Process Of Geometry Research Articles

Determining the needs of teachers for teaching geometry education activities to children with visual impairments in early childhood using digital learning tools

The purpose of this research is to determine the needs of teachers for teaching geometry education activities to early childhood children with visual impairments using digital learning tools. The data for the study was collected during the fall semester of 2024-2025 through need analysis forms filled out by a total of 9 preschool and special education teachers working in state schools for the visually impaired located in Turkey's three largest cities: İzmir, Istanbul, and Ankara. The study is designed as a case study, one of the qualitative research designs. A single embedded case design was used in the study. In a single embedded case design, there are often multiple sub-units or layers within a single case (Yıldırım and Şimşek, 2018). The data collected in this study was analyzed using the content analysis method. When the results obtained from this research are generally examined, it was determined that the needs of teachers regarding the process of teaching and learning geometry to early childhood children with visual impairments are composed of the sub-themes of achievements, activities, and materials under the theme of the geometry teaching and learning process, and the sub-themes of learning and teaching under the theme of difficulties experienced in the geometry teaching and learning process. Additionally, the needs of teachers concerning the use of digital tools and technology in the geometry teaching and learning process were identified under the sub-themes of benefits, in-service training, and recommendations.

The Content-Validated Geometry Lessons in Islam Observed Brain-based Learning

This study examined the process of learning geometry in content-validated lessons with the integration of Islamic values as perceived to have observed brain-based learning principles. Anchored in a grounded theory, theoretical sampling was utilized among sixteen 4th and 5th grade students in geometry class including three teacher-observers and one teacher-demonstrator playing the “emic-etic” role or participant observer. Lessons in geometry with Islamic contexts were sporadically presented with citations of verses from the Holy Qur’an coupled with Islamic value-infusions. Designed in a qualitative grounded theory approach, an interview script was used for individual and focus group interviews. Ten content validated -lessons in geometry were designed to capture the Islamized learning phenomenon wherein field notes of observations and video footages were qualitatively analyzed using the lens of systematic approach coined as constant comparative method of analysis. Results indicated that substantive theory on the process of learning geometry in content-validated lessons with Islamic value-infusions as perceived to have brain-based learning was evidently observed which revolved on five sub-elements: (a) connection; (b) attention;(c) imagination and action; (d) emotions and recollection; and (e) associations. The approach to integrating Islamic values in content-validated lessons recognized the presence and the process of brain-based learning principles. Observed in cyclical context, emotion and memory play a significant role to learning guided by the content-validated lessons in geometry. The infusion of religious values and appreciation of creation informs one’s understanding of the emotions and their importance for learning which are therefore critical to brain-based learning principles.

Teaching Math through Art: a didactic sequence proposal with scripts for the construction of conics by the string art technique

The interdisciplinary studies in the teaching of mathematics through art makes this articulation a source that generates comprehensive and significant knowledge for both areas, with the possibility of exploring playfulness and creativity for educational purposes. In this context, the string art technique (which consists of building different figures as a result of the orderly manipulation of strings on points fixed on a solid surface) is shown as a potential didactic resource for the development of methodologies that can improve aspects of teaching and learning of geometric figures and their properties, such as conical sections (little explored in relation to other geometric shapes). The exploration of the technique can help the teacher in the teaching process of Analytical Geometry, through dynamic classes using manipulative materials, with the possibility of obtaining better learning results. In this sense, the present work explores the context of interdisciplinary between Mathematics and Arts and proposes a didactic sequence directed to the teaching of conic sections in High School, with string art. The didactic sequence evidences a methodology oriented to the participation of students as active in the construction of their own knowledge, based on the guidelines for the construction of geometric figures by the mediator teacher. In the professional perspective, the objective of the didactic sequence (product of this work) is to help the teacher in the construction of new teaching methodologies that contribute to improve the student's knowledge about conics, in order to obtain satisfactory results in the teaching of Geometry and overcome difficulties observed in classroom practice.

Precision Analysis of Chain Wheel Geometry Reconstruction Based on Contact and Optical Measurement Data

This study focuses on the detailed reconstruction of chain wheel geometry utilizing measurement data gathered from the MarSurfXC20 contact system and the iNEXIVE VMA 2520 optical system. Supplementary data were also gathered from a digital micrometer and a caliper to provide a comprehensive data set for the analyzed geometry. The geometric model of the chain wheel was then constructed using Siemens NX software. The reconstructed model was subsequently compared with the original design specifications to assess the fidelity of the reconstructed model. Results demonstrate a high degree of correlation between the model generated by reverse engineering and the original design model. Despite the satisfactory correlation, potential inaccuracies were identified, necessitating further research to mitigate these discrepancies and optimize the procedures for parameters beyond the established tolerance. The study affirms the feasibility of utilizing contact and optical measuring systems in the reverse engineering process of chain wheel geometry, although it underscores the need for additional refinement to improve the model's accuracy.

Portrait of Junior High School Students’ Motivation in Learning Geometry

Geometry is a branch of mathematics that deals with shapes and dimensions. In learning geometry it is not uncommon for students to experience difficulties and mistakes in understanding concepts. Motivation is an important factor that needs to be considered so that students remain enthusiastic in the learning process of geometry. Motivation becomes a driving force and trigger for students to be active in the learning process. This research aims to provide a portrait of the motivational condition of junior high school students in learning geometry. This research is quantitative descriptive. The research was conducted on 136 junior high school students who were randomly selected from 3 different cities, namely Medan, Tulungagung and Lombok. The data collection technique was carried out using a motivational questionnaire instrument. Data analysis was performed with descriptive statistical analysis. The results of this research indicate that junior high school students' motivation in learning geometry is high with a score of 3.96 on a scale of 1-5.

Efficient simulation of the heat transfer in fused filament fabrication

Heat transfer simulations of the fused filament fabrication process are an important tool to predict bonding, residual stresses and strength of 3D printed parts. But in order to capture the significant thermal gradients that occur in the FFF printing process, a fine mesh discretization and short time steps are required, leading to extensive computational efforts. In this work a simulation framework is presented which combines several efficiency measures with the objective of reducing the computational efforts required in simulating the FFF printing process without simplifying the deposition physics or reducing the overall accuracy. Thus, the material deposition has been modeled with a hybrid element activation approach and elements are adaptively coarsened through an error-based coarsening condition. Additionally, an appropriate coarsening technique is presented for geometries with air-filled infill patterns. The accuracy of the numerical framework is experimentally validated and the efficiency of the framework is validated numerically by comparing the performance of models with and without any efficiency measures. Finally, its effectiveness is shown by simulating the printing process of a larger geometry.

Research activity of students in the study of the section «Stereometry»

The article discusses the importance of developing the experience of students' research activities in the study of geometry, and in particular the section «Stereometry». The relevance of the research lies in the development of pedagogical practice of mathematics teachers for the formation of research skills of high school students, which better determine the search ability, critical thinking through reflection, comprehension when solving problems. In the process of conducting a study to develop the student's thinking ability, his own pedagogical teaching practice was analyzed. In geometry lessons, teaching methods were used to form students' research abilities in solving problems: the ability to work with text, write a short note, apply theoretical material, work with additional lines. In order to develop theoretical material, determine the research activities of students, the advanced works of scientists and teachers, and research practice by the method of pedagogical analysis were studied. As a result of observation and research of pedagogical practice of teaching, it was noticed that children began to be more interested in geometry, to think spatially, a meaningful understanding of the subject appeared. Students' research activities were organized through mathematical projects. When working with the project, students were active in studying new topics, self-esteem, motivation for development, skills for search work, the ability to explore. When observing the process of learning geometry, it was found that the development of research abilities in solving problems increased the percentage of learning quality. Therefore, it is necessary for a mathematics teacher to introduce more stereometric tasks into his teaching practice, which are designed to form critical thinking and represent spatial thinking. To form motivation, self-esteem of the student, mathematics teachers can organize work on projects.

Learning Geometry by Using Virtual Reality

With the rapid change in the society, education must evolve to adapt to the digital native students of the 21st century. A change in the current educational paradigm is thus necessary. Information and Communication Technology (ICT) is a vehicle to achieve this objective of paradigm shift in education [ 2 ]. In this paper, we propose gamification approach [ 3 ] via a virtual reality (VR) through a report of a didactic experience. A mixed method research design was adopted for this study in which students’ classification of polyhedral will be reported for the two different learning experiences using either wooden polyhedral or a VR tool within an immersive learning environment. The VR environment allows the learning of geometry in three-dimensional with a friendly interface that offers a multitude of options. It is worth highlighting the benefits of this VR tool in the teaching-learning process of geometry, making explicit the fundamental role played by ICT in meaningful learning of mathematics.

Automatização na geração de malha de um transdutor de ondas gravitacionais cilíndrico de safira

ABSTRACT: The main objective of this work is to develop an automation for a mesh generation process of a cylindrical geometry made of sapphire. The use of commercial programs that have as main technology the Finite Element Method (Ansys, Comsol Multiphysics, Abaqus) in development of gravitational wave transducers encompasses most of the theses and articles performed. The great importance of using these technologies is due to the difficulty of obtaining materials with high electrical, mechanical quality factors and experiments performed with prototypes. Given this, the idea of the author of this article is to create an automation process for mesh generation using an Open Source software called Salome-Meca. Salome is a solution that provides a generic platform for pre- and post-processing numerical simulation.

An efficient hyper-elastic model for the preforming simulation of Carbon-Kevlar hybrid woven reinforcement

An efficient hyper-elastic model that can reflect the primary mechanical behaviors of Carbon-Kevlar hybrid woven reinforcement was developed and implemented with VUMAT constitutive code for preforming simulation. The model parameters were accurately determined through the uniaxial and bias-extension tests. To calibrate the simulation code, preforming experiments of hybrid woven reinforcement over the hemisphere mold and tetrahedron mold were respectively conducted to validate the proposed hyper-elastic model. The comparison between the simulations and experiments shows that the model can not only accurately capture shear angle distribution and geometry shape after deformation, but also accurately predict the force–displacement curve and potential fiber tensile failure during the preforming process. This result indicates that the proposed model can be used to predict the preforming behavior of Carbon-Kevlar hybrid woven reinforcement, and simulate its manufacturing process of complicated geometry.

Advanced method of including housing stiffness into calculation of gear systems

One of the central goals during the design of helical gear systems is the achievement of a well-distributed contact load in the gear mesh. An equal load distribution is a key factor for a high load carrying capacity, the economic use of materials and a long lifetime. Mesh misalignment can be caused by tooth deflections, manufacturing deviations or elastic deformation of the shaft-bearing system and the gearbox housing. Those deformations have to be taken into account during the design process of adequate tooth-flank geometry. Elastic deformations of gearbox housings can be significant, especially in the case of automotive applications with aluminium cases. This paper presents an advanced method of including housing stiffness into the calculation of gear systems. A validation of the approach is carried out by comparing the calculated deformations with measurements of a static test rig of a hypoid gearbox.Many calculation programs offer the opportunity to analyse the deformation behaviour of the shaft-bearing-housing system. Most of the components in these programs are described by analytic approaches. However, components that are geometrically more complex, like the housing or planet carriers cannot be represented as easily as that by analytic expressions. There are several alternatives to take into account the elasticity of those objects. One way is to model the stiffness of the bores using imported stiffness matrices. These matrices contain the elasticity of the bores itself as well as crossover influences between the bearings. The reduced stiffness matrices may be the result of a static reduction of the geometry using the finite element method (FEM). As state of the art, the reduction is mostly carried out at the centre points of the bearing bores. The proposed advanced method uses the static reduction of geometries on several points at the bores, distributed over the circumference. This approach offers a more detailed modelling of the elastic behaviour of complex geometries within the analytic deformation calculation of gear systems. To validate the advanced approach, the calculation results of the elastic deflections of the shaft-bearing-housing system is compared with measurements of a static test rig. In the course of these comparisons, the influence of different modelling methods of gearbox housings on the accuracy of the calculation results is discussed.

Case of Actualizing Geometry Knowledge in Abstraction Thinking Level for Constructing a Figure

The purpose of studying geometry is for the development of student thinking, able to abstract and reason, against concepts in the object. Note on some study results that the combination of the student's conceptualization process and knowledge of geometry are a source of barriers to their learning. This study aims to investigate how students actualize their geometry knowledge for the development of thinking to the level of abstraction. Investigations on input, internal processing, and output. This study was conducted on high school students use questions regarding object and product of thought in geometry thinking at analysis and abstraction level. Based on study findings, students actualize their knowledge through figural aspects then developed into the conceptual aspect, and the two aspects are integrated with the relationship between properties. There is a mathematical connection to the integration process. However, because most students' understanding of geometry knowledge is still prototypical figural concepts, so there is an interaction issue between figural and conceptual aspects, namely the validity of relationship between properties. Therefore, students learn geometry in order to investigate the connections between objects and properties as a whole.

Augmented reality application: What are the constraints and perceptions of the students during the covid 19 pendemic’s 3D geometry learning process?

The Covid 19 epidemic has altered the interplay of the classroom learning process. To facilitate the learning process of 3D geometry, secondary school teachers adopt several technology items. Augmented reality technology is one of those technological goods. This study therefore aims to explain the constraints and perceptions of secondary school students during the COVID-19 pandemic, during the 3D geometry learning process. This study used a qualitative research design descriptive of it. The number of participants to this study was five, namely 3 male students and two female students. Techniques for collecting data using sheets of observations and interviews. Although data analysis by Miles and Huberman [1] adopts data analysis, which consists of data selection, data reduction, data presentation and conclusions or verification processes. Study results show that there are still many challenges faced during the learning process using augmented reality technologies, namely: (a) Constraints when downloading the program on the cellphones of the instructor and the pupil. (b) Marker constraints pertaining to AR identification. (c) Constraints on the student’s smartphone requirements. (d) Limit and network restrictions for accessing the Resources section. (e) Students found too many constraints on appraisal questions on the test checklist. While several challenges do remain, the majority of the students have a good understanding of the learning experience using augmented reality technologies.

Parametric modeling of uncut chip geometry for predicting crater wear in gear skiving

In gear skiving, tool wear is one of the primary issues owing to the large thermomechanical cutting load. However, the effective rake angle and depth-of-cut can vary continuously throughout a single cut, leading to a complex uncut chip geometry that significantly hinders the understanding of the cutting characteristics and adds further difficulty to the prediction of tool wear. This study proposes a parametric modeling method for calculating the uncut chip geometry for each cutting pass. Developments in the rake angle and depth-of-cut (as subjected to an uncut chip) were comprehensively investigated with an aim to advance the understanding of the cutting characteristics during a single cut. Based on the uncut chip geometry, the crater wear was successfully predicted using the derived stress and temperature data, followed by a single-tooth skiving wear test verification. By comparing numerical and experimental results for crater wear, an error of less than 5 % was obtained in both depth and area. The proposed method provides a non-CAD/CAM-engine-software/environment-based alternative for calculating the process of an uncut chip geometry, clearly advancing the flexibility in further potential applications such as cutting parameter optimization and cutter design.

Potentials of an adaptive blank positioning to control material and process fluctuations in deep drawing

Series production of sheet metal components in press shops is permanently subjected to an increasing pressure in time, cost and quality. Varying sheet metal properties due to batch fluctuations and changing process conditions lead to an increase of try out time phase and scrap rate, resulting in a demand for adaptive control strategies for deep drawing. Today, these chal-lenges are met by integrating sensors and actuators into tool structure which measure and control part quality, mainly through blank draw-in. However, such tool-based control systems require a complex and cost-intensive modification of the existing die or press technology. Against this background, the active adjustment of blank position prior the deep drawing process realized with an intelligent transfer and positioning system as a promising approach towards economic and technical aspects. This paper deals with blank positioning and its sensitivity to quality-related failures of deep drawn sheet metal components like splits and wrinkles. Therefore, a numerical study was conducted on a deep drawing process of an exemplary structural part geometry, wherein a typical fluctuation of material parameters and variation of local friction conditions was simulated. Subsequently, correlations between process disturbance and blank draw-in were elaborated, thus using local draw-in values as controlled variables for a closed loop system. Sim-ulation results showed that the manipulating parameter, i.e. the blank position prior deep draw-ing, reveals a significant influence on the draw-in and therefore on the component s quality. An essential finding of this study is the numerical proof of concept for this new deep drawing control strategy, demonstrated for different process conditions. Finally, disturbances in the deep drawing process considered could be successfully controlled by adapting the blank position.

Design and Commissioning of a Combustor Simulator Combining Swirl and Entropy Wave Generation

Modern aero-engine combustion chambers burn a lean and premixed mixture, generating a turbulent flame which involves large heat-release fluctuations, thus producing unsteady temperature phenomena commonly referred to as entropy waves (EWs). Furthermore, to enhance the fuel air mixing, combustion air is swirled, leading to vorticity disturbances. These instabilities represent one of the biggest challenges in gas turbine design. In this paper, the design and testing of a novel entropy wave generator (EWG) equipped with a swirler generator (SG) are described. The novel EWG will be used in future works on the high-speed test rig at Politecnico di Milano to study the combustor–turbine interaction. The paper shows the process of the EWG geometry and layout. The EWG is able to produce an engine-representative EW, the extreme condition is at the maximum frequency of 110 Hz, a peak-to-valley temperature value of 20 °C and swirling angles of ±25° are measured. By virtue of these results, the proposed system outperforms other EWG devices documented in the literature. Furthermore, the addition of a swirling generator makes this device one of a kind.

КОНЕЧНО-ЭЛЕМЕНТНОЕ МОДЕЛИРОВАНИЕ ПРОЦЕССА ФОРМОИЗМЕНЕНИЯ ШАРНИРНО-СТЕРЖНЕВОЙ СИСТЕМЫ ПРИ УПРАВЛЯЕМОМ КИНЕМАТИЧЕСКОМ ВОЗДЕЙСТВИИ

For regular hinge-rod systems, an engineering technique for analyzing the stress-strain state is developed, taking into account the transformation of the shape of the structure by folding repeated fragments in the plane of the smallest stiffness. As a result, the original straight shape turns into an arched truss. The proposed meth-od is based on the extension of the modified Lagrange method to the problem of analyzing the stress-strain state of a spatial truss structure with kinematically directed shape change. A step-by-step adjustment of the structure geometry is used, taking into account the resulting nodal displacements. For the software implemen-tation of the proposed calculation algorithm, a macro is compiled in the APDL language embedded in the ANSYS Mechanical software package. A step-by-step procedure was tested that simulates the transformation process of the spatial farm geometry.

A triple‐band circularly polarized annular ring antenna with asymmetric ground plane for wireless applications

AbstractHerein a compact triple‐band circularly polarized (CP) microstrip patch antenna, loaded with a single annular ring patch with eight symmetrical slots along its periphery and a series of octagonal closed ring resonators (CRRs) on the opposite side of the substrate, is proposed. Evolution process of the antenna geometry reveals that the eight symmetrical slots and the CRRs are responsible for increased impedance bandwidth (IBW), while simulated (high‐frequency structure simulator (HFSS) and computer simulation tool) triple CP bands obtained due to the uses of crossshaped slit resonating at 7.5 GHz (152.2 MHz); asymmetric ground plane at 10.2 GHz (161 MHz); and square open‐loop at 12.2 GHz (112.5 MHz). Series of parasitic strips improved CP radiation and remove ripple in the radiation pattern. The antenna presented here, is compact, fabricated with an optimized dimension of 35 × 30 × 1.6 mm3, on low cost FR‐4 substrate with copper cladding. The measured <10‐dB IBW ranges from 4.08‐5.05 GHz and 5.98 GHz up to 13.6 GHz. Simulated maximum peak gain found to be 4.45 dBi at 13 GHz. The antenna proposed herein is appropriate for wireless applications.

Optimization of the Impeller Geometry for an Automotive Torque Converter Using Response Surface Methodology and Desirability Function

Response surface methodology (RSM) based on desirability function approach (DFA) is applied to obtain an optimal design of the impeller geometry for an automotive torque converter. The relative importance of six design parameters including impeller blade number, blade thickness, bias angle, scroll angle, inlet angle and exit angle is investigated using orthogonal design approach. The impeller inlet angle, exit angle and bias angle are found to exert the greatest influence on the overall performance of a torque converter, with two flow area factors being considered, namely 17% and 20%. Then, RSM together with central composite design (CCD) method is used to in-depth evaluate the interaction effect of the three key parameters on converter performance. The results demonstrate that impeller exit angle has the strongest impact on peak efficiency, with larger angles yielding the most favorable results. The stall torque ratio maximization is attainable with the increase of impeller bias angle and inlet angle together with smaller exit angle. In the end, an optimized design for the impeller geometry is obtained with stall torque ratio and peak efficiency increased by 1.62% and 1.1%, respectively. The new optimization method can be used as a reference for performance enhancement in the design process of impeller geometry for an automotive torque converter.

A Signal-Processing Neural Model Based on Biological Retina

Image signal processing has considerable value in artificial intelligence. However, due to the diverse disturbance (e.g., color, noise), the image signal processing, especially the representation of the signal, remains a big challenge. In the human visual system, it has been justified that simple cells in the primary visual cortex are obviously sensitive to vision signals with partial orientation features. In other words, the image signals are extracted and described along the pathway of visual processing. Inspired by this neural mechanism of the primary visual cortex, it is possible to build an image signal-processing model as the neural architecture. In this paper, we presented a method to process the image signal involving a multitude of disturbance. For image signals, we first extracted 4 rivalry pathways via the projection of color. Secondly, we designed an algorithm in which the computing process of the stimulus with partial orientation features can be altered into a process of analytical geometry, resulting in that the signals with orientation features can be extracted and characterized. Finally, through the integration of characterizations from the 4 different rivalry pathways, the image signals can be effectively interpreted and reconstructed. Instead of data-driven methods, the presented approach requires no prior training. With the use of geometric inferences, the method tends to be interpreted and applied in the signal processor. The extraction and integration of rivalry pathways of different colors allow the method to be effective and robust to the signals with the image noise and disturbance of colors. Experimental results showed that the approach can extract and describing the image signal with diverse disturbance. Based on the characterization of the image signal, it is possible to reconstruct signal features which can effectively represent the important information from the original image signal.