Properties Of Triangles Research Articles

CHPT: an improved coverage-hole patching technique based on tree-center in wireless sensor networks

The occurrence of coverage-hole (CH) in a wireless sensor network degrades the performance of the network in terms of data transmission. Therefore, after the detection of CH, hole-patching is the next important task in order to reduce the energy consumption and to improve the network lifetime. In this paper, we propose an improved coverage-hole patching technique (CHPT) based on the concept of center of tree. The prerequisite to hole-patching is the hole-detection, which is done based on Delaunay Triangle and empty circle property. Subsequently, using the Inner empty circle property, the hole-area is estimated. And finally, CHPT is used to determine the hole-boundary and formulate the sub-trees for identifying the patch-positions to be covered by deploying additional sensor nodes. Experimental results show that the average percentage of coverage in CHPT increases up to 98.6% in terms of additional sensors and with a given sensing radius.

Learning Feature Interactions with Lorentzian Factorization Machine

Learning representations for feature interactions to model user behaviors is critical for recommendation system and click-trough rate (CTR) predictions. Recent advances in this area are empowered by deep learning methods which could learn sophisticated feature interactions and achieve the state-of-the-art result in an end-to-end manner. These approaches require large number of training parameters integrated with the low-level representations, and thus are memory and computational inefficient. In this paper, we propose a new model named “LorentzFM” that can learn feature interactions embedded in a hyperbolic space in which the violation of triangle inequality for Lorentz distances is available. To this end, the learned representation is benefited by the peculiar geometric properties of hyperbolic triangles, and result in a significant reduction in the number of parameters (20% to 80%) because all the top deep learning layers are not required. With such a lightweight architecture, LorentzFM achieves comparable and even materially better results than the deep learning methods such as DeepFM, xDeepFM and Deep & Cross in both recommendation and CTR prediction tasks.

Random Triangles in a Metric Space of Sequences

We investigate probabilistic properties of random triangles in the space of finite sequences with the Hamming metrics. As a triangle is understood any triple of points with distances between them. Probability measure is given by the classical way. In particular, it is shown that randomly chosen triangle is approximately equilateral with high probability. We also introduce a quantity that characterizes degree of “equilaterality” of triangles in the metric space in average.

On Triangles with Sides That Form an Arithmetic Progression

Properties of triangles such that the squares of their sides form an arithmetic progression were studied in 2018. In this paper, triangles with sides that form an arithmetic progression are described. Let a, b, c be sides of an arbitrary triangle ABC. If sides b, a, c of the triangle ABC form an arithmetic progression then, for example, the equality a=(b+c)/2 (b<a<c) holds. The class of triangles for which a=(b+c)/2 is greater than the class of triangles for which b, a, c form an arithmetic progression. In this paper, we study the properties of triangles for which this equality holds. Thus, triangles with sides that form an arithmetic progression are described with the help of the parameters p, R, r. Classes of rectangular triangles, triangles with angle 30°, triangles with angle 60°, triangles with angle 120° are studied and described.

Resolving the four – Bar Link Mechanism by Kinamatics and Revolving Angle Solution

Four bar link mechanism now days are beneficial for various vehicles for power transmission and Mechanical stability with respect to the motion on various Terrains. The stability regarding the motion transitional is easier rather than motion related to rotational. Author trying to resolve the complexity with respect to Matlab codes helpful in the automation of various four bar link mechanism vehicles. The author indicated the source code for four bar link mechanism, as well as simulating the module based on the real time system, lines of code determines the new configurations of the mechanism for an incrementally varying position of the crank. This is based on the standard cosine formulas and other triangle properties used for analyzing four-bar linkages. . Obviously, torque and power are not the amount that has been in the kinematics and whatever kinematic amount we use to characterize the presentation of the instrument, this amount will just inexact the static power qualities of the component.

Developing of teaching materials for junior high school students based on ethnomathematics on traditional woven cloth (Tembe Nggoli) of Mbojo tribe

This research is based on the absence of teaching materials about the concept of geometry that is able to facilitate the students connecting the culture, especially tembe nggoli which is one of the traditional woven cloth of mbojo-NTB with the concept of mathematics. Ethnomathematics is a mathematical bridge with culture, and ethnography recognizes the different ways of doing mathematics in community activities. The result of this study is to produce teaching materials in the form of students’ worksheets. The method used is design research which includes: (1) preliminary design, in this phase is made Hypothetical Learning Trajectory (HLT); (2) experiments, in this phase existing designs are tested to students; (3) retrospective analysis, in this phase the researchers compare the HLT with the actual student learning process. The results of this research showed that tasks which were presented in teaching materials by considering learning obstacle and preliminary study able to facilitate students to define the properties of triangles based on their angle.

Simulation and Application of Reuleaux Triangle In Geometric Measurement

The reuleaux triangle is studied and calculated by a large number of scholars because of its special properties of equal width, which has many applications in engineering, computer, biological science, etc. Geometry geodesy is a science that establishes mathematical models of geometric parameters for the earth. There are many designs and constructions using the shape of the reuleaux triangle in modern architecture. However, there are still few references in this part of the application modeling and research analysis. Therefore, based on the basic theory and special properties of the reuleaux triangle, the trajectory of the vertices and the center point are researched in the scene of rotate and scroll. Then, the geometric measurement algorithm based on the reuleaux triangle is proposed, which is applied to the measurement and calculation of the design of the earth building design. The algorithm solves the problem effectively that the building cannot be stabilized due to the height. Finally, the geometric position of the building at the ground point is determined. At the end of the paper, the geometry of Shanghai Central Building is simulated by MATLAB, and the effectiveness of the simulation algorithm is proved.

The Many Sides of the Pythagorean Theorem

SummaryThe Pythagorean theorem gives a fundamental relationship between the lengths of the three sides of a right-angled triangle. We make the case for which theorems of elementary Euclidean geometry should be called the “Pythagorean theorem for an arbitrary triangle” and the “Pythagorean theorem for a quadrilateral.” In making this presentation, we stress the use of the basic properties of triangles over use of the cosine formula.

The Doppler effect and similar triangles

Abstract The Euclidean version of Doppler effect will be explained using the properties of similar triangles. These properties will serve to explain the relationship between frequencies of propagated wavefronts, number of wavefronts and the time of emitting and receiving of these wavefronts. This explanation of Doppler effect represents not only a new method of obtaining equations which deal with Doppler effect, but using this geometric construction we will have an easier and deep understanding of some problems related to this effect, such as the general formulas of the Doppler effect and time Doppler effect, which are replaced by the new proposed formulas.

A Kato class for the Khon Laplacian

In this paper we establish an upper estimate and a 3G-theorem for the Green function of the Khon Laplacian $$\Delta _{{\mathbb {H}}}$$ on a domain D of the Heisenberg group $${{\mathbb {H}}^n}$$ . We also establish a generalized triangle property which allows us to introduce a new Kato class for the ball.

From map reading to geometric intuitions.

The origins and development of our geometric intuitions have been debated for millennia. The present study links children's developing intuitions about the properties of planar triangles to their developing abilities to read purely geometric maps. Six-year-old children are limited when navigating by maps that depict only the sides of a triangle in an environment composed of only the triangle's corners and vice versa. Six-year-old children also incorrectly judge how the angle size of the third corner of a triangle varies with changes to the other two corners. These limitations in map reading and in judgments about triangles are attenuated, respectively, by 10 and 12 years of age. Moreover, as children get older, their map reading predicts their geometric judgments on the triangle task. Map reading thus undergoes developmental changes that parallel an emerging capacity to reason explicitly about the distance and angle relations essential to euclidean geometry. (PsycINFO Database Record

Detection of Accommodation and Assimilation Speed by Students of Grade VII in Learning Special Triangle

Each student is born as an individual with different abilities both in absorbing and processing information received. Students have different speeds in analysing the acquisition of new information or knowledge, some are low, medium and high. similarly the time required is short, there is also a long time. As he absorbs, processes, and analyses the information, he has adapted accommodation and assimilation within his cognitive structure. This study aims to determine the speed of assimilation and accommodation of VII grade students who are highly capable, medium, and low in learning special triangle. The approach used is qualitative by using task-based interview. The researcher interviewed the subject using interview guidelines that have been compiled and tested. The questions are intended to guide the subject in performing the assigned task as a way of recording the speed of the accommodation and assimilation process. The tasks assigned to the subject are triangular questions containing new concepts such as special triangle properties, triangular lines, triangular drawings and triangular lines, calculating the number of outside corners and special triangles, and calculating the area From a variety of special triangles. Another tool in this study was the stopwatch to detect the speed of accommodation and assimilation of each student. Data analysis was done by three stages: studying data transcript, data reduction, and coding. The results of this study were from obtained high-ability students detected quickly in the process of accommodation and assimilation.

Experimental Non-Violation of the Bell Inequality.

A finite non-classical framework for qubit physics is described that challenges the conclusion that the Bell Inequality has been shown to have been violated experimentally, even approximately. This framework postulates the primacy of a fractal-like ‘invariant set’ geometry in cosmological state space, on which the universe evolves deterministically and causally, and from which space-time and the laws of physics in space-time are emergent. Consistent with the assumed primacy of , a non-Euclidean (and hence non-classical) metric is defined in cosmological state space. Here, p is a large but finite integer (whose inverse may reflect the weakness of gravity). Points that do not lie on are necessarily -distant from points that do. is related to the p-adic metric of number theory. Using number-theoretic properties of spherical triangles, the Clauser-Horne-Shimony-Holt (CHSH) inequality, whose violation would rule out local realism, is shown to be undefined in this framework. Moreover, the CHSH-like inequalities violated experimentally are shown to be -distant from the CHSH inequality. This result fails in the singular limit , at which is Euclidean and the corresponding model classical. Although Invariant Set Theory is deterministic and locally causal, it is not conspiratorial and does not compromise experimenter free will. The relationship between Invariant Set Theory, Bohmian Theory, The Cellular Automaton Interpretation of Quantum Theory and p-adic Quantum Theory is discussed.

Elementary properties of triangle in normed spaces

Based on concepts of trigonometric on plane, In this paper we generalized those concept in normed spaces. About the orthogonality concept between two vectors already well known, we are interested to develop elementary properties of triangle, especially the properties of its angle. We propose a non-linear (Wilson) functional to define an angle and explore its properties.

Triangle Shape Feature based on Selected Centroid for Arabic Subword Handwriting

Features are normally modelled based on color, texture and shape. However, some features may have different constraints based on types, styles and pattern of an image. The Arabic subword handwriting, for example, cannot be recognized by color and not suitable to be characterized based on texture. Therefore, features based on shape are suitable to be used for recognizing Arabic subword handwriting since each of the character has various characteristics such as diacritics, thinning and strokes. These characteristics can contribute to particular a shape that is unique and can represent Arabic subword handwriting. Currently, geometry shape such as triangle has been adopted to extract useful features based on triangle properties without implicating any triangle form. In order to increase classification accuracy, these properties have been categorized into several zones where the number of features produced is directly proportional to the number of zones. Nevertheless, shape representation does not implicate any triangle properties such as ratio of side, angle and gradient. By using shape representation, it helps in reducing the number of features. Thus, this paper presents feature based on triangle shape that can represent the identity of Arabic subword handwriting. The method based on triangle shape identifies three main coordinates of triangle formed based on selected centroids. The AHDB dataset is used as a testing data. The Support Vector Machine (SVM) and Random Forest (RF), respectively were used to measure the accuracy of the proposed method using triangle shape as a feature. The accuracy results have shown better outcome with 77.65% (SVM) and 76.43% (RF), which prove the feature based on triangle shape is applicable for Arabic subword handwriting recognition.

Effect of the structural characteristics of solution styrene–butadiene rubber on the properties of rubber composites

ABSTRACTSolution‐polymerized styrene–butadiene rubber (SSBR) has been widely used in the high‐quality tire industry, and various brands of SSBR have been synthesized. Five kinds of SSBR were selected from multiple products to investigate the effects of different brands of SSBR on the comprehensive properties. Different characterization tools, such as Fourier transform infrared spectroscopy, 1H‐NMR, and differential scanning calorimetry, were used to characterize the microstructures of the SSBRs. The results show that the microstructures of the SSBRs distinctly affected the comprehensive properties of the SSBR composites, especially the properties of the “magic triangle.” For instance, the content of trans‐1,4‐butadiene positively corresponded to the Akron abrasion for the SSBR composites with different brands, and cis‐1,4‐butadiene could partly replace the influence of vinyl when the content of trans‐1,4‐butadiene was small. SSBR 2564S, SSBR 4526‐2, and SSBR 2535E were selected because of the excellent magic‐triangle properties. They were used to investigate the effects of different brands of SSBR with different ratios of natural rubber (NR) to SSBR on the comprehensive properties of the NR–SSBR rubber blend composites. The results indicate that the properties of magic triangle were distinctly enhanced. However, there was an optimized content of SSBR to enhance the wear resistance (≤15 phr). For SSBR 4526‐2, the Payne effect was negatively correlated to the content of SSBR, whereas for SSBR 2564S and SSBR 2535E, the Payne effect was positively correlated to the content of SSBR. On the basis of these results, the SSBR 2564S seemed to exhibit the best comprehensive properties to prepare a tire tread tailored for high‐performance tires. © 2017 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2018, 135, 45749.

101.35 Some properties of the Kepler triangle

101.35 Some properties of the Kepler triangle

101.21 A homothetic property of orthic triangles

101.21 A homothetic property of orthic triangles

Making versus observing manipulations of geometric properties of triangles to learn geometry using dynamic geometry software

Human movement has been found to have positive effects on learning performance. This study examined the effects of using Dynamic Geometry Software (DGS) CABRI to manipulate geometric properties of triangles or observing those manipulations made by an instructor on learning geometric properties with DGS-CABRI. Participants were 60 year 5 students, who received instructions on geometric problems and were randomly assigned to three conditions: A condition in which they performed mouse movements to manipulate geometric properties of triangles, a condition in which they observed the teacher performing those manipulations, and a conventional condition in which they studied a static format of the learning materials without any manipulations. We hypothesized that learning conditions involving manipulations of geometric properties of triangles would result in lower cognitive load and higher performance on a retention and transfer test than the conventional condition. Moreover, we hypothesized that making manipulations of the geometric properties of triangles through mouse movements would be superior to observing those manipulations being made by an instructor in terms of cognitive load, retention- and transfer test performance. Whereas the first hypothesis was confirmed, the latter hypothesis was only confirmed for retention test performance. Possible implications for educational practice are discussed.

CPV: Delay-Based Location Verification for the Internet

The number of location-aware services over the Internet continues growing. Some of these require the client’s geographic location for security-sensitive applications. Examples include location-aware authentication, location-aware access policies, fraud prevention, complying with media licensing, and regulating online gambling/voting. An adversary can evade existing geolocation techniques, e.g., by faking GPS coordinates or employing a non-local IP address through proxy and virtual private networks. We devise Client Presence Verification (CPV), a delay-based verification technique designed to verify an assertion about a device’s presence inside a prescribed geographic region. CPV does not identify devices by their IP addresses. Rather, the device’s location is corroborated in a novel way by leveraging geometric properties of triangles, which prevents an adversary from manipulating measured delays. To achieve high accuracy, CPV mitigates Internet path asymmetry using a novel method to deduce one-way application-layer delays to/from the client’s participating device, and mines these delays for evidence supporting/refuting the asserted location. We evaluate CPV through detailed experiments on PlanetLab, exploring various factors that affect its efficacy, including the granularity of the verified location, and the verification time. Results highlight the potential of CPV for practical adoption.