Plane Figures Research Articles

Virtual Seifert surfaces

A virtual knot that has a homologically trivial representative [Formula: see text] in a thickened surface [Formula: see text] is said to be an almost classical (AC) knot. [Formula: see text] then bounds a Seifert surface [Formula: see text]. Seifert surfaces of AC knots are useful for computing concordance invariants and slice obstructions. However, Seifert surfaces in [Formula: see text] are difficult to construct. Here, we introduce virtual Seifert surfaces of AC knots. These are planar figures representing [Formula: see text]. An algorithm for constructing a virtual Seifert surface from a Gauss diagram is given. This is applied to computing signatures and Alexander polynomials of AC knots. A canonical genus of AC knots is also studied. It is shown to be distinct from the virtual canonical genus of Stoimenow–Tchernov–Vdovina.

Nonlinear Structural Performance of a Historical Brick Masonry Inverted Dome

ABSTRACT Traditional domes are obtained by double curvature shells, which can be rotationally formed by any curved geometrical plane figure rotating about a central vertical axis. They are self-supported and stabilized by the force of gravity acting on their weight to hold them in compression. However, the behavior of inverted domes is different since the dome is downward and masonry inverted domes and their structural behaviors in the literature received limited attention. This article presents a nonlinear finite element analysis of historical brick masonry inverted domes under static and seismic loads. The brick masonry inverted dome in the tomb of scholar Ahmed-El Cezeri, town of Cizre, Turkey, constructed in 1508 is selected as an application. First, a detailed literature review on the masonry domes is given and the selected inverted dome is described briefly. 3D solid and continuum finite element models of the inverted masonry dome are obtained from the surveys. An isotropic Concrete Damage Plasticity (CDP) material model adjusted to masonry structures with the same tensile strength assumed along the parallel and meridian directions of the inverted dome is considered. The nonlinear static analyses and a parametric study by changing the mechanical properties of the brick unit of the inverted masonry dome are performed under gravity loads. The acceleration records of vertical and horizontal components of May 1, 2003 Bingöl earthquake (Mw = 6.4), Turkey, occurred near the region, are chosen for the nonlinear seismic analyses. Nonlinear step by step seismic analyses of the inverted dome are implemented under the vertical and horizontal components of the earthquake, separately. Static modal and seismic responses of the inverted masonry dome are evaluated using mode shapes, minimum and maximum principal strains and stresses, and damage propagations.

Designing of realistic mathematics learning based on ethnomathematics and plane figure

The goal of this research is to make the design of multimedia based on mathematics learning using Java. This research method is research and development. The method of this research is research and development (RnD). The location of the researches is at elementary school which based culture in Purwakarta Regency. Then the team conducted a SWOT analysis and designed “plane” applications with realistic approaches mathematics education based ethno mathematics. The material used is plane figure using a realistic mathematical approach. The result of this research is the design of mathematics learning which will be used as the material of making application which used in the process of learning mathematics in elementary school.

Ethnomathematics in Balinese culture as a learning material for logic and reasoning geometry

Indonesia’s inVolvement in international tests, one of which PISA (Program for International Student Assessment), shows that Indonesia learners are less capble of using mathematical concepts to solve problems associated with real life. This is because these students tend to be taught practical formulas that will be used to answer questions in the exam. This research aimed at describing ethnomathematics in some Balinese cultural elements; ceniga, the yard size based on asta kosala-kosali, and also the pattern of Legong dancer position. Those three cultural elements were used because it is appropriate with plane figure geometry material for seventh grade students and further it is hoped to create ethnomathematics-based geometry problems. This research was a descriptive qualitative. The data were collected by conducting Balinese culture based geometry test to know the seventh grade students’ logic and mathematics reasoning ability that had been chosen as the subject of the research based on the performance rubrics. The results of research show that there are significant mathematical abilities of students to logic and reasoning in solving geometry-based culture of Bali.

Misconceptions of seventh grade students in solving geometry problem type national examinations

The general aim of mathematics is stated as making an individual acquire the mathematical knowledge needed in the daily basis, teaching how to solve problems, making him/her have a method of solving problems and acquiring reasoning methods. For this purpose to acquire mathematical concepts one should be able to visualize the mathematics problems. In other words, mathematics is the field in which preconditions are crucial so before the teaching process student backgrounds on the subject should be tested. The principal aim of this study is to find the weaknesses of secondary school students at geometry questions of measures, angles, and shapes in SMP N 2 Pundong. The year 7 curriculum contains 4 geometry topics out of 17 mathematics topics. In addition to this, this study aims to find out the mistakes, 7th-grade students made in solving geometry problem type national examinations. To collect data, students were tested using 10 questions on geometry to analyze their problem-solving skills and to test how much they acquired the last academic year. Frequency distribution table were used in data analysis. A descriptive qualitative methodology and teacher interview were used in the study to analyze and interpret the results. The results from this study revealed that 7th-grade secondary school students have a number of misconceptions, lack of background knowledge, reasoning and basic operation mistakes at the topics mentioned. The misconceptions divide into three categories namely errors in using formula of geometry, errors in identifying the characteristic of planar figure, and errors in interpreting story problems in mathematical form.

Epistemological obstacle on the topic of triangle and quadrilateral

This study aims to investigate how students understanding of triangle and quadrilateral topic. It was part of didactical design research which was conducted on 33 students who have learned about triangle and quadrilateral. Data were collected through the students answers and interview related to how students find solution to problems on the topic of geometry. The result found of the type of learning obstacle that is epistemological obstacle that impact on the concept error in solving the problem. The limited knowledge of students when understanding the basic topics in identify the elements and the properties of a plane figure is a factor causing the emergence of common errors in the topic of geometry.

数学における創造性態度と学業成績の関係 : 中学校1年「平面図形」を対象として

数学における創造性態度と学業成績の関係 : 中学校1年「平面図形」を対象として

The Use of Probing Prompting Learning (PPL) and Inside Outside Circle (IOC) Model to Learning Outcome of Plane Figure Material

This study aims to discover: (1) the difference of the learning outcomes of plane (geometry) material between the use of Probing Prompting Learning (PPL) model and Inside Outside Circle (IOC) model; (2) the difference of the learning outcomes of plane figure material between students with high prior knowledge and students with low prior knowledge; (3) the influence of the interaction between the models and students’ prior knowledge towards the learning outcomes of plane figure material. This study uses true experimental design as the research design. The population of the study consists of students from two elementary school in Surabaya in total of 134 students. The instruments used in this study are the prior knowledge test and the learning result test. The data analysis method used to test and to verify the hypotheses was two-way ANOVA test. The result of the study indicates that: (1) there is a difference in the learning outcomes of plane figure material between the PPL model and the IOC model; (2) there is a difference in the learning outcomes of plane figure material for students with high prior knowledge and low prior knowledge; (3) there is a correlation between the model and prior knowledge towards the learning outcomes of plane figure material.

Un percorso di storia della matematica nella scuola media: la quadratura di figure piane

This contribution describes a didactic experience in mathematics for ninth grade students. The project aims to study the possible quadrature of some plane figures, framing the activity in its historical context, from Greek mathematicians of the fifth century BC to Ferdinand Lindemann in 1882. Thanks to exploration and collaboration, the students come to realize a booklet with the quadrature of the main polygons meant for schoolmates of other classes.

Pengaruh Penggunaan Software Geometer Sketchpad V4 Terhadap Kemampuan Pemahaman Konsep Bangun Datar

The background of the research is students’ comprehension of two dimentional figure was low. It caused learning meadia that used by teacher was less varied and it cannot attract students’ attention in learning. So, students’ have difficulties to retell a concept that they have learned with classified characteristic of plane figure, determine circumference and area of plane figure. The purpose of this research was conducted to know the effect of using Software Geometer Sketchpad V4 toward students’ figure concept comprehension at VII class of SMP Negeri 11 Padangsidimpuan. The theories that used in this research is Bruner Theory about the important of comprehension about the best way for student’s to learning concepts or in mathematics principle was constructed a representation from the concepts itself, and Ausubel theory is about learning meaning concepts. This research is quantitative research with experiment method used Pretest-Posttest Control Group Desain. The population in this research is students at VII Class SMP Negeri 11 Padangsidimpuan that has total class is 3 class, with 70 students. The researcher taken the sample used cluster random sampling techniqueis 43 students. Sample in experiment class that give treated are 23 students and control class that untreated are 23 students. Data processing and data analysis is done with used formula Uji t. Based on normality test and homogeneity test from the both of classes were normally distributed and homogeneous. The Test of t-test is obtained from the result of hypotheses that show Tcount = 3,603 >Ttable = 2,015, so Ho was rejected and Ha was be ajjected. It concluded there is a significant effect of software geometer sketchpad V4 toward students’ two dimentional figure comprehension concept at VII Class of SMP NegeriPadangsidimpuan.

IMPROVING PROBLEM-SOLVING SKILL IN PLANE FIGURE AND SOLID FIGURE ESSAY THROUGH THE ASSURANCE, RELEVANCE, INTEREST, ASSESSMENT, SATISFACTION (ARIAS) LEARNING METHODOLOGY

<p><em>The students’ability level of solving the problem is still low. Regarding the importance of having the problem-solving skill itself, there should be alternative methods to support the students to solve the problem. The aim of this research is to examine the increased level of problem-solving skill on a plane figure and a solid figure essay by Assurance, Relevance, Interest, Assessment, Satisfaction (ARIAS) learning model for grade V students of SD Negeri Tunggulsari II No. 179 Surakarta academic year 2017/2018. This research conducted in two cycles with the teacher and 29 students from grade V as the subject. </em><em>The data were collected by interview, observation, test, and document review. Data validaty is tested by content validity,triangulation of source and technique.</em><em>The results show that the use of ARIAS learning model improving the problem-solving skill on a plane figure and solid figure essay. It can be proven by the increasing percentage of classical completeness on the pre-cycle of 17,24%, increased to 27,59%</em><em> </em><em>in the first cycle and increased to </em><em>86,21</em><em>% in the second cycle. The conclusion of this research is the ARIAS learning model can improve the problem-solving skill of plane figure and solid figure essay on grade V students of SD Negeri Tunggulsari II No. 179 Surakarta academic year 2017/2018.</em></p>

Creativity of Secondary Mathematics Teacher within Solve the 2-Dimentional Figure Problem Based On Teaching Experiences

Creativity is an ability produced from the cognitive activities to get ideas in solving problems by combining the concepts that have been mastered to mark by fluency, flexibility, novelty, and elaboration. This study aims to get description about the creativity of the junior mathematics teachers and senior mathematics teachers on the problems on plane figures. This study is an explorative study with qualitative approach. The instruments used in this study are the researcher itself as the main instrument supported with the written assignments on the problems on plane figures, and the valid and reliable interview guidelines. Data collection was conducted by doing task-based interviews. There are two subjects in this study which are junior mathematics teachers and senior mathematics teachers. The result of this study shows that junior secondary mathematics teachers in solving the problems on plane figures more creative than senior secondary mathematics teachers in the aspect of fluency, flexibility, novelty, and elaboration.

DEVELOPMENT OF SPECIFIC MATHEMATICAL COMPETENCES FOR PLANE FIGURES IN THE EDUCATION IN MATHEMATICS FOR GRADES 1 - 4

INТRODUCTION: The development of specific mathematical competences from the competency cluster “Plane figures” is one of the important factors for achieving effective education in mathematics in primary school.PURPOSE OF STUDY: The purpose of this article is the presentation of the competences concept and especially the concept of the objective specific mathematical competences as well as the options for their development in and through education in mathematics in Grades 1-4. METHODS: During the experimental work the researchers performed qualitative and quantitative study of the topics presented above. The following methods were applied: a didactical experiment, observation, test, content analysis, and a mathematical-statistical method for data processing.RESULTS: As a result of the experimental work it was determined that the percentage of fourth graders who failed to solve a geometry text task decreased from 49.61% to 9.32%. The percentage of those students who failed to draw a circle with a given radius and an angle according to a given grade decreased from 38.95% to 8.17%. Additionally, the percentage of the students who correctly solved a geometry text tasks increased from 15.2% to 23.1%. The difference in the results is proven to be of statistical significance. CONCLUSIONS: Owing to the applied methodology system of work where productive strategies, methods and approaches were used, the specific mathematical competences from the competency cluster “Plane figures” were developed in their completeness in primary school students.

Enhanced Thermoelectric Properties of Suspended Mono- and Bilayer of MoS2 From First Principles

The past decade has seen the emergence of two-dimensional MoS2 as a very promising material for numerous applications in nanoelectronics and photonics and investigation of its thermoelectric properties is highly significant. The thermoelectric performance of suspended monolayer (ML) and bilayer (BL) of MoS2 has been investigated using density functional theory simulations and the semiclassical Boltzmann's theory. Using the BotzTrap code within the constant relaxation time approximation, we report in plane (armchair direction) figures of merit ( ZT ) values close to one and Seebeck coefficients ( S ) greater than 2000 μV/K for these layers at the optimal doping concentration of ∼1021 cm–3 . The general trend for both the layers with temperature is a decrease in S and increase in thermal conductivities $(\kappa/\tau)$ . ZT values on the other hand show a decrease in the ML and an increase in the BL with values of 0.97 and 0.87 for the ML and 0.98 and 1.04 for the BL at temperatures of 300 and 1000 K, respectively, for the n-type. These very attractive ZT values for the suspended ML and BL as compared to the bulk value of 0.18 at 300 K hold great promise for low-dimensional MoS2 as an efficient thermoelectric performer.

Nonuniqueness of Sixpartite Points

It is known that the area of any bounded, convex plane figure can be divided into equal sixths by three concurrent lines, and it is not hard to see that the same is true for perimeters. Calling the points of intersection of such lines area sixpartite points and perimeter sixpartite points, it is known that they are unique for triangles. We prove that they are not unique in general. Moreover, given any finite set of points in the plane we construct a convex polygon in which each of these points is an area sixpartite point, and a second polygon in which each is a perimeter sixpartite point.

A Comparative Study of `Euclidean and Śulbasūtra Constructions

The difference between Indian mathematics and Greek mathematics lies not only in the methods employed by them and the purpose of study, but also in their definitions, propositions and proofs. But the geometric constructions in both these cultures are almost similar. The present paper discusses a comparison between geometric constructions in ‘ Śulbasūtras ’ (800 BC-200 BC) and Euclid’s ‘Elements’ (300 BC). There are three types of constructions in both of these treatises. The first type is the construction of plane figures like squares, rectangles, parallelograms, triangles, trapeziums etc. The second type is the construction of geometric figures by transformation of another geometric figure without changing area. The third type is the construction of similar figures. Comparing the methods of constructions we see that the propositions behind the geometric constructions of the first type in ‘ Śulba ’ and ‘Elements’ are similar. But in the case of the second and third type of constructions, the methods are extremely different in both of these treatises.

Design research on plane figure learning by using picture story and pairing game to improve mathematical communication skills of second grade of primary school students

This research aims to produce the learning trajectory to improve mathematical communication skills of second grade students on the plane figure by using picture story and pairing game. It uses design research which consists of three stages: preliminary design, design experiment, and retrospective analysis. In the stage of preliminary design, researcher designed the Hypothetical Learning Trajectory (HLT). In the stage of design experiment, researcher then applied the HLT in teaching second grade students to improve mathematical communication skills from informal knowledge to formal knowledge through mathematics activities. The activities are picture story by using tangram context and pairing game. Finally, in the of retrospective analysis, the result of HLT application was analyzed to acquire the final result namely; Learning Trajectory (LT) of picture story and pairing game. Second grade students were involved as samples of this research. The data were collected through interview, observation, test, documentation, and field note. The data were analyzed through triangulation of data and interpretation cross. The result of this research is LT of the plane figure by using tangram context picture story and pairing game to improve mathematical communication skills of second grade students.

The Priority of Object over Method in Early Greek Mathematics

In modern mathematics, whose origins date back to the 17th c., method takes priority over the object, as the generality of method (which relies on a set of axioms and the laws of formal logic, applicable to any kind of objects whatsoever) implies the generality of the studied object. This epistemological attitude was alien to Greek mathematics, in which the generality of method did not necessarily mean the general character of its object. This is manifest, e.g., in Euclid's Elements, where the axiomatic-deductive method does not eradicate the particularity of the studied objects: numbers, lengths, plane figures, and solids. The aim of this paper consists in showing that in the early stages of Greek mathematics, when axiomatic-deductive way of argumentation was still unknown, object took priority over method in the sense that an investigation was not accomplished according to a definite method, fixed in advance, but rather relied upon methods that were suggested, in each particular case, by the structure of the appropriate objects. I will examine such a state of affairs by proposing reconstructions of archaic demonstrations of theorems taken from early geometry, arithmetic, and the theory of ratios and proportions.

Is the renal pyramidal thickness a good predictor for pyeloplasty in postnatal hydronephrosis?

We evaluated the feasibility and value of renal pyramidal thickness (PT) as a predictor of pyeloplasty in high-grade postnatal hydronephrosis. We retrospectively reviewed the charts of patients who presented with postnatal hydronephrosis from 2008 to 2013. Included cases had grade 3 or 4 hydronephrosis. We included only units diagnosed as ureteropelvic junction obstruction. Gender, laterality, hydronephrosis side, renogram data, and follow-up data were recorded. Two investigators reviewed all patients' ultrasounds images. We measured PT and pelvic anteroposterior diameter (APD) in the last ultrasound before surgery. For those managed conservatively, measurements were obtained from the ultrasound with worst hydronephrosis. PT was measured in supine position in the middle third of the sagittal plane (Figure). We assessed the reliability of PT measurement using the intraclass correlation coefficient (ICC). Univariate and multivariate analyses were used to correlate the collected parameters to pyeloplasty incidence. Receiver operating characteristic curve was used to evaluate the cutoff value of PT that predicts pyeloplasty. The total included cases were 155 patients (165 units). One hundred and fourteen units had grade 3 hydronephrosis and 51 units had grade 4 hydronephrosis. Fifty-two cases (55 units) underwent pyeloplasty. The median follow-up period was 37.6 months. PT measurement was reliable (ICC=0.94). Univariate analysis revealed that SFU grading, APD, PT, T1/2, and MAG-3 curves were associated with surgery. Multivariate analysis showed that PT was a single independent predictor for pyeloplasty. PT≤3mm had 98.1% sensitivity and 89.7% specificity in predicting pyeloplasty. PT is the first portion of renal parenchyma that is affected in high-grade hydronephrosis. Moreover, it changes little over the first 9 years of life. PT measurement in hydronephrosis was not previously evaluated. We found that PT was easily measured in most kidneys with high negative predictive value. The PT value as an indicator for pyeloplasty should undergo extensive assessment by other institutions with different protocols. Being a slowly growing part of the parenchyma, PT can be a good measurable parameter to predict pyeloplasty. Measurement of PT in hydronephrosis is reliable. PT≤3mm can predict pyeloplasty with 98.1% sensitivity and 89.7% specificity.

Discrete version of the Pythagorean theorem

The following observations are motivated by the facts that the area of a planar figure displayed on a screen can be expressed by a certain number of pixels; and if the figure is drawn by a plotter, then its area can be characterised by the total length of a line which fills it in.The generalisations of the Pythagorean theorem are of three kinds. Firstly, the squares on the sides of the right triangle are substituted by other geometrically similar planar figures (Euclid's Elements Book VI, Proposition 31 [1]). Secondly, the assumption of the right angle is omitted (the law of cosines), or both of these generalizations occur simultaneously (Pappus’ area theorem [2], see also H. W. Eves [3]). Thirdly, mathematical spaces other than the plane are considered (for example, de Gua-Faulhaber theorem about trirectangular tetrahedra [3], further generalised by Tinseau [4], Euclideann-spaces, Banach spaces [5], see also [6]).