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In this study, a finite-element simulation (FEM) was developed and validated by experiments using push-off specimens of ultra-high-performance concrete (UHPC). The ABAQUS program is used to model (rectangular groove, circular groove, triangular groove, and dowel bars interface), in addition to control specimen. A study of the result in terms of load displacement and maximum load indicates that the interface formed by the dowels and grooves improves shear resistance. Concrete strengths and the number of dowel bars in comparison to numerical specimens are included in a parametric study. Numerical results showed that increasing the number of dowel bars (1 and 2) increased the ultimate load by 23% while increasing the number of dowel bars (3 and 4) increased the ultimate load by 14%. Furthermore, increasing the compressive strength from (120 to 200 MPa) obtained higher ultimate load by (59 and 60 %) for the specimens with rectangle grooves and circle grooves respectively. [ABSTRACT FROM AUTHOR]

In this paper, the aim is to design a novel O-shaped Features a rectangle and a patch microstrip antenna that operate in the C-band frequency range. The current system and the planned work both provide data sets to this research. With a height of 1.6 mm and a relative permittivity of around 4.4, the FR4 epoxy substrate is an excellent choice. The O-shaped antenna is superior than the rectangular MPA because to its lower return loss and higher resonating frequency of 7.1 GHz. This study was carried out utilizing Ansoft HFSS 15.0 for both design and analysis. The proposed antenna is superior to its rivals as its return loss value is lower than that of rectangular MPA. A statistically significant return loss (P=0.006) is shown by the simulation results. [ABSTRACT FROM AUTHOR]

The background of this research is the lack of interesting, non-monotonous, and technology-based learning resources that teachers in elementary schools can use according to the needs of schools and students. This study is observational on the importance of developing an interactive digital module based on character education, containing local culture in mathematics. Observation activities were carried out in 10 elementary schools in Kudus Regency. The research method used is research and development with a modified Borg and Gall model. Observation activities were conducted by giving questionnaires to teachers and students in grade 4 elementary school and interviews with teachers. Observation results show that teachers have never used interactive digital modules. They are also still trying to find learning resources based on character education that includes the local culture of the Kudus Regency. The results of daily assessments on the area and perimeter of squares, rectangles, and triangles obtained a relatively low average score of 61. Based on the results of questionnaires from students, this is because 76% because the area and perimeter materials are challenging to understand, 75% answered that there is a formula in the material so that it seems rote, and 85% answered because of the lack of learning resources. 93% of students want technology-based learning resources to use anytime and anywhere. This can support their understanding of the material being studied. Thus, it can be concluded that 93% of students and 100% of teachers choose to agree if the researcher develops an interactive digital module based on character education containing the local culture of Kudus Regency in the mathematics subject matter of area and perimeter of squares, rectangles, and triangles. [ABSTRACT FROM AUTHOR]

Mathematics learning can be linked to local wisdom/local culture. The purpose of this study was to explore by describing the geometric elements found in typical South Sumatran snacks which involved prospective teacher students at PGRI Palembang Elementary School. Data and information will be taken through observation or observation and literature. This research is a qualitative research with a descriptive approach. In this study, the research subjects who were asked for information were prospective elementary school teacher students. The results of the exploration and analysis of this research data show that there is a geometric concept in traditional snacks in South Sumatra. The results obtained from the exploration of finding geometric concepts contained in these snacks include: 1) flat shapes (square, rectangle, triangle, circle,. 2) build spaces (balls, cubes, blocks, pyramids, and tubes). The results of this exploration can be used for new learning resources in learning mathematics. Starting with showing the pictures first to the students, then showing the original shape of the snacks, the last step is making geometric shaped snacks. [ABSTRACT FROM AUTHOR]

In the present paper, in the Hilbert space W ~ 2 (2 , 1) (0,1] of periodic complex-valued functions, an optimal quadrature formula with exponential weight function is constructed. The optimality of the formula of rectangles in the space W ~ 2 (2 , 1) (0,1] of periodic functions for ω=0 is shown. In addition, the numerical results show that the order of convergence of the optimal quadrature formula constructed in the space W ~ 2 (2 , 1) (0,1] is equal to 2. [ABSTRACT FROM AUTHOR]

Ethnomathematics facilitates the relationship between mathematics and culture so that the mathematical potential of a cultural site can be utilized as a source of student learning. The Keraton Ngayogyakarta Hadiningrat (Ngayogyakarta Palace) is one of the royal sites that has a lot of mathematical potential, both from the shape of the building to the ornaments contained in the building. This research is ethnographic qualitative-explorative research with the validity of the data using the triangulation method. Data were collected through observation, interviews, and documentation methods. It was found that geometric shapes such as squares, rectangles, trapezoids, rhombuses, triangles, and circles were found in the wards and buildings in the Ngayogyakarta Palace. These findings can be used to teach the material properties of plane shapes, the area and perimeter of shapes, similarity, and symmetry in school mathematics. [ABSTRACT FROM AUTHOR]

The purpose of this study was to describe the obstacles of student semantic representation in solving geometry problems. In this study, there are various obstacles found, namely ontogeny, epistemological, and didactic. Ontogeny obstacles arise when students are able to represent questions that have been read even though the student is not able to describe a quadrilateral of a bowstring, this can be seen when students feel confused about writing the answers to the questions. Epistemological obstacles regarding students' inability to understand geometric concepts, namely triangle concept, will be proven to be congruent. Students must draw a rectangle correctly to prove that triangles are congruent, they have never faced this geometry problem, this will make it difficult for students to solve the problems. Didactic obstacles that arise in the use of learning strategies and methods can cause obstacles. The use of books also affects the occurrence of obstacles that students have. Didactic obstacles occur in the process of representing rectangular shapes, many students have difficulty and because they have never been taught by lecturers. [ABSTRACT FROM AUTHOR]

In ethnomathematics studies, many have studied the existence of mathematical concepts, especially the concept of geometry in Indonesian culture, one of which is Batik. However, the results of previous research examining geometric concepts in Batik Sidomulyo are still very limited. Therefore, this study aims to explore the geometric concepts found in Batik Sidomulyo. This study uses an ethnographic methodology to respond to four typical queries, that is "Where do I look for it?", "How do I find?", "How do I recognize that found something significant?", and "How to what understand it?". By answering this question, the researcher succeeded in studying the geometry concepts contained in Batik Sidomulyo which consists of (1) geometric transformation concepts like as translation and reflection, (2) geometric concepts of fields lias rhombuses, triangles, squares, rectangles, and circles, and (3) revival and congruence. It is hoped that the results of this research can be material to introduce Batik Sidomulyo through contextual mathematics learning at all levels of education. This article also explains how to apply sample problems using the context of Batik Sidomulyo in mathematics learning. [ABSTRACT FROM AUTHOR]

Intuitionistic Fuzzy Set or IFS is a set that is used to describe problems related to uncertainty and vagueness. To deal with more complex problems that involve interval-based membership degrees, this set has been expanded to the Interval-Valued Intuitionistic Fuzzy Set or IVIFS. Theoretically, the difference between IFS and IVIFS lies in the area around the membership and non-membership coordinates. In IVIFS, the surrounding area is in the form of a rectangle with the center being the coordinates of membership and non-membership degrees. However, the use of intervals as approximations is still too general and broad, so that the idea to create other approximations is generated. Circular Intuitionistic Fuzzy Set (CIFS) was proposed as an alternative representation of uncertain and vague information. It is a set characterized by membership, non-membership, and radius on the element. Several basic operations have been introduced since then, accompanied by some operations on the radius. However, the operations on the radius are only limited to max and min. Hence, some other operations on the radius are proposed here to enrich the CIFS theory. The proposed operations are based on the previous operations on IFS and are reinforced by the t-norm and s-norm forms. The contribution of this paper lies in the expansion of basic operators, based on algebraic sums and products, which are not only applied to membership andxnon-membershipxdegrees but also to radius. In addition, it also applies to the negation operators which displays the operations based on the radius. The results of this paper are the modification of the basic operators and negation on the CIFS along with the adjustment of the properties that previously established for IFS. [ABSTRACT FROM AUTHOR]

One of the main components of the transmission system is the insulator. The insulator will be exposed to pollutants from the environment that can interfere with the work of the insulator. Based on the problems above, this research aimed to analyze the effect of stub position, the effect of pollutants, and the effect of variations in the shape and size of the leveling electrode on the voltage distribution of the chain insulator and compare the flatness factor. Variations The grading electrodes used are spherical, square, and rectangular. The tests carried out in this study was the insulator's condition in clean conditions, polluted conditions, and changing stub positions using variations in the shape and size of the leveling electrode. The results show that the best effect on equalizing the voltage distribution is by using a round grading electrode with a diameter of 30 cm on an insulator with mild NaCl polluted conditions at stub 1, which is 30.95%. In contrast, the flattening factor of the square grading electrode is 34.13%, and the flatness factor of the electrode. The rectangle's alignment is 33.09%. [ABSTRACT FROM AUTHOR]

In this paper, we also consider the problem of constructing inclusion-minimal Shannon-perfect ciphers. Sufficient conditions are proved for absence of non-endomorphic (endomorphic) perfect ciphers of Latin rectangles (squares) in the encryption tables. Here the concept of equivalence of encryption keys is used, namely: two different keys are equivalent in cipher value xi if the cipher value xi on these keys is encrypted in the same cipher designation. In this case, pairwise different keys k1, k2,...,kn−1, kn form a cycle of length n, if there is such a sequence of cipher values that: 1) adjacent cipher values are different; 2) keys k1, k2,...,kn−1, kn are sequentially equivalent to each other in the corresponding cipher values. It is proved that if pairwise distinct keys k1, k2,..., kn−1, kn contained in the encryption table form a cycle of length n=2m +1, m ∈ N, then under natural conditions there are no Latin rectangles in such an encryption table. [ABSTRACT FROM AUTHOR]

Sri Yantra and Sri Chakra - these are the terms use to describe a two dimensional and three-dimensional geometrical representation of the cosmic energy. It is the combination of different shapes like triangle, rectangle, square, petals and so on. There are so many different types of Yantra like Mahalaxmi yantra, Ganesh yantra, Saraswathi yantra they have different geometrical structure. Sri Yantra is the Queen of all the yantra. By worshiping Sri Yantra, we can fulfill our material & spiritual desires. In this article I explained the energy level of that Yantras at different section and proposed freehand drawing technique of Sri Yantra by scientific mathematical study using Fibonacci and Golden ratio. [ABSTRACT FROM AUTHOR]

In this paper, the influence of one-dimensional circular thickness variation and one-dimensional circular Poisson's ratio variation on frequency modes of nonhomogeneous and non-uniform clamped and simply supported rectangular plate was investigated. We further investigated the impact bi linear temperature and aspect ratio on the behavior of frequency modes by using Rayleigh Ritz technique. A comparison is also given with the existing result to support our study [ABSTRACT FROM AUTHOR]

This study aims to produce HLT which can help students to apply the concept of rectangle area in daily life. The context used is sewing patchwork into a tablecloth. This study used design research type validation studies. The stages carried out are preliminary design, teaching experiment, and retrospective analysis. However, this article only discusses the initial design, namely at the preliminary design stage. Data were collected by documentation and analyzed descriptively. This study resulted in an HLT consisting of four activities, namely sewing square pacthwork into a rectangular tablecloth, modeling a rectangular tablecloth, counting the number of squares by grouping, and finding the concept of a rectangular area. [ABSTRACT FROM AUTHOR]

The decay characteristics of rectangular and triangular jets issuing from convergent nozzles are studied experimentally. The rectangular nozzle is of aspect ratio (AR) 2 and the triangular nozzle is equilateral. The exit and inlet areas of aspect ratio 2 rectangular nozzle and equilateral triangular nozzle are maintained same and the nozzles are tested at NPR's 2 to 4 corresponding to the underexpansion levels of sonic jets. From the measured centerline pressure at nozzle pressure ratios 2, 3 and 4, it is observed that the triangle jet offers superior mixing properties compared to the rectangle jet. The triangular jet has a shorter core length than the rectangular jet at all pressure ratios. Also, the triangular jet showed better decay than the rectangular jet. The core length of both the jets increased with increasing pressure ratio. The present work demonstrates that the nozzle geometry has a significant impact on the sonic jet's mixing, as the triangular sonic jet is found to possess shorter core and it decays faster than the equivalent rectangular jet. [ABSTRACT FROM AUTHOR]

A new method for the first derivative of the solution of a nonlocal boundary value problem with integral boundary condition for Laplace's equation on a rectangular domain is proposed and justified. The solution of the given problem is defined as a solution of the Dirichlet problem by constructing the approximate value of the unknown boundary function on the side of the rectangle where the integral boundary condition was given. Further, the five point approximation of the Laplace operator is used on the way of finding the estimation of the error of the solution of the first derivative which is order of O(h), where h is the mesh size. [ABSTRACT FROM AUTHOR]

Students with low-functioning autism are students who experience interaction and communication disorders and are with low intelligence levels. This disorder causes obstacles in learning in the classroom; individuals with this disorder have a difficulty understanding concepts. Geometry is a mathematical concept that is very relevant to everyday life. This study aimed to describe the profile of an autistic student's understanding of basic geometric concepts, especially on rectangles and squares. The subject in this research was an elementary school student with low-functioning autism. Data were derived from a task-based interview using an instrument measuring the understanding of the concept of geometry. The geometric concept understanding profile uses the devices of interpreting, exemplifying, classifying, summarizing, inferring, comparing, and explaining. Some characteristics of autism were very perceptible in the student when he was attempting to understand the concept of geometry. The subject interpreted squares and rectangles as solid figures, naming them boxes. There were several real objects that he could imagine as squares and rectangles, but they were very limited in number. He was able to classify shapes into squares, rectangles, and shapes that were neither squares nor rectangles. He was experiencing limitations in expressing what he thought about the characteristics of the two shapes. He thought that the two shapes are similar in the sense that both are boxes and that they differ in color (referring to the pieces used herein); this was far from the correct concept. He thought that a square can also be referred to as a rectangle because the two shapes are boxes. That a box is a visualization of a square or a rectangle had been embedded in the subject's imagination. [ABSTRACT FROM AUTHOR]

This paper presents the enhancement of the combustion chamber efficiency owing to mixing by changing the fuel outlet cross-section triangle, square, and circle. Measurements of centerline velocity corresponding to Mach 0.2. to 0.35 and similar measurements were carried out for all cross-section of fuel injection outlet at Mach 0.2,0.25,0.35,0.35 circle, rectangle and triangle 50.1%, 57.5%, 57.6%, 58.35% & 51.81%, 56.46%, 56.52%, 57.31% And 54.66%, 58.83%, 58.83%, 59.62% respectively It was found that maximum efficiency was achieved by employing triangle cross-section of injector since it has two-point contact with the incoming air, which in turns enhances the mixing property. [ABSTRACT FROM AUTHOR]

Dhaka is one of the most seismic vulnerable regions in Bangladesh. Before constructing any building in this area, it has to be made sure that the building is earthquake resistant. The ability of resistance is highly dependent on the shape and structural system of the building. The objective of the study is to conduct an analysis on different regular and irregular shaped reinforced building considering the same dimension for each beam, column and slab following Bangladesh National Building Code (BNBC), 2020. Ten storied (G+9) building structures of six different shapes have been analyzed by using ETABS 2016 program for Dhaka (seismic zone 2). Out of these six different shapes, two are of regular plans (square & rectangle). Rest of the four shapes are with plan irregularity (W-shape, T-shape, L-shape & I-shape). Plan irregularities, vertical irregularities, storey displacement, storey drift and storey shear have been inspected for all models. Results show that in most cases, the buildings with irregularities have larger value of storey displacement and storey drift. The highest value for storey drift and displacement come for L and W shape model while the least value come for Rectangle shape model. On the other hand, storey shear changes little for irregular buildings. Besides, irregular buildings tend to fail more than buildings of regular shape. L shape model have not been able to pass the criteria of sway limitation, storey drift and torsion irregularity. W shape model has also crossed the sway limitation threshold. Shear walls have been introduced to the buildings who fail to make these buildings resistant towards earthquake. Results show that shear walls reduce the value of aforementioned three parameters. This research can be useful for the construction of buildings with different shapes and irregularities to take proper measurements for safety in Dhaka City. [ABSTRACT FROM AUTHOR]

This paper studies numerically the effect of channel shape on the overall performance of (EAHE) through winter season. Five shapes cross section of (EAHE) channel (circular; square; elliptical; triangle and rectangle) are studied numerically according to the climate conditions for Nasiriyah city in southern of Iraq. First the built numerical model was validated against experimental model and the results of comparison showed good consensus. After the validation and by using CFD modeling the overall performance of EAHE system with all shapes of channel was analyzed with ranges of air velocity, inlet air temperature and by assuming that the volume and the cross-section area for all shape of EAHE channel are constant. The results illustrated that, the system of EAHE is suitable for using in heating applications, also the results proved that, the circular cross section channel has the best performance. [ABSTRACT FROM AUTHOR]

This study aims to obtain an overview of students' obstacles in the topics of squares and rectangles. The method of this study was qualitative research. The subjects of this study were 51 grade 5 students of elementary schools in Bandung and Banda Aceh. Data collection techniques were carried out by tests on the concept of square and rectangle, interview, and documentation. The results show that elementary school students' learning obstacles in the concept of squares and rectangles include: 1) students' low spatial ability because of the limited learning media and students' insufficient knowledge of geometry; 2) students' low understanding of prerequisite concepts; 3) students' difficulty in connecting the relationship between squares and rectangle; 4) many students who were less able to mention the properties of a rectangle; 5) students were less able to solve problems that require creativity. Thus it can be concluded that students faced ontogenic, didactic, and epistemological learning obstacles. This research could provide teachers and education practitioners an overview in making and designing teaching materials according to student needs based on their learning obstacles. [ABSTRACT FROM AUTHOR]

Student activity is an important factor in learning. Students who are active in learning will greatly support the achievement of learning objectives. This study aims to determine the activeness of students in the application of the use of Lulingpat media on rectangle and triangle learning. This research was conducted at SMP Sunan Kalijogo Malang. This research method uses a qualitative approach because the researcher wants to explore the activeness of students in the application of the use of Lulingpat media on rectangle and triangles material. The research subjects were 22 class VIIA students of SMP Sunan Kalijogo Malang in the 2019/2020 school year. Based on the results of the analysis of student activeness observations obtained an average percentage of 91.28%, this indicates that the activeness of class VIIA students in the material of rectangle and triangles using Lulingpat media is very good. With the results of this study, it is hoped that teachers and students can use Lulingpat media so that students can be active in learning. [ABSTRACT FROM AUTHOR]

This article proposes a numerical method for solving unconnected static boundary value problems of the theory of thermoelasticity, based on the finite-difference approach. Mathematical and numerical models of a two-dimensional unconnected static boundary value problem of thermoelasticity for an isotropic rectangle with boundary conditions of the first and second types are considered. Finite-difference schemes have been constructed that allow, in combination with the iterative method, to find the desired nodal displacement values. The influence of the temperature field on the stress-strain state of the considered solid is estimated. [ABSTRACT FROM AUTHOR]

In this article, forced vibrations of a viscoelastic three-layer plate of a particular type are considered and some solution of numerical computation by Maple is given. Fundamental frequency of a viscoelastic three-layer plate is very useful for weight efficiency assessment of construction that is significant in engineering calculations.The article deals with the problem of fundamental frequency calculation for rectangular of a viscoelastic three-layer plate with free edges and all corners simply-supported. In this formulation the problem has no analytical solution yet. This is due to the necessity of exact satisfaction of static boundary conditions on free edges of the plate; which is very hard to do.Fundamental frequencies are calculated using this analytical formula for several variants of plates with different combinations of plate dimensions. [ABSTRACT FROM AUTHOR]

The present paper deals with the influence of the circular aperture located at the center, and the cracks arise from its circumference on the free vibration characteristics of a rectangular plate. The work has been conducted experimentally and numerically. The presence of holes and cracks in a rectangular plate significantly changes the structure's natural frequencies and mode shapes. Understanding the effects associated with the flight control process when the mechanical design of the structure is essential. The experimental method for determining typical properties of a plate with a central circular aperture and multiple slits was verified by finite element analysis (FEA) using ANSYS Mechanical APDL ver. 15. Factors affecting the free vibration were studied, including plate geometry, hole radius, crack length, crack number, and boundary conditions (all edges are clamped, and all edges are simply-supported). The obtained results showed that the fundamental natural frequency is increased with increasing the hole diameter and decreased with increasing the circumferential crack diameter. The achieved results showed a maximum discrepancy of 3.5% between the numerical and experimental results. Therefore, the relationship between vibration patterns and parameter variables was clarified. Thus, these results were used as a guide to analyze patterns and detect the damage associated with the rectangular plate with holes and cracks. [ABSTRACT FROM AUTHOR]

The aim of this research is to describe the creative thinking process of eighth graders in solving open-ended problems on triangles and quadrilaterals. This research uses descriptive qualitative descriptive research methods. The description of the creative thinking process of eighth graders in solving open-ended problems on triangles and quadrilaterals uses three indicators namely fluency, flexibility, and originality. Based on results of the research, it can be concluded that the students' creative thinking process of eighth graders in solving open-ended problems described using three indicators: fluency, flexibility, and originality. For fluency indicators, the subjects present a variety of images and strategies for solving problems correctly and clearly. For flexibility indicators, the subjects present images with different points of view. At the beginning of thought, some subjects only present rectangles and triangles. After thinking with different points of view, the subjects combine several images into combination forms. For the indicator of originality, the subjects bring up ideas that are new and unique. The subjects have a new thought to present images using the definition of 1 unit area. [ABSTRACT FROM AUTHOR]

In a rectangular domain, we discuss about an approximation of the first order derivatives for the solution of the mixed boundary value problem. The boundary values on the sides of the rectangle are supposed to have the second order derivatives satisfying the Hölder condition. Under these conditions for the approximate values of the first derivatives of the solution of mixed boundary problem on a square grid, as the solution of the constructed difference scheme a uniform error estimation of order O(h) (h is the grid size) is obtained. Numerical experiments are illustrated to support the theoretical results. [ABSTRACT FROM AUTHOR]

An exact solution is constructed for the boundary value problem of the theory of elasticity in a rectangle, in which two opposite (horizontal) sides are free, and normal stresses are given on the other two (the ends of the rectangle) (even-symmetric deformation relative to the central axes). The solution is constructed in the form of expansions in Papkovich–Fadle eigenfunctions. The expansion coefficients are determined by simple closed formulas. [ABSTRACT FROM AUTHOR]

The problem we discuss was proposed by an industrial partner. The aim is to locate light sources around a rectangular field so that the whole field is covered. We assume these lighted areas to be rectangular as well, parallel to the field. Covering an area with multiple light sources is allowed. There are multiple types of light sources, priced differently with different attributes. Our aim is to minimize the cost of the cover. We propose two solution approaches for solving this covering problem. In the first direct approach, we formulate the problem by a single MIP model, using constraints that force every rectangle to have proper neighbors. In the second constraint generation approach, we formulate a MIP model to locate the light sources such that a finite number of predetermined points of the field have to be covered. If the result solves the original problem, since it covers the whole field, then we stop. Otherwise, a constraint generation model calculates a non-covered point such that the first model has to improve its previous solution to cover this new point as well. [ABSTRACT FROM AUTHOR]

Research indicated that U.S. students had a weak understanding of spatial measurement concepts and they tended to take measurement concepts as procedures rather than meaningful knowledge. Research also found undergraduates' confusion about mathematical definitions and theorems. The formula to calculate the area of a rectangle tends to be regarded as a definition rather than as a deduced result. This study investigated preservice elementary teachers' understanding of definition of the area of a rectangle and their understanding of mathematical definitions in general. I found that most preservice elementary teachers did not know the right way to define the area of a rectangle and they tended to focus on external features when producing and evaluating mathematical definitions. Teachers also demonstrated a lack of understanding of the roles mathematical definitions play in the axiomatic system. [ABSTRACT FROM AUTHOR]

In this study we investigated eighth grade students' informal justification for the circle area formula to expand accounts of the measurement knowledge for middle-school age students. Data were collected during three paired interviews of a three-year teaching experiment. Here we describe schemes students exhibited as they operated on measurement tasks at a level we have described as "conceptual area measurer"; the tasks prompted the use of square units to quantify a figure that is not rectilinear. We found students could follow and rehearse a rationale for the validity of the circle area formula with substantive opportunities for movement and figural operations with units, or with decompositions from unit images that coordinated circle and rectangle images. [ABSTRACT FROM AUTHOR]

In this paper we first demonstrate higher effectiveness of Hermite bicubic finite elements on rectangles and tricubic elements on cubes in comparison with the Lagrange ones of the same degree. Then we propose new Hermite biquadratic elements on rectangles and triquadratic elements on cubes. Finally we demonstrate some pointwise superconvergence properties of studied finite elements. [ABSTRACT FROM AUTHOR]

The paper gives an overview and proposes solutions regarding to the most common mistakes for toponym placement for the best known and most-used web maps and GIS services where toponym placement is not harmonized with the cartographic principles, cartographic visualization conditions or cartographic generalization rules. The problem is solved by use of geometry where toponyms or toponym letters are approximated with a rectangle and/or with a rhombus for italic letters. In the end, we introduce the concept of predicting the path along which a toponym label can be placed through a simple geometry test for intersections of lines and rectangles. Approximations of words or single letters of a word with rectangles or rhombuses is offered as a simple solution for web map label placement calculations in real time which makes it convenient for web maps. [ABSTRACT FROM AUTHOR]

We shall show the existence of infinitely many time-periodic solutions of BVP for a 2D nonlinear wave equation defined in a rectangle domain. [ABSTRACT FROM AUTHOR]

I. PURPOSE The Purpose of this presentation is to explain why "length x width" is difficult even in middle school, in spite of the repeated instruction given in grades 4-8. For more than 20 years, NAEP has reported that this formula is used only by about half of the seventh graders and 65 percent of the eighth graders when a rectangle is presented with its dimensions. The common solution to this problem recommended by educators is to cover a rectangle with small squares and to explain the multiplicative relationship with columns and rows of small squares. It will be explained why this solution is not likely to work and what else we might try. [ABSTRACT FROM AUTHOR]

The game of Cutblock is the three-player variant of Cutcake, a classical combinatorial game. Even though to determine the solution of Cutcake is trivial, solving Cutblock is challenging because of the identification of queer games, i.e., games where no player has a winning strategy. New results about the classification of the instances of Cutblock are presented. [ABSTRACT FROM AUTHOR]

This poster shares sixth-grade student work and transcripts from a design experiment. It illustrates teacher and students using similar rectangles to make visual and verbal connections across seven successively abstract representations of ratio- from paper strips to slope. Measuring rectangle sides enabled mutually sensible conversations distinguishing discrete between-ratio strategies and continuous within-ratio strategies, encouraging the latter for determining slope. ..PAT.-Conference Proceeding [ABSTRACT FROM AUTHOR]