Circle Equations Research Articles

РОЗРАХУНОК РЕГУЛЮВАЛЬНИХ ХАРАКТЕРИСТИК РЕЗОНАНСНИХ ПЕРЕТВОРЮВАЧІВ МЕТОДОМ СУПЕРПОЗИЦІЇ

The work presents the calculations of the control characteristics of the full-bridge resonant converter with a series resonant LLC circuit and frequency control by two methods - the first harmonic method and the superposition method. The theoretical results were verified by the analytical-structural modeling method. The power circuit of the resonant converter for the analysis of electromagnetic processes is replaced by a linear T-shaped circuit with two series resonant RLC-circuits and equivalent generators of rectangular voltages, which simulate a transistor inverter and a diode rectifier in the quasi-continuous current mode. Analytical-structural modeling method consists in partly analytical and partly structural ways of building a numerical model of the resonant converter in the form of the simulation model in the MATLAB-Simulink environment. Linear structural links of the model are created on the basis of integral equations of circles. Non-linear links are created based on the non-linear functions and causal relationships. The structural model based on these links takes into account the nonlinearity of the elements of the power circuit of the resonant converter and is based on simpler mathematical expressions compared to the equivalent mathematical model of the resonant converter. The structural model corresponds to the idea of the resonant converter in the form of the resonant circuit with independent equivalent voltage generators and allows to adjust the magnetic coupling coefficient between the transformer windings and simulate processes with arbitrary control functions of equivalent generators. The peculiarity of the use of the superposition method for calculating the static characteristics of the resonant converter is the need to match the voltage phases of the equivalent generators of the equivalent circuit during the changes of the operating frequency or relative load voltage. The dependence of the input voltage of the rectifier, which is simulated by the second equivalent generator, on the processes of the power circuit of the real resonant converter, determines the conditions for matching (adjusting) the phases of the equivalent generators. References 30, figures 5.

Attitudes and Performance of Grade 11 Students in Pre-Calculus Using Strategic Intervention Material

Strategic Intervention Material (SIM) served as instructional support to help students review key ideas and techniques to help them master a competency-based ability they could not achieve during routine class discussions. This study aimed to determine the attitudes and the performance of Grade 11 students in Pre-Calculus using SIM at the three-identified public national high schools in Cebu, Philippines. It employed the descriptive-correlational method to collect data from 97 samples using two questionnaires (A standardized Attitudinal Test by Fennema-Sherman and researchers-made Performance Test in Equations of Circles). The Chi-square test, t-test, frequency, simple percentage, mean, standard deviation, and attitude toward success were used to analyze the respondents' attitudes about pre-calculus regarding confidence in learning, attitude toward success, mathematics as a male domain, and usefulness. The findings demonstrated that SIMs were appropriate for the respondents' needs, with more excellent knowledge gained from the SIM leading to a better understanding of Pre-Calculus, specifically Equations of Circles, which is beneficial when SIM is used as a teaching tool. The study concluded that using SIM in Pre-Calculus as instructional support significantly affected the student's performance in Pre-Calculus, which is effective in learning the subject. The proposed intervention plan was recommended to be implemented, monitored, and evaluated to boost the math performance of the Grade 11 senior high schools.

Analysis of The Ability Student of SMA Al Islam Krian to Understanding Mathematical Concepts in Terms of Learning Styles

This research aims to analyze and describe the ability of students of SMA Al Islam Krian to Understanding Mathematical Concepts in Terms of Student Learning Styles for the 2022/2023academic year on the material of circle equations in terms of learning stylesusing include auditory, visual, and kinesthetic learning styles with a qualitative descriptive approach. The data collection techniques used were tests and interviews, with research instruments in the form of learning-style questionnaires, test questions, and interviews. The results of the study, it was found that from the visual learning style students with high abilities were able to understand mathematical concepts, whereas students with low abilities were not yet able to understand mathematical concepts. Meanwhile, from the auditory learning style, students with high and low abilities are less able to understand mathematical concepts. If from the kinesthetic learning style students with high abilities are less able to understand mathematical concepts, while students with low abilities are not yet able to understand mathematical concepts.

IMPROVING STUDENTS LEARNING OUTCOMES ON CIRCLE EQUATION MATERIAL USING GEOGEBRA SOFTWARE

This study aims to describe learning using GeoGebra software on circle equations material that can improve students learning outcomes of class XI MIPA5 SMAN 1 Mengwi. The research method used is Class Action Research (CAR) which consists of four stages, namely planning, implementation, observation, and reflection. The subject of this study is all students of class XI MIPA5 SMAN 1 Mengwi, while the object of research is the entire process and results of mathematics learning using GeoGebra software on circle equation material as an effort to improve students learning outcomes of the class. The data collection techniques used are observation, interviews, and tests. This research was carried out in two CAR cycles. The results showed that the application of mathematics learning using GeoGebra software on circle equations material can improve the learning outcomes of class XI MIPA5 SMAN 1 Mengwi students. This is shown by the average student learning outcomes in the final test I, which is 83 with a classical completion percentage of 75% increasing to 90 in the final test II with a classical completion percentage of 89%.

Pixel Coordinates for Obtaining 3D Body Measurements from 2D Images

In this research, a new method developed with pixel coordinates is presented to obtain 3D body measurements from 2D images, to eliminate the need of the body to take measurements and to solve unfit problem in e-shopping. Front and side photographs are processed with new developed programmes named PixelList1.0 and Python 2.0. The sharp silhouettes, presented in authors’ another publication, are benefited with algorithms to reach pixel coordinates of feature points. Number of pixels in between feature points are saved, absolute values of differences consecutively are calculated, and 3D body measurements in pixels are obtained with different mathematical models. A conversion coefficient is introduced and size of a pixel is calculated accurately, 0.239 cm/pixel. 3D body measurements in centimeters are obtained by multiplying number of pixels by the size of one pixel in circle, ellipse, and hippodrome circumference equations. An overall accuracy rate of 93 % is concluded with the ellipse circumference equation.

Left-definite Hamiltonian systems and corresponding nested circles

This work aims to construct the Titchmarsh-Weyl $M(\lambda )-$theory for an even-dimensional left-definite Hamiltonian system. For this purpose, we introduce a suitable Lagrange formula and selfadjoint boundary conditions including the spectral parameter $\lambda $. Then we obtain circle equations having nesting properties. Using the intersection point belonging to all the circles we share a lower bound for the number of Dirichlet-integrable solutions of the system.

Exploration of Vocational School Students' Misconceptions of Circle Material

Misconceptions are ideas not following scientific understanding or understandings coined by experts in a field and can be in the form of an inaccurate understanding of concepts, use of wrong concepts, wrong classification of examples, or confusion of incorrect concepts. Understanding the correct concept is essential because there are still many misunderstandings (misconceptions); therefore, information about misconceptions is needed to avoid continuing misconceptions. This study aims to describe the misconceptions and causes of misconceptions in class XI AP 1 students at a private school in the city of Cirebon on the subject of circle equations. The form of research carried out in this study is qualitative research, with case study research methods. The data collection techniques used are 1) the test method, 2) the method of documenting the results of the answers of students who experience misconceptions, and 3) the interview method carried out on students who experience misconceptions. Based on the data analysis and discussion, it is concluded that 1) There is a misconception about a) the concept of a circle, b) the concept of the radius of a circle, c) the concept of the equation of a circle, and the position of a point on the circle. 2) The causes of misconceptions come from the teacher and the students themselves.

Some Symmetric Properties and Location Conjecture of Approximate Roots for (p,q)-Cosine Euler Polynomials

In this paper, we introduce (p,q)-cosine Euler polynomials. From these polynomials, we find several properties and identities. Moreover, we find the circle equations of approximate roots for (p,q)-cosine Euler polynomials by using a computer.

APPLICATION OF CIRCLES FOR CONJUGATION OF FLAT CONTOURS OF THE FIRST ORDER OF SMOOTHNESS

In geometric modeling of contours, especially for conjugation of sections of flat contours of the first order of smoothness, arcs of circles can be applied. The article proposes ways to determine the equations of a circle for two ways of its problem: the problem of a circle with a point and two tangents, none of which contains a given point, and the problem of a circle with three tangents. The equations of the circles were determined in both cases using a projective coordinate system.
 In the first case, when a circle is given by a point and two tangents, neither of which contains this point, the center of the conjugation circle is defined as the point of intersection of two locus of points - the bisector of the angle between the tangents and the parabola, the focus of which is a given point. given tangents. In the general case, there are 2 conjugation circles for which canonical equations are defined. Parametric equations of conjugate circles, the parameters of which are equal to 0 and ∞ on tangents and equal to one at a given point, with the help of affine and projective coordinates of points of contact are determined first in the projective coordinate system, and then translated into affine system.
 For the second case, when specifying a circle using three tangent lines, the equation of the second-order curve tangent to these lines is first determined in the projective coordinate system. The tangent lines are taken as the coordinate lines of the projective coordinate system. The unit point of the projective coordinate system is selected in the metacenter of the thus obtained base triangle. The equation of the tangent to the base lines of the second order contains two unknown variables, positive or negative values ​​which determine the location of four possible tangents of the second order. After writing the vector-parametric equation of the tangent curve of the second order in the affine coordinate system, the equation is written to determine the parameters of cyclic points. In order for the equation of the tangent curve of the second order obtained in the projective plane to be an equation of a circle, it must satisfy the coordinates of the cyclic points of the plane, which allows to write the second equation to determine the parameters of cyclic points. By solving a system of two equations, we obtain the required equations of circles tangent to three given lines.

Research on Automatic Labeling of Contact Profiler Based on Big Data

This article mainly studies the problem of labeling various parameter values of the contact profiler. The contour size of the instrument is analyzed by the least square method for the mathematical theory, and the data analysis information of each line and arc is established based on the background of big data. As a result, the corresponding mathematical model is established to realize the labeling of outline dimensions. First, perform precision processing on the horizontal data of the workpiece, use Excel software to make a scatter diagram, use the difference method to quickly search and locate the special inflection point coordinates, borrow these feature points to obtain the dimension of each data in turn, and combine the equations of straight lines and circles Find out the width and radius of the notch, find out the various indicators in turn, and finally sort and summarize them through the table. Next, the tilt data and the original data given for the workpiece are represented by a scatter graph. Using coordinate rotation and translation, the tilt angle is 7°24’59” clockwise and the radian is -0.13017. Compare the two sets of data After the difference, finally use segmented fitting to carry out horizontal correction.

Geometric modeling of a flat contour using a circle

In geometric modeling of contours, in most cases it is convenient to use the equations of curves written in a parametric form. In this case, when modeling flat contours of the first order of smoothness, can be used circular arcs. The article proposes a method for determining the parametric equation of a circle (arc of a circle) for two ways: defining a circle over three points, as well as defining a circle over two points and a tangent in one of them. The definition of the parametric equations of circles in both cases was carried out using a projective coordinate system. In the first case, the conditions for the membership of three given points of this curve were imposed on the classical parametric equation of a second-order curve in the projective coordinate system to determine the unknown coefficients of the equation, and the given points were taken as three basis points of the projective system. Passing the obtained second-order curve through cyclic points made it possible to determine all unknown coefficients of the equation and, thus, determine the desired parametric equation of the circle in the projective coordinate system.In the second case, for simplicity, a local system of affine coordinates was chosen in which two given points were located on the Ox axis symmetrically with respect to the Oy axis, and the point on the tangent was located on the Oy axis. These 3 points were taken as 3 basis points of the projective coordinate system, and the fourth point of the projective coordinate system — the unit point — was defined in the affine system as a point belonging to this circle. The classical equation of a second-order curve in a projective coordinate system that passes through 3 basis points of the projective system and touches the coordinate lines in two of them, provided that the unit point belongs to the circle, is the desired equation of circle.After determining both of the desired equations in the projective coordinate system, using the transfer formulas from the projective system to the affine, the desired parametric equations of the circles in the affine system are determined.

Peningkatan Kemampuan Pemecahan Masalah pada Materi Persamaan Garis Singgung Lingkaran melalui Pembelajaran Discovery Learning

This study aimed to improve student’s problem-solving abilities of tangent circle equations using discovery learning. This research was done in class XI IPA 4 SMA N 1 Palembang. This research method is used Classroom Action Research with discovery learning models. The instrument is used test instrument in the form of an evaluating matter of the tangent circle equation in the description form and the observation sheet for observation of the learning activity of the students. The results of the study showed that there is an increase in students' problem-solving abilities in tangent circle equation material using discovery learning. This increase can be seen from the results of the post-test students with an average score of 93,6 which increased when compared with the results of the pre-test with an average value of 58,2. The percentage of students who complete learning increases from 30% pre-test to 100% at post-test with KKM (maximum mastery criteria) ≥ 70. Based on the data analysis, it can be concluded that learning with discovery learning models can improve student learning outcomes in the tangent of circle equation material.

Design of pure rolling line gear mechanisms for arbitrary intersecting shafts

Design of pure rolling line gear mechanisms for an arbitrary angle intersecting shafts was presented in this article. Based on the active design method of meshing line function for orthogonal shafts, three meshing types of conjugated tooth surfaces for an arbitrary angle intersecting shafts were discussed, including the parametric equations of different generatrix circles, the mathematical models of tooth surfaces, and central curves to be constructed, respectively. The validity of the active designed meshing line function was verified according to meshing equations, and the theoretical sliding rations were analyzed to prove pure rolling meshing. Then basic design parameters of pure rolling line gear mechanisms for the geometry design were determined, and the main structural parameters were obtained therefrom. Lastly, three groups of numerical examples were proposed according to mathematical models. Resin samples of line gears were processed by rapid prototyping technology and the kinematic performance of the pure rolling line gear mechanisms were validated. This paper laid the foundation of geometry and parameter design for pure rolling line gear mechanisms for an arbitrary angle intersecting shafts.

Distributed Localization: A Linear Theory

Fifth-generation (5G) networks providing much higher bandwidth and faster data rates will allow connecting vast number of stationary and mobile devices, sensors, agents, users, machines, and vehicles, supporting Internet-of-Things (IoT), real-time dynamic networks of mobile things . Positioning and location awareness will become increasingly important, enabling deployment of new services and contributing to significantly improving the overall performance of the 5G system. Many of the currently talked about solutions to positioning in 5G are centralized, mostly requiring direct communication to the access nodes (or anchors, i.e., nodes with known locations), which in turn requires a high density of anchors. But such centralized positioning solutions may become unwieldy as the number of users and devices continues to grow without limit in sight. As an alternative to the centralized solutions, this paper discusses distributed localization in a 5G-enabled IoT environment where many low power devices, users, or agents are to locate themselves without a direct access to anchors. Even though positioning is essentially a nonlinear problem (solving circle equations by trilateration or triangulation), we discuss a cooperative linear distributed iterative solution with only local measurements, local communication, and local computation needed at each agent. Linearity is obtained by reparametrization of the agent location through barycentric coordinate representations based on local neighborhood geometry that may be computed in terms of certain Cayley–Menger determinants involving relative local inter-agent distance measurements. After a brief introduction to the localization problem, and other available distributed solutions primarily based on directly addressing the nonlinear formulation, we present the distributed linear solution for stationary agent networks and study its convergence, its robustness to noise, and extensions to mobile scenarios, in which agents, users, and (possibly) anchors are dynamic.

Simple measuring rod method for the coaxiality of serial holes.

Aiming at the rapid coaxiality measurement of serial hole part with a small diameter, a coaxiality measuring rod for each layer hole with a single LDS (laser displacement sensor) is proposed. This method does not require the rotation angle information of the rod, and the coaxiality of serial holes can be calculated from the measured values of LDSs after randomly rotating the measuring rod several times. With the mathematical model of the coaxiality measuring rod, each factor affecting the accuracy of coaxiality measurement is analyzed by simulation, and the installation accuracy requirements of the measuring rod and LDSs are presented. In the tolerance of a certain installation error of the measuring rod, the relative center of the hole is calculated by setting the over-determined nonlinear equations of the fitting circles of the multi-layer holes. In experiment, coaxiality measurement accuracy is realized by a 16 μm precision LDS, and the validity of the measurement method is verified. The manufacture and measurement requirements of the coaxiality measuring rod are low, by changing the position of LDSs in the measuring rod, the serial holes with different sizes and numbers can be measured. The rapid coaxiality measurement of parts can be easily implemented in industrial sites.

ESTUDO DA CIRCUNFERÊNCIA NO ENSINO MÉDIO: SUGESTÕES DE ATIVIDADES COM A UTILIZAÇÃO DO SOFTWARE GEOGEBRA

http://dx.doi.org/10.5902/2179460X14252This article proposes three activities that can be developed to study the circle for High School students. All proposed activities use the free software of the dynamic geometry Geogebra as learning tool. The suggested activities have as goal to teach, through instruction scripts, the following content: circle equations (reduced and general), relative position between point and circle and relative position between line and circle. In addition, we will portray an analysis of the activities that based the proposal of our task when these were executed in three Technical Learning Integrated to High School’s third year junior groups. We conclude the validity of the activities by student performance on assessments, showing a better knowledge of the subject in relation to students in classes in which there GeoGebra was not used.

RIALS: RSU/INS‐aided localization system for GPS‐challenged road segments

AbstractThis paper introduces a new vehicle localization approach for global positioning system‐challenged road segments (e.g., tunnels), which takes advantage of roadside units (RSUs) and in‐vehicle inertial navigation system (INS). In the proposed approach, namely RSU/INS‐aided localization system (RIALS), vehicles only need one RSU in their transmission range for an accurate positioning. The beacons received from the RSU along with the information provided by the INS system are used for establishing and maintaining particular locus circles. After linearization, the system of locus circle equations is solved using the linear least square estimation technique, and the estimated vehicle's position is obtained. In the presence of speed variations and existing ranging and INS estimation errors, the proposed RIALS adaptively sets the sufficient number of required locus circles, aiming at keeping the localization error below a given threshold. We study the effects of ranging and INS estimation errors on localization accuracy of RIALS from analytical and simulation perspectives. Results of extensive simulations show that the localization error is more sensitive to the ranging error than the INS error. Moreover, the network traffic overhead of the proposed method is considerably lower than other competitive localization approaches. Copyright © 2015 John Wiley & Sons, Ltd.

Linear Theory for Self-Localization: Convexity, Barycentric Coordinates, and Cayley–Menger Determinants

Localization, finding the coordinates of an object with respect to other objects with known coordinates—hereinafter, referred to as anchors, is a nonlinear problem, as it involves solving circle equations when relating distances to Cartesian coordinates, or, computing Cartesian coordinates from angles using the law of sines. This nonlinear problem has been a focus of significant attention over the past two centuries and the progress follows closely with the advances in instrumentation as well as applied mathematics, geometry, statistics, and signal processing. The Internet-of-Things (IoT), with massive deployment of wireless tagged things, has renewed the interest and activity in finding novel, expert, and accurate indoor self-localization methods, where a particular emphasis is on distributed approaches. This paper is dedicated to reviewing a notable alternative to the nonlinear localization problem, i.e., a linear-convex method, based on Khan et al. ’s work. This linear solution utilizes relatively unknown geometric concepts in the context of localization problems, i.e., the barycentric coordinates and the Cayley–Menger determinants. Specifically, in an $m$ -dimensional Euclidean space, a set of $m+1$ anchors, objects with known locations, is sufficient (and necessary) to localize an arbitrary collection of objects with unknown locations—hereinafter, referred to as sensors, with a linear-iterative algorithm. To ease the presentation, we discuss the solution under a structural convexity condition, namely, the sensors lie inside the convex hull of at least $m+1$ anchors. Although rigorous results are included, several remarks and discussion throughout this paper provide the intuition behind the solution and are primarily aimed toward researchers and practitioners interested in learning about this challenging field of research. Additional figures and demos have been added as auxiliary material to support this aim.

Computation of Yvon-Villarceau circles on Dupin cyclides and construction of circular edge right triangles on tori and Dupin cyclides

Ring Dupin cyclides are non-spherical algebraic surfaces of degree four that can be defined as the image by inversion of a ring torus. They are interesting in geometric modeling because: (1) they have several families of circles embedded on them: parallel, meridian, and Yvon-Villarceau circles, and (2) they are characterized by one parametric equation and two equivalent implicit ones, allowing for better flexibility and easiness of use by adopting one representation or the other, according to the best suitability for a particular application. These facts motivate the construction of circular edge triangles lying on Dupin cyclides and exhibiting the aforementioned properties. Our first contribution consists in an analytic method for the computation of Yvon-Villarceau circles on a given ring Dupin cyclide, by computing an adequate Dupin cyclide-torus inversion and applying it to the torus-based equations of Yvon-Villarceau circles. Our second contribution is an algorithm which, starting from three arbitrary 3D points, constructs a triangle on a ring torus such that each of its edges belongs to one of the three families of circles on a ring torus: meridian, parallel, and Yvon-Villarceau circles. Since the same task of constructing right triangles is far from being easy to accomplish when directly dealing with cyclides, our third contribution is an indirect algorithm which proceeds in two steps and relies on the previous one. As the image of a circle by a carefully chosen inversion is a circle, and by constructing different images of a right triangle on a ring torus, the indirect algorithm constructs a one-parameter family of 3D circular edge triangles lying on Dupin cyclides.

DEFINITION OF DYNAMIC INDUCTANCES OF THE ASYNCHRONOUS ENGINE WITH REGARD TO PROCESSES OF SATURATION

Development of mathematical model of asynchronous machines in (d, q) coordinate system with taking into account the saturation of magnetic circuits is performed. In the paper, we used the method of dynamic inductances, which is connected with the use of a systematic study of motor properties. An analytical model of asynchronous motor magnetic circuit, which is taken into account action of the tangential and radial dynamic inductances is created. On the basis of this the sensor dynamic inductances of rich machine, which was recorded in (d, q) coordinate system of equations of rotor and stator circles of asynchronous motor with the saturation were built. The author suggests to use the method of dynamic inductances at construction of asynchronous engine mathematical model, that allows to take into account the saturation of the main magnetic path for the modes with a wide range of changes in the flow of mutual induction between the stator and the rotor, saturation flow path, the scattering modes that are characterized by large current circuits of the machine, induction, due to processes of saturation, between mutually perpendicular to the contours of the machine, as well as the joint saturation worker thread and threads scattering modes that are characterized by the significant size of the workflow and large values of currents contours of the machine. The mathematical model allows to take into account the change of the magnetic state of asynchronous motor as necessity to build adequate systems of control drives and driving