(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...

Section 2 sets the stage by describing the parameter triangle T for real cubic maps, either of shape + + or of shape + , and by describing basic properties of topological entropy. Section 3 describes the monotonicity problem for the topological entropy function, and states the Monotonicity Conjecture. Section 4 describes the family of stunted sawtooth maps, and proves the analogous conjecture f...

Several algorithms that use graphics hardware to accelerate processing require conservative rasterization in order to function correctly. Conservative rasterization stands for either overestimating or underestimating the size of the triangles. Overestimation is carried out by including all pixels that are at least partially overlapped by the triangle, whereas underestimation includes only the p...

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...

Fractals play an important role in nonlinear science. The most parameter when modeling a fractal is the dimension. Existing information dimension can calculate of probability distribution. However, calculating given mass function, which generalization probability, still open problem immense interest. main contribution this work to propose function. Numerical examples are show effectiveness our ...

We propose a new version of potentially optimal intervals for the DIRECT algorithm. A two-points based sampling method is presented. The method starts from a distingished point (the peak point) by forming an initial triangle. The idea is to sample the midpoint of a specific interval: the basis of the resulting triangle. This specific interval is obtained by translating the initial interval towa...

In this article, we demonstrate how the Binomial Theorem in turn arises from a one-parameter generalization of the Sierpinski triangle. The connection between them is given by the sum-of-digits function, s(k), defined as the sum of the digits in the binary representation of k (see [1]). For example, s(3) = s(1·2+1·2) = 2. Towards this end, we begin with a well-known matrix formulation of Sierpi...

This article considers a family of functionals J to be maximized over the planar convex sets K for which the perimeter and Steiner point have been fixed. Assuming that J is the integral of a quadratic expression in the support function h, the maximizer is always either a triangle or a line segment (which can be considered as a collapsed triangle). Among the concrete consequences of the main the...

We Coulomb explode argon and neon dimers, trimers, and tetramers by multiple ionization in an ultrashort 800 nm laser pulse. By measuring all momentum vectors of the singly charged ions in coincidence, we determine the ground state nuclear wave function of the dimer, trimer, and tetramer. Furthermore we retrieve the bond angles of the trimer in position space by applying a classical numerical s...