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...

In a Steiner triple system of order v, STS(v), a set of three lines intersecting pairwise in three distinct points is called a triangle. A set of lines containing no triangle is called triangle-free. The minimum number of triangle-free sets required to partition the lines of a Steiner triple system S, is called the triangle chromatic index of S. We prove that for all admissible v, there exists ...

Some gyrocommutative gyrogroups, also known as Bruck loops or K-loops, admit scalar multiplication, turning themselves into gyrovector spaces. The latter, in turn, form the setting for hyperbolic geometry just as vector spaces form the setting for Euclidean geometry. In classical mechanics the centroid of a triangle in velocity space is the velocity of the center of momentum of three massive ob...

A generalised tetrahedron group is the colimit of a triangle of groups whose vertex groups are generalised triangle groups and whose edge groups are finite cyclic. We prove an improved Spelling Theorem for generalised triangle groups which enables us to compute the precise Gersten-Stallings angles of this triangle of groups, and hence obtain a classification of generalised tetrahedron groups ac...

We introduce a new class of planar graphs called triangle graphs. First, we present a formal way of constructing and characterizing triangle graphs, and then show that they characterize the adjacencies of arbitrary triangulations and they are three-colorable for a certain subclass of triangulations. Subsequently, we discuss an application of triangle graphs to the parallel nite element solution...

The quad/triangular subdivision, whose control net and refined meshes consist of both quads and triangles, provides better visual quality of subdivision surfaces. While some theoretical results such as polynomial reproduction and smoothness analysis of quad/triangle schemes have been obtained in the literature, some issues such as the basis functions at quad/triangle vertices and design of inte...

In this chapter we will be investigating the intricacies of a seemingly innocuous mathematical object Pascal’s Triangle. After a brief refresher of our understanding of the triangle, we will delve into Cellular Automata as a method of building patterns, and then relate this to a specific pattern within Pascal’s Triangle. Then we shall investigate specific divisibility identities that can aid in...