Properties Of Rectangle Research Articles

THE GEOMETRIC THINKING PROCESS OF STUDENTS IN CONSTRUCTING THE CONCEPT OF AREA

Students often experience difficulties in learning geometry at the junior high. It is important in learning geometry to provide opportunities for students to build their own geometric concepts with guidance from educators. The purpose of this study was to describe the geometric thinking process of students in constructing the formula for the area of rectangles, squares and triangles and how the geometric thinking processes of students in solving contextual problems related to the area of flat shapes. This study uses a descriptive qualitative approach. The research out on 22 students of class VIII SMP PGRI Buntudatu. Research instrument using worksheets, and data collection through observations on the learning process and student work. The results showed that the geometric thinking process of students in building knowledge about the concept of the area of rectangles, squares and triangles had not gone well and smoothly. Students still need to be given regular guidance and instructions to help construct their knowledge. Students have not been able to use geometric reasoning well in terms of applying the properties of rectangles, squares and triangles in solving contextual problems related to the area of flat shapes

Special Cases of Hyperbolic Parallelograms on the Lobachevsky Plane

In this paper, we consider particular cases of hyperbolic parallelograms obtained by transferring characteristic properties of rectangles and squares on the Euclidean plane associated with their diagonals to the Lobachevsky plane. The existence of these quadrangles in the Cayley–Klein model in a circle of the Euclidean plane is proved.

Students’ Misconceptions on Properties of Rectangles

This research aims to describe students’ misconception of junior high school on the concept of the properties of rectangles and the alternative to overcome them. This research was qualitative descriptive research using test with the CRI (Certainty of Response Index) method and interview method. There were three students as subjects in this study who was identified to have the most misconceptions among students in the class . Based on the data analysis, the subjects showed similar misconceptions. One of student misconception was on the properties of rectangles. Student thought that rectangles were always regularly shaped, or in other word no rectangle was irregular shaped. Students’ misconception caused by picture given to the problem. The misconceptions may due to the lack of understanding of rectangle properties. Alternatives can be done such as re-explain (remediation) or by using cognitive conflict strategies. In particular, our results indicated that 8th grade students had misconceptions in understanding the properties of rectangles. By knowing the misconceptions, students can possibly know how new knowledge is interpreted as well as having an impact on student’s ability to learn correct information in the future.

Square or oblong?

In these activities two-year-olds investigate the properties of rectangles while practising fine motor skills. The emphasis is on developing hand and finger strength, hand eye co-ordination and object manipulation.

Best Proximity Point Theorems for Asymptotically Relatively Nonexpansive Mappings

ABSTRACTLet (A, B) be a nonempty bounded closed convex proximal parallel pair in a nearly uniformly convex Banach space and T: A ∪ B → A ∪ B be a continuous and asymptotically relatively nonexpansive map. We prove that there exists x ∈ A ∪ B such that ‖x − Tx‖ = dist(A, B) whenever T(A) ⊆ B, T(B) ⊆ A. Also, we establish that if T(A) ⊆ A and T(B) ⊆ B, then there exist x ∈ A and y ∈ B such that Tx = x, Ty = y and ‖x − y‖ = dist(A, B). We prove the aforementioned results when the pair (A, B) has the rectangle property and property UC. In the case of A = B, we obtain, as a particular case of our results, the basic fixed point theorem for asymptotically nonexpansive maps by Goebel and Kirk.

Mirror, Mirror

Each month, elementary school teachers receive a problem along with suggested instructional notes and are asked to use the problem in their own classrooms and report solutions, strategies, reflections, and misconceptions to the journal audience. This month's problem integrates two areas: Students must consider the properties of rectangles, rhombuses, and squares in the context of reflecting shapes. A whole-class discussion during which students share their solutions and ideas is a crucial component of the task, allowing students to further develop and solidify their understanding of the underlying geometric concepts.

Optimization in first semester calculus: a look at a classic problem

Optimization problems in first semester calculus have historically been a challenge for students. Focusing on the classic optimization problem of finding the minimum amount of fencing required to enclose a fixed area, we examine students' activity through the lens of Tall and Vinner's concept image and Carlson and Bloom's multidimensional problem-solving framework. We are particularly interested in students' evoked concept images for the mathematical concepts that play a role in the construction of the function whose minimum is needed. Data analysis revealed several gaps in students’ understanding of the optimization process. We highlight the mathematical concepts that play a role in these gaps, focusing on variables, function notation, function composition, properties of rectangles and the relationships between them, the role of the optimizing function, and the graphical representation of the function.

Constructing Geometric Properties of Rectangle, Square, and Triangle in the Third Grade of Indonesian Primary Schools

Previous studies have provided that when learning shapes for the first time, young children tend to use the prototype as the reference point for comparisons, but often fail when doing so since they do not yet think about the defining attributes or the geometric properties of the shapes. Most of the time, elementary students learn geometric properties of shapes only as empty verbal statements to be memorized, without any chance to experience the contepts meaningfully. In the light of it, a sequence of instructional activities along with computer manipulative was designed to support Indonesian third graders in constructing geometric properties of square, rectangle, and triangle. The aim of the present study is to develop a loval instructional theory to support third graders in constructing geometric properties of rectangle, square, and triangle. Thirty seven students of one third grade classes in SD Pupuk Sriwijaya Palembang, along with their class teacher, were involved in the study. Our findings suggest that the combination of computer and non-computer activities suppots third graders in constructing geometric properties of square, rectangle, and triangle in that it provides opportunities to the students to experience and to develop the concepts meaningfully while using their real experiences as the bases to attain a higher geometric thinking level. Key concepts: Geometric properties, rectangle, square, triangle, design research, realistic mathematics education  DOI : http://dx.doi.org/10.22342/jme.4.2.414.160-171

Information Cost Tradeoffs for Augmented Index and Streaming Language Recognition

This paper makes three main contributions to the theory of communication complexity and stream computation. First, we present new bounds on the information complexity of augmented-index. In contrast to analogous results for index by Jain, Radhakrishnan, and Sen [J. ACM, 56 (2009), article 33], we have to overcome the significant technical challenge that protocols for augmented-index may violate the “rectangle property” due to the inherent input sharing. Second, we use these bounds to resolve an open problem of Magniez, Mathieu, and Nayak [Proceedings of the 42nd Annual ACM Symposium on Theory of Computing, 2010, pp. 261--270] that asked about the multipass complexity of recognizing Dyck languages. This results in a natural separation between the standard multipass model and the multipass model that permits reverse passes. Third, we present the first passive memory checkers that verify the interaction transcripts of priority queues, stacks, and double-ended queues. We obtain tight upper and lower bounds for these problems, thereby addressing an important subclass of the memory checking framework of Blum et al. [Algorithmica, 12 (1994), pp. 225--244].

Study on the capacitance performance of Sn4+-doped V2O5

Sn4+-doped V2O5 cathode materials were prepared by a sol–gel method. The results showed that the modified cathode material was a mixture of V4+ and V5+. It was a kind of typical mesopore material with pores of 2–4 nm diameter. Symmetrical curves were obtained by cyclic voltammetry (CV) tests performed at different scanning rates and voltage ranges. In particular, the CV curve showed more obvious rectangle property and better redox properties when the scanning rate was 5 mV s−1. At the current density of 200 mA g−1, the maximum specific energy, specific power, and coulomb efficiency of the material were 27.25 mA h g−1, 494.87 W kg−1, and 97%, respectively. It was indicated that small amounts of Sn4+ doping would improve the surface morphology and electronic conductivity of V2O5. The Sn4+-doped V2O5 showed good capacitance characteristics.

A Dynamic Way to Teach Angle and Angle Measure

These quotation reflect the properties of rectangles that students thought were important when they were directed, “In your own words, define a rectangle.”

Transnormality and the infinitesimal rectangle property

A.S. Besicovitch [1] and L. W. Danzer [3] characterized the circle among closed convex curves in the plane by the so-called rectangle property (for a precise definition see below). T. Zamfirescu [10] introduced an infinitesimal version of this property and proved, that a closed Jordan curve in the plane satisfying the infinitesimal rectangle property must be a convex curve of constant width. This generalizes the BesicovitchDanzer Theorem to closed Jordan curves.

On the rectangle property for plane continua and immersed topological hypersurfaces

A subset of Euclidean space is said to satisfy the rectangle property if no rectangle has exactly three vertices in this subset. According to Besicovitch and Dnazer, circles are characterized by this property among convex curves. Here, more general characterizations of this type are presented.