex, multifactor process. To encapsulate this complexity into an intuitively appealing, simple, and straightforward manner, we present an organizational framework in the form of an invasion triangle. The invasion triangle is an adaptation of the disease triangle used by plant pathologists to help envision and evaluate interactions among a host, a pathogen, and an envir...

Triangle-free graphs play a central role in graph theory, and triangle detection (or triangle finding) as well as triangle enumeration (triangle listing) play central roles in the field of graph algorithms. In distributed computing, algorithms with sublinear round complexity for triangle finding and listing have recently been developed in the powerful CONGEST clique model, where communication i...