Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 13

Geometry Related Abstracts

13 Triangulations via Iterated Largest Angle Bisection

Authors: Yeonjune Kang

Abstract:

A triangulation of a planar region is a partition of that region into triangles. In the finite element method, triangulations are often used as the grid underlying a computation. In order to be suitable as a finite element mesh, a triangulation must have well-shaped triangles, according to criteria that depend on the details of the particular problem. For instance, most methods require that all triangles be small and as close to the equilateral shape as possible. Stated differently, one wants to avoid having either thin or flat triangles in the triangulation. There are many triangulation procedures, a particular one being the one known as the longest edge bisection algorithm described below. Starting with a given triangle, locate the midpoint of the longest edge and join it to the opposite vertex of the triangle. Two smaller triangles are formed; apply the same bisection procedure to each of these triangles. Continuing in this manner after n steps one obtains a triangulation of the initial triangle into 2n smaller triangles. The longest edge algorithm was first considered in the late 70’s. It was shown by various authors that this triangulation has the desirable properties for the finite element method: independently of the number of iterations the angles of these triangles cannot get too small; moreover, the size of the triangles decays exponentially. In the present paper we consider a related triangulation algorithm we refer to as the largest angle bisection procedure. As the name suggests, rather than bisecting the longest edge, at each step we bisect the largest angle. We study the properties of the resulting triangulation and prove that, while the general behavior resembles the one in the longest edge bisection algorithm, there are several notable differences as well.

Keywords: Geometry, Applied Mathematics, angle bisectors, triangulation

Procedia PDF Downloads 258
12 Educatronic Prototype for Learning Geometry, Based on a Multitouch Surface

Authors: Vicario Marina, Bustos Freddy, Olivares Jesús, Gómez Pilar

Abstract:

This paper presents a didactic model and a tool as educational resources to support the learning of geometry; they focus on topics difficult to understand. The target population is elementary school students. The tool is based on a collaborative educational approach using multi-touch devices. The proposal is based on the challenges found in the instructional design and prototype implementation. Traditionally, elementary students have had many problems assimilating mathematical topics; this new Educatronic prototype facilitates the learning experience using exercises and they were tested with different children demonstrating the benefits of the prototype by improving their mathematical skills.

Keywords: Geometry, Mathematics, Educational Computing, primary school, educational informatics, educatronic prototype, multitouch surface

Procedia PDF Downloads 169
11 A Novel Design of Inset Feed Patch Antenna for Ultra Wide Band Application

Authors: Priyanka Aggarwal, Priyanka Mangla

Abstract:

This work has focused on the aspect of UWB antenna design, which is very suitable for portable UWB applications. The design of new UWB antenna faces some challenges. The antenna should be compact, preferably conformal, and low cost for manufacture, and have good electrical performance, such as good matching, directional radiation performance over a wide band, good time response, etc. Keeping these goals in mind a compact and directional compact open-slot antenna was built. The antenna radiating structure is in the form of two exponentially tapered arms that lie on the opposite sides of the substrate. The antenna operates over the frequency band from 2.95 GHz to more than 12.1 GHz. It exhibits a directive radiation performance with a peak gain which is between 5.4 dBi and 8.3 dBi in the specified band. The antenna has linear phase response over the entire UWB frequency range and hence constant group delay which is vital for transmission and reception of sub-nanosecond pulses. Due to its planar profile, physically compact size, wide impedance bandwidth, directive performance over a wide bandwidth proposed antenna is a good candidate for portable UWB applications and other UWB integrated circuits.

Keywords: Geometry, Antenna, inset feed patch antenna, ultra wide band, radiation performance

Procedia PDF Downloads 303
10 Generating Spherical Surface of Wear Drain in Cutting Metal by Finite Element Method Analysis

Authors: D. Kabeya Nahum, L. Y. Kabeya Mukeba

Abstract:

In this work, the design of surface defects some support of the anchor rod ball joint. The future adhesion contact was rocking in manufacture machining, for giving by the numerical analysis of a short simple solution of thermo-mechanical coupled problem in process engineering. The analysis of geometrical evaluation and the quasi-static and dynamic states are discussed in kinematic dimensional tolerances onto surfaces of part. Geometric modeling using the finite element method (FEM) in rough part of such phase provides an opportunity to solve the nonlinearity behavior observed by empirical data to improve the discrete functional surfaces. The open question here is to obtain spherical geometry of drain wear with the operation of rolling. The formulation with (1 ± 0.01) mm thickness near the drain wear semi-finishing tool for studying different angles, do not help the professional factor in design cutting metal related vibration, friction and interface solid-solid of part and tool during this physical complex process, with multi-parameters no-defined in Sobolev Spaces. The stochastic approach of cracking, wear and fretting due to the cutting forces face boundary layers small dimensions thickness of the workpiece and the tool in the machining position is predicted neighbor to ‘Yakam Matrix’.

Keywords: Geometry, Simulation, FEM, tool, part, spherical surface engineering, workpiece

Procedia PDF Downloads 147
9 The Optimization Process of Aortic Heart Valve Stent Geometry

Authors: Arkadiusz Mezyk, Wojciech Klein, Mariusz Pawlak, Jacek Gnilka

Abstract:

The aortic heart valve stents should fulfill many criterions. These criteria have a strong impact on the geometrical shape of the stent. Usually, the final construction of stent is a result of many year experience and knowledge. Depending on patents claims, different stent shapes are produced by different companies. This causes difficulties for biomechanics engineers narrowing the domain of feasible solutions. The paper present optimization method for stent geometry defining by a specific analytical equation based on various mathematical functions. This formula was implemented as APDL script language in ANSYS finite element environment. For the purpose of simulation tests, a few parameters were separated from developed equation. The application of the genetic algorithms allows finding the best solution due to selected objective function. Obtained solution takes into account parameters such as radial force, compression ratio and coefficient of expansion on the transverse axial.

Keywords: Geometry, Finite Element Method, optimization process, aortic stent

Procedia PDF Downloads 152
8 The Fashion Fiesta: An Approach for Creating an Environment of Celebration by Uniting Two Art Forms; Fashion and Dance

Authors: Salman Jamil, Iqra Khan, Ghousia Saeed

Abstract:

Fashion is the soul of styles. People of all times want to look trendy, eye catching and unique among all. For this reason, people always adopt different flairs in their outfits including their clothes, shoes, bags and other accessories. However, unfortunately, there is lack of opportunity for accommodating the fashion exposure activities expressed with the folk dances of different regions so as to exhibit the fashion of Pakistan to the world. The paper focuses on the vibrant setting of the whole building according to the social patterns, folk and local trends and existing environment of Lahore. This is done by studying each of the aspect obtained from objectives through research questions evolved from the objectives. The answers to these questions are found through case studies and the existing theories in the world in relevance to the topic. The paper finds out how the geometry of dance works with design principles to create transparent geometry of fashion building. This all creates the fiesta environment taken from the locality of the region from the local and cultural lifestyles of the locals and then assembling it together to create a full festivity experience throughout the building.

Keywords: Geometry, Fashion, transparent, folk dance, local trends, social patterns

Procedia PDF Downloads 197
7 Application of Learning Media Based Augmented Reality on Molecular Geometry Concept

Authors: F. S. Irwansyah, I. Farida, Y. Maulana

Abstract:

Studying chemistry requires the ability to understand three levels of understanding in the form of macroscopic, submicroscopic and symbolic, but the lack of emphasis on the submicroscopic level leads to the understanding of chemical concepts becoming incomplete, due to the limitations of the tools capable of providing visualization of submicroscopic concepts. The purpose of this study describes the stages of making augmented reality learning media on the concept of molecular geometry and analyze the feasibility test result of augmented reality learning media on the concept of molecular geometry. This research uses Research and Development (R & D) method which produces a product of AR learning media on molecular geometry concept and test the effectiveness of the product. Research stages include concept analysis and learning indicators, design development, validation, feasibility, and limited testing. The stages of validation and limited trial are aimed to get feedback in the form of assessment, suggestion and improvement on learning aspect, material substance aspect, visual communication aspect and software engineering aspects and media feasibility in terms of media creation purpose to be used in learning. The results of the overall feasibility test obtained r-calculation 0,7-0,9 with the interpretation of high feasibility value, whereas the result of limited trial got the percentage of eligibility with the average value equal to 70,83-92,5%. This percentage indicates that AR's learning media product on the concept of molecular geometry, deserves to be used as a learning resource.

Keywords: Geometry, Augmented Reality, android, chemical learning

Procedia PDF Downloads 65
6 Uncovering Geometrical Ideas in Weaving: An Ethnomathematical Approaches to School Pedagogy

Authors: Jaya Bishnu Pradhan

Abstract:

Weaving mat is one of the common activities performed in different community generally in the rural part of Nepal. Mat weavers’ practice mathematical ideas and concepts implicitly in order to perform their job. This study is intended to uncover the mathematical ideas embedded in mat weaving that can help teachers and students for the teaching and learning of school geometry. The ethnographic methodology was used to uncover and describe the beliefs, values, understanding, perceptions, and attitudes of the mat weavers towards mathematical ideas and concepts in the process of mat weaving. A total of 4 mat weavers, two mathematics teachers and 12 students from grade level 6-8, who are used to participate in weaving, were selected for the study. The whole process of the mat weaving was observed in a natural setting. The classroom observation and in-depth interview were taken with the participants with the help of interview guidelines and observation checklist. The data obtained from the field were categorized according to the themes regarding mathematical ideas embedded in the weaving activities, and its possibilities in teaching learning of school geometry. In this study, the mathematical activities in different sectors of their lives, their ways of understanding the natural phenomena, and their ethnomathematical knowledge were analyzed with the notions of pluralism. From the field data, it was found that the mat weaver exhibited sophisticated geometrical ideas in the process of construction of frame of mat. They used x-test method for confirming if the mat is rectangular. Mat also provides a good opportunity to understand the space geometry. A rectangular form of mat may be rolled up when it is not in use and can be converted to a cylindrical form, which usually can be used as larder so as to reserve food grains. From the observation of the situations, this cultural experience enables students to calculate volume, curved surface area and total surface area of the cylinder. The possibilities of incorporation of these cultural activities and its pedagogical use were observed in mathematics classroom. It is argued that it is possible to use mat weaving activities in the teaching and learning of school geometry.

Keywords: Geometry, ethnomathematics, ethnography, mat weaving, school pedagogy

Procedia PDF Downloads 11
5 Mathematics Professional Development: Uptake and Impacts on Classroom Practice

Authors: Karen Koellner, Nanette Seago, Jennifer Jacobs, Helen Garnier

Abstract:

Although studies of teacher professional development (PD) are prevalent, surprisingly most have only produced incremental shifts in teachers’ learning and their impact on students. There is a critical need to understand what teachers take up and use in their classroom practice after attending PD and why we often do not see greater changes in learning and practice. This paper is based on a mixed methods efficacy study of the Learning and Teaching Geometry (LTG) video-based mathematics professional development materials. The extent to which the materials produce a beneficial impact on teachers’ mathematics knowledge, classroom practices, and their students’ knowledge in the domain of geometry through a group-randomized experimental design are considered. Included is a close-up examination of a small group of teachers to better understand their interpretations of the workshops and their classroom uptake. The participants included 103 secondary mathematics teachers serving grades 6-12 from two US states in different regions. Randomization was conducted at the school level, with 23 schools and 49 teachers assigned to the treatment group and 18 schools and 54 teachers assigned to the comparison group. The case study examination included twelve treatment teachers. PD workshops for treatment teachers began in Summer 2016. Nine full days of professional development were offered to teachers, beginning with the one-week institute (Summer 2016) and four days of PD throughout the academic year. The same facilitator-led all of the workshops, after completing a facilitator preparation process that included a multi-faceted assessment of fidelity. The overall impact of the LTG PD program was assessed from multiple sources: two teacher content assessments, two PD embedded assessments, pre-post-post videotaped classroom observations, and student assessments. Additional data were collected from the case study teachers including additional videotaped classroom observations and interviews. Repeated measures ANOVA analyses were used to detect patterns of change in the treatment teachers’ content knowledge before and after completion of the LTG PD, relative to the comparison group. No significant effects were found across the two groups of teachers on the two teacher content assessments. Teachers were rated on the quality of their mathematics instruction captured in videotaped classroom observations using the Math in Common Observation Protocol. On average, teachers who attended the LTG PD intervention improved their ability to engage students in mathematical reasoning and to provide accurate, coherent, and well-justified mathematical content. In addition, the LTG PD intervention and instruction that engaged students in mathematical practices both positively and significantly predicted greater student knowledge gains. Teacher knowledge was not a significant predictor. Twelve treatment teachers self-selected to serve as case study teachers to provide additional videotapes in which they felt they were using something from the PD they learned and experienced. Project staff analyzed the videos, compared them to previous videos and interviewed the teachers regarding their uptake of the PD related to content knowledge, pedagogical knowledge and resources used. The full paper will include the case study of Ana to illustrate the factors involved in what teachers take up and use from participating in the LTG PD.

Keywords: Geometry, pedagogical content knowledge, mathematics professional development, teacher learning

Procedia PDF Downloads 13
4 The Impact of Professional Development on Teachers’ Instructional Practice

Authors: Karen Koellner, Nanette Seago, Jennifer Jacobs, Helen Garnier

Abstract:

Although studies of teacher professional development (PD) are prevalent, surprisingly most have only produced incremental shifts in teachers’ learning and their impact on students. There is a critical need to understand what teachers take up and use in their classroom practice after attending PD and why we often do not see greater changes in learning and practice. This paper is based on a mixed methods efficacy study of the Learning and Teaching Geometry (LTG) video-based mathematics professional development materials. The extent to which the materials produce a beneficial impact on teachers’ mathematics knowledge, classroom practices, and their students’ knowledge in the domain of geometry through a group-randomized experimental design are considered. In this study, we examine a small group of teachers to better understand their interpretations of the workshops and their classroom uptake. The participants included 103 secondary mathematics teachers serving grades 6-12 from two states in different regions. Randomization was conducted at the school level, with 23 schools and 49 teachers assigned to the treatment group and 18 schools and 54 teachers assigned to the comparison group. The case study examination included twelve treatment teachers. PD workshops for treatment teachers began in Summer 2016. Nine full days of professional development were offered to teachers, beginning with the one-week institute (Summer 2016) and four days of PD throughout the academic year. The same facilitator-led all of the workshops, after completing a facilitator preparation process that included a multi-faceted assessment of fidelity. The overall impact of the LTG PD program was assessed from multiple sources: two teacher content assessments, two PD embedded assessments, pre-post-post videotaped classroom observations, and student assessments. Additional data was collected from the case study teachers including additional videotaped classroom observations and interviews. Repeated measures ANOVA analyses were used to detect patterns of change in the treatment teachers’ content knowledge before and after completion of the LTG PD, relative to the comparison group. No significant effects were found across the two groups of teachers on the two teacher content assessments. Teachers were rated on the quality of their mathematics instruction captured in videotaped classroom observations using the Math in Common Observation Protocol. On average, teachers who attended the LTG PD intervention improved their ability to engage students in mathematical reasoning and to provide accurate, coherent, and well-justified mathematical content. In addition, the LTG PD intervention and instruction that engaged students in mathematical practices both positively and significantly predicted greater student knowledge gains. Teacher knowledge was not a significant predictor. Twelve treatment teachers were self-selected to serve as case study teachers to provide additional videotapes in which they felt they were using something from the PD they learned and experienced. Project staff analyzed the videos, compared them to previous videos and interviewed the teachers regarding their uptake of the PD related to content knowledge, pedagogical knowledge and resources used.

Keywords: Geometry, Professional Development, pedagogical content knowledge, teacher learning

Procedia PDF Downloads 37
3 Vehicle Maneuverability on Horizontal Curves on Hilly Terrain: A Study on Shillong Highway

Authors: Sapan Tiwari, Surendra Choudhary

Abstract:

The driver has two fundamental duties i) controlling the position of the vehicle along the longitudinal and lateral direction of movement ii) roadway width. Both of these duties are interdependent and are concurrently referred to as two-dimensional driver behavior. One of the main problems facing driver behavior modeling is to identify the parameters for describing the exemplary driving conduct and car maneuver under distinct traffic circumstances. Still, to date, there is no well-accepted theory that can comprehensively model the 2-D driver conduct (longitudinal and lateral). The primary objective of this research is to explore the vehicle's lateral longitudinal behavior in the heterogeneous condition of traffic on horizontal curves as well as the effect of road geometry on dynamic traffic parameters, i.e., car velocity and lateral placement. In this research, with their interrelationship, a thorough assessment of dynamic car parameters, i.e., speed, lateral acceleration, and turn radius. Also, horizontal curve road parameters, i.e., curvature radius, pavement friction, are performed. The dynamic parameters of the various types of car drivers are gathered using a VBOX GPS-based tool with high precision. The connection between dynamic car parameters and curve geometry is created after the removal of noise from the GPS trajectories. The major findings of the research are that car maneuvers with higher than the design limits of speed, acceleration, and lateral deviation on the studied curves of the highway. It can become lethal if the weather changes from dry to wet.

Keywords: Geometry, Terrain, maneuverability, trajectory, VBOX

Procedia PDF Downloads 1
2 Role of Symbolism in the Journey towards Spirituality: A Case Study of Mosque Architecture in Bahrain

Authors: Ayesha Agha Shah

Abstract:

The purpose of a mosque or a place of worship is to build a spiritual relation with God. If the sense of spirituality is not achieved, then sacred architecture appears to be lacking depth. Form and space play a significant role to enhance the architectural quality to impart a divine feel to a place. To achieve this divine feeling, form and space, and unity of opposites, either abstract or symbolic can be employed. It is challenging to imbue the emptiness of a space with qualitative experience. Mosque architecture mostly entails traditional forms and design typology. This approach for Muslim worship produces distinct landmarks in the urban neighborhoods of Muslim societies, while creating a great sense of spirituality. The universal symbolic characters in the mosque architecture had prototype geometrical forms for a long time in history. However, modern mosques have deviated from this approach to employ different built elements and symbolism, which are often hard to be identified as related to mosques or even as Islamic. This research aims to explore the sense of spirituality in modern mosques and questions whether the modification of geometrical features produce spirituality in the same manner. The research also seeks to investigate the role of ‘geometry’ in the modern mosque architecture. The research employs the analytical study of some modern mosque examples in the Kingdom of Bahrain, reflecting on the geometry and symbolism adopted in the new mosque architecture design. It buttresses the analysis by the engagement of people’s perceptions derived using a survey of opinions. The research expects to see the significance of geometrical architectural elements in the mosque designs. It will find answers to the questions such as; what is the role of the form of the mosque, interior spaces and the effect of the modified symbolic features in the modern mosque design? How can the symbolic geometry, forms and spaces of a mosque invite a believer to leave the worldly environment behind and move towards spirituality?

Keywords: Geometry, Symbolism, Spirituality, Mosque Architecture

Procedia PDF Downloads 1
1 Immediate Geometric Solution of Irregular Quadrilaterals: A Digital Tool Applied to Topography

Authors: Miguel Mariano Rivera Galvan

Abstract:

The purpose of this research was to create a digital tool by which users can obtain an immediate and accurate solution of the angular characteristics of an irregular quadrilateral. The development of this project arose because of the frequent absence of a polygon’s geometric information in land ownership accreditation documents. The researcher created a mathematical model using a linear approximation iterative method, employing various disciplines and techniques including trigonometry, geometry, algebra, and topography. This mathematical model uses as input data the surface of the quadrilateral, as well as the length of its sides, to obtain its interior angles and make possible its representation in a coordinate system. The results are as accurate and reliable as the user requires, offering the possibility of using this tool as a support to develop future engineering and architecture projects quickly and reliably.

Keywords: Geometry, Solution, mathematical model, digital tool, quadrilateral

Procedia PDF Downloads 1