Abstract: The objective of Peter Chew Triangle Diagram is to clearly illustrate the topic solution of triangle and provide a complete design for the knowledge of AI age. Peter Chew's triangle diagram will suggest a better single rule that allows us to solve any problem of topic solution of triangle simple , directly and more accurately. There are two important rules for solving the topic solution of triangle today [1,2], namely the sine rule and the cosine rule. The sine rule is used to find a non-included angle when are given two sides and a non-included angle or the opposite side angle given when are given two angles and one side. The cosine rule normally is used to find the included angle when are given three sides or the third side when are given two sides and the included angle. Peter Chew Method[3] allow us to find the third side simple and directly when given two sides and a non-included angle. Peter Chew rule [4] allow us to find a non included angle simple, directly and more accurately when given 2 sides and an included angle. Aply Peter Chew Triangle Diagram to Education 4.0 Calculator , Peter Chew Triangle Diagram Calculator allows the Calculator to solve any problems in the topic solution of triangle simple, directly and more accurate. This can be effective in increasing students' interest in using technology while learning mathematics and will help in the learning of mathematics, especially when similar covid-19 issues arise in the future.

In this work we study the following problem, from a computational point of view: If three points are selected in the unit square at random, what is the probability that the triangle obtained is obtuse, acute or right? We provide two convergent strategies: the frst derived from the ideas introduced in [2] and the second built on the combinatorics theory. The combined use of these two methods allows us to address the random triangle theory from a new perspective and, we hope, to work out a general method of dealing with some classes of computational problems.

Let $\mathcal{N}$ be an arbitrary class of matroids, closed under isomorphism. For $k$ a positive integer, we say that $M \in \mathcal{N}$ is \emph{$k$-minor-irreducible} if $M$ has no minor $N \in \mathcal{N}$ such that $1\leq\left|E\left(M\right)\right|-\left|E\left(N\right)\right|\leq k $. Tutte's Wheels and Whirls Theorem establish that, up to isomorphism, there are only two families of 1-minor-irreducible matroids in the class of 3-connected matroids. More recently, Lemos classified the 3-minor-irreducibles with at least 14 elements in the class of triangle-free 3-connected matroids. Here we prove a local characterization for the 2-minor-irreducible matroids with at least 11 elements in the class of triangle-free 3-connected matroids. This local characterization is used to establish two new families of 2-minor-irreducible matroids in this class.

There are abundant coal, oil and natural gas resources in "Golden Triangle" energy region. Energy resources development, coal chemical industry, coal power and other industries play an important role in promoting regional economic growth, but facing the insufficient water supply. Under the condition of marginal equilibrium of water resources, the paper firstly analyzes the water utilization, and calculates the potential water-saving amount. Then, the paper constructs a cooperative game model and allocates the newly increased GDP by using the weight distribution method. Finally, the paper puts forward some policy suggestions to reduce the efficiency gap of water utilization among regions.

The worldwide number of migrants has had a rapid increase during the last fifteen years. Despite the extensive research studies that elucidate the increase in migrants' recipient countries, we know little about the relationship between the climate factors and human mobility in the countries of origin. Hence, this study focuses on the effects of weather and the propensity of individuals to leave a territory by measuring the importance of rain precipitation or the lack of it in one of the critical food corridors of Central America, formed by El Salvador, Honduras, and Guatemala. To study the mobility process, we develop a stochastic frontier model; the main result shows a greater propensity to migrate when there is a significant drought event in the place of origin. Some other factors that motivate people to leave their homeland are the effect of other climate events measured through the control system (ENSO), homicide levels, economic performance, and exchange rate. The findings allow differentiating between drought and excess precipitation on a population and mobility to other territories. In addition, these results permit us to derive observable implications of the different effects of flooding and drought and create public policies of prevention, mitigation, and resilience.

In this short paper we study some properties of the lines associated with van Aubel’s theorem in the special case when squares are replaced with equilateral triangles constructed on the sides of an arbitrary quadrilateral.

This paper presents a new approach to a different proof of "Fermat's Last Theorem.” For the proof of the theorem, it is proposed to use a more straightforward geometrical approach. A special family of curves, the Elba curves, is introduced to facilitate the proof. This approach makes the proof easier to comprehend by mathematicians and those interested in the subject.

This paper presents a new approach to a different proof of "Fermat's Last Theorem.” For the proof of the theorem, it is proposed to use a more straightforward geometrical approach. A special family of curves, the Elba curves, is introduced to facilitate the proof. This approach makes the proof easier to comprehend by mathematicians and those interested in the subject.

The brain, rather than being homogeneous, displays an almost infinite topological genus, because is punctured with a very high number of topological vortexes, i.e., .e., nesting, non-concentric brain signal cycles resulting from inhibitory neurons devoid of excitatory oscillations. Starting from this observation, we show that the occurrence of topological vortexes is constrained by random walks taking place during self-organized brain activity. We introduce a visual model, based on the Pascal’s triangle and linear and nonlinear arithmetic octahedrons, that describes three-dimensional random walks of excitatory spike activity propagating throughout the brain tissue. In case of nonlinear 3D paths, the trajectories in brains crossed by spiking oscillations can be depicted as the operation of filling the numbers of the octahedrons in the form of “islands of numbers”: this leads to excitatory neuronal assemblies, spaced out by empty area of inhibitory neuronal assemblies. These procedures allow us to describe the topology of a brain of infinite genus, to assess inhibitory neurons in terms of Betti numbers, and to highlight how non-linear random walks cause spike diffusion in neural tissues when tiny groups of excitatory neurons start to fire.

This article concerns the adoption of small-scale irrigation farming as a climate-smart agriculture practice and its influence on household income in the Chinyanja Triangle. Chinyanja Triangle is a region that experiences mid-season dry spells and an increase in occurrences of drought due to low and erratic rainfall patterns which is attributed largely to climate variability and change. This poses high agricultural production risks, which aggravate poverty and food insecurity. For this region, adoption of small-scale irrigation farming as a climate-smart agriculture practice is very important. Through a binary logistic and ordinary least squares regression, the article determines factors that influence the adoption of small-scale irrigation farming as a climate-smart agriculture practice and its influence on income among smallholder farmers. The results show that off-farm employment, access to irrigation equipment, access to reliable water sources and awareness of water conservation practices, such as rainwater harvesting have a significant influence on the adoption of small-scale irrigation farming. On the other hand, the farmer’s age, distance travelled to the nearest market and nature of employment negatively influenced the adoption of small-scale irrigation farming decisions. Ordinary least squares regression results showed that the adoption of small-scale irrigation farming as a climate-smart agriculture practice has a significant positive influence on agricultural income. We therefore conclude that to empower smallholder farmers to quickly respond to climate variability and change, practices that will enhance adoption of small-scale irrigation farming in the Chinyanja Triangle are critical as this will significantly impact on agricultural income.

In this paper we discuss a problem of generalization of binomial distributed triangle, that is sequence A287326 in OEIS. The main property of A287326 that it returns a perfect cube n as sum of n-th row terms over k; 0 ≤ k ≤ n−1 or 1 ≤ k ≤ n, by means of its symmetry. In this paper we have derived a similar triangles in order to receive powers m = 5; 7 as row items sum and generalized obtained results in order to receive every odd-powered monomial n^2m+1; m ≥ 0 as sum of row terms of corresponding triangle.