Quadrilaterals Research Articles

Analysis of the thoracic and abdominal mobility in elderly through computer photogrammetry

Background: Computerized photogrammetry has become a promising aspect for respiratory analysis, being a technology of low cost, good reproducibility and accuracy, compatible with the Brazilian public health situation. Objectives: To verify the applicability of the computerized photogrammetry method for analysis of thoracoabdominal mobility in the elderly. Methods: This is a methodological study, performed with 16 elderly women from Santa Cruz, RN, Brazil. Morphofunctional evaluation of body mass, stature, body mass index and thoracoabdominal mobility were performed through the computerized photogrammetry, whose technique was based on the capture of images at the maximum ventilation moments (maximal inspiration and expiration followed by apnea) of the elderly. For the delimitation of the thoracic wall were used 20mm diameter markers positioned at specific anatomical points, and the images were treated through the irregular quadrilaterals system in the AutoCAD 2007 Software. Results: Using computerized photogrammetry was possible to identify areas of compartments and sub-compartments of the thoracic wall with higher values at the inspiratory moment when compared to the expiratory moment, and with a greater contribution of the thoracic compartment in the pulmonary ventilation process of the elderly at the inspiratory moment. In addition, in the studied sample there was a higher prevalence of overweight elderly women (56%). Computerized photogrammetry was sensitive to the nutritional status of these elderly women, presenting areas of the abdominal compartment and sub-compartments with values higher than those presented by the elderly women with low weight. Conclusions: Computerized photogrammetry proved to be an effective and reliable technique for the thoracoabdominal mobility analysis of elderly women.v

Intrinsic non-flat-foldability of two-tile DDC surfaces composed of glide-reflected irregular quadrilaterals

Functional origami tessellations have certain geometric or physical properties - such as flat-foldability and rigid-foldability - which make them of particular interest for a broad range of applications in science, engineering, and architecture. While some simple variations of certain functional origami tessellations can be designed trivially, a systematic symmetry-reduction scheme is proved to be productive for the computational generation of more complex, non-trivial variations. Such a scheme has been previously applied to the developable double corrugation (DDC) surface, widely known as the Miura-ori, resulting in the development of novel crystalline derivatives, the symmetry groups of which are subgroups of the parent pattern. Computational algorithms can search for and find flat-foldable solutions for a large number of derivatives of the DDC surface, but fail to find solutions for all of them. In this paper, we exploit the symmetry reduction scheme along with classical plane geometry to analytically demonstrate why some crystallographic derivatives of this pattern do not exist. To this end, by applying the local flat-foldability condition at the vertices of different orbits associated with each tessellation, we show that such patterns are never flat-foldable, regardless of the geometric specifications of their constituting quadrilateral facets. In particular, we prove that two-tile DDC surfaces composed of glide-reflected irregular quadrilaterals are intrinsically non-flat-foldable, resulted from geometric incompatibilities between the properties of certain unit cells and the local flat-foldability condition.

How can quadrilaterals be constructed from Poly-Universe triangles?

How can quadrilaterals be constructed from Poly-Universe triangles?

Pascal-points quadrilaterals inscribed in a cyclic quadrilateral

This paper presents some new theorems about the Pascal points of a quadrilateral. We shall begin by explaining what these are.Let ABCD be a convex quadrilateral, with AC and BD intersecting at E and DA and CB intersecting at F. Let ω be a circle through E and F which meets CB internally at M and DA internally at N. Let CA meet ω again at L and let DB meet ω again at K. By using Pascal’s theorem for the crossed hexagons EKNFML and EKMFNL and which are circumscribed by ω, the following results can be proved [1]:– (a)NK, ML and AB are concurrent (at a point P internal to AB)(b)NL, KM and CD are concurrent (at a point Q internal to CD)

Peningkatan Kemampuan Penalaran Matematik Dan Kemandirian Belajar Siswa SMP Melalui Pendekatan Problem Solving

The aim of this study is for examine the learning independence of junior high school students whose learning use problem solving approach compared by scientific approach. Increased mathematical reasoning abilities of students who learn using the problem solving approach compared by scientific approach. The method used in this study lis quasi-experimental by taking two classes not randomly, in the first class get learned by using problem solving approach and the second class get learned by using scientific approach. The population is students in Bandung City with a sample that took two classes of VII which consisted of experimental class and the control class. The instrument used is reasoning abilities question on triangle and quadrilaterals problem and students learning independence questionnaires by using a Likert scale to see students’ learning independence toward problem solving approaches. The data prossesed in this study are pretest, posttest and n-gain scores using the help of Microsoft Office Excel 2010 and IBM SPSS Statistic 24. The result obtained are mathematical reasoning abilities and learning independence of junior high school students whose learning uses problem solving approaches better than those who using scientific approach, an increase in mathematical reasoning ability is better than one that uses scientific approach.

A New Approach to Automesh Generation of all β graded triangular and quadrilateral Finite Elements over Analytical Surfaces by using the Parabolic Arcs passing through four points on the Boundary Curve

This paper presents a new mesh generation method for a simply connected curved domain of a planar region which has curved boundary described by one or more analytical equations. We first decompose this curved domain into simple sub regions in the shape of curved triangles. These simple regions are then triangulated to generate a fine mesh of linear triangles in the interior and curved triangles near to the boundary of curved domain. These simple regions are then triangulated to create 6-node triangles by inserting midside nodes to these triangles. Each isolated 6-node triangle is then split into four triangles according to the usual scheme, that is, by using straight lines to join the midside nodes. To preserve the mesh conformity a similar procedure is also applied to every triangle of the domain to fully discretize the given convex curved or cracked convex curved domains into all triangles, thus propagating refinements and .The quadrangulation of graded 3-node linear triangles is done by inserting three midside nodes and a centroidal node.Then each graded triangle is split into three quadrilaterals by using straight lines to join the centroid to the midside nodes. This simple method generates a high quality mesh whose elements confirm well to the requested shape by refining the problem domain. We have approximated the curved boundary arcs by equivalent parabolic arcs.To preserve the mesh conformity, a similar procedure is also applied to every triangle of the domain to fully discretize the given curved domain into all triangles and quadrilaterals, thus propagating a uniform refinement. This simple method generates a high quality mesh whose elements confirm well to the requested shape by refining the problem domain. Examples of a circular disk and a cracked circular disk are presented to illustrate the simplicity and efficiency of the new mesh generation method. We have appended the MATLAB programs which incorporate the mesh generation scheme developed in this paper. These programs provide valuable output on the nodal coordinates ,element connectivity and graphic display of the all triangular and quadrilateral mesh for application to finite element analysis.

A New Approach to Automatic Generation of All Graded Triangular and Quadrilateral Finite Element Mesh Over Polygonal Domains

This paper presents a new automesh generation method for a convex and cracked convex polygonal domains. We first decompose the polygon into simple sub regions in the shape of triangles. These simple regions are then triangulated to generate a mesh of graded 3-node triangular elements. We propose then an automatic 6-node triangluar conversion scheme by inserting midside nodes to these triangles. Each isolated 6-node triangle is split into four triangles according to the usual scheme,that is,by joining the midside nodes by straight lines. To preserve the mesh conformity a similar procedure is also applied to every triangle of the domain to fully discretize the given convex or cracked convex polygonal domain into all triangles, thus propagating a uniform or graded refinement. The quadrangulation of graded 3-node linear triangles is done by inserting three midside nodes and a centroidal node.Then each graded triangle is split into three quadrilaterals by joining the centroid to the midside nodes. This simple method generates a high quality mesh whose elements confirm well to the requested shape by refining the problem domain. Examples are presented to illustrate the simplicity and efficiency of the new mesh generation method for standard and arbitrary shaped polygonal domains. We have appended MATLAB programs which incorporate the mesh generation scheme developed in this paper. These programs provide valuable output on the nodal coordinates ,element connectivity and graphic display of the all triangular and quadrangular meshes for application to finite element analysis.

Quadrilaterals and Bretschneider's Formula

We all learn at a young age how to calculate areas of squares or rectangles, but areas of irregular quadrilaterals are seldom mentioned. However, irregular quadrilaterals often appear in the real world. For instance, in a house, computing the area of walls, floors, or ceilings might be necessary to determine the amount of material needed for painting, tiling, and so on. Knowing the areas of backyards or fields is necessary for planting and computing yields. City personnel must determine areas of properties to compute prices and taxes. In our own research, computing areas of irregular quadrilaterals was needed for the interpretation of an ancient Aztec document that discussed surveying (see Jorge y Jorge et al. 2011). In this article, we talk about a formula deduced by Bretschneider in the mid-nineteenth century that not only allows the computation of areas of planar quadrilaterals, regular and irregular, but also provides a more thorough understanding of the geometry of such figures.

EKSPLORASI PEMAHAMAN SISWA DALAM PEMBELAJARAN BANGUN DATAR SEGI EMPAT DI SD MENGGUNAKAN KONTEKS CAK INGKLING

Primary school curricullum lays the foundation of geometry knowledge; students learn geometry by exploring their environment. Many researchers found that students have difficulties in understanding quadrilaterals. Most of them assumed that quadrilateral is square. Therefore, the aim of this research is to develop activities that support students to know the different types and forms of quadrilaterals. A teacher and thirty nine of fifth grade students were invole in this research. We used Cak Ingkling -Indonesian hopscoth- as a context in line with PMRI -Indonesian version of Realistic Mathematics Education- approach. The research finding showed that the use of Cak Ingkling context can help students understand the definitions and types of quadrilaterals. Students have had the understanding that it has many quadrilateral shapes such as square, rectangle, rhombus, parallelogram, trapezoid, and kite. Key words: quadrilaterals, Cak Ingkling, PMRI and design research

A fallacy involving similar quadrilaterals

A fallacy involving similar quadrilaterals

Some inequalities in bicentric quadrilateral

Abstract In this paper we prove some results concerning bicentric quadrilaterals. We offer a new proof of the Blundon-Eddy inequality, which we use to obtain other inequalities in bicentric quadrilaterals.

96.42 Dividing a right-angled trapezium into two similar quadrilaterals

96.42 Dividing a right-angled trapezium into two similar quadrilaterals

The Runge–Kutta control volume discontinuous finite element method for systems of hyperbolic conservation laws

AbstractIn this paper, a new high‐order and high‐resolution method called the Runge–Kutta control volume discontinuous finite element method (RKCVDFEM) was proposed to solve 1D and 2D systems of hyperbolic conservation laws. Its main advantage lies in the local conservation, and it is simpler than the Runge–Kutta discontinuous Galerkin finite element method (RKDGM). The theoretical analysis showed that the RKCVDFEM has formally an optimal convergence order for 1D systems. Based on logically rectangular grids of irregular quadrilaterals, a scheme for 2D systems was constructed. Some classical problems were simulated and the validity of the method was presented. Copyright © 2010 John Wiley & Sons, Ltd.

Intensity Distribution and Phase Vortices of Speckle Fields Generated by Multi-Aperture Random Scattering Screens

The intensity distribution and phase vortices of the speckle fields generated by multi-aperture random scattering screens are simulated, and it is found that the vortices exhibit layer-like structures and the dislocation phenomena occur in the local phase patterns produced by the two-pinhole aperture, whose phase distributions appear as striped structures. For three- or four-pinhole aperture, there are many circular bright spots appearing in the speckle grains, and there is one vortex between the neighboring circular bright spots. The positive and negative phase vortex lattices appear in the phase distributions, and the regions circled by the isothetic phase lines form irregular quadrilaterals or hexagons. Moreover, the relative positions of the vortices or bright spots can be adjusted by changing those of the pinhole apertures.

A discrete square global grid system based on the parallels plane projection

We developed a direct partitioning method to construct a seamless discrete global grid system (DGGS) with any resolution based on a two‐dimensional projected plane and the earth ellipsoid. This DGGS is composed of congruent square grids over the projected plane and irregular ellipsoidal quadrilaterals on the ellipsoidal surface. A new equal area projection named the parallels plane (PP) projection derived from the expansion of the central meridian and parallels has been employed to perform the transformation between the planar squares and the corresponding ellipsoidal grids. The horizontal sides of the grids are parts of the parallel circles and the vertical sides are complex ellipsoidal curves, which can be obtained by the inverse expression of the PP projection. The partition strategies, transformation equations, geometric characteristics and distortions for this DGGS have been discussed. Our analysis proves that the DGGS is area‐preserving while length distortions only occur on the vertical sides off the central meridian. Angular and length distortions positively correlate to the increase in latitudes and the spanning of longitudes away from a chosen central meridian. This direct partition only generates a small number of broken grids that can be treated individually.

Butterflies in Quadrilaterals: A Comment on a Note by Sidney Kung

Butterflies in Quadrilaterals: A Comment on a Note by Sidney Kung

Hexahedral mesh smoothing using a direct method

This paper develops a generalisation of the mesh smoothing direct method proposed by Balendran, to three dimensions by applying its methodology to smoothed hexahedral meshes. A geometric criteria is used where irregular quadrilaterals are converted to regular quadrilaterals on each face of the hexahedron using a local stiffness matrix. This matrix is then converted to a spatial stiffness matrix with reference to absolute coordinates in order to assemble the geometrical stiffness matrix as a global stiffness matrix. The fixing of boundary conditions is analysed and results obtained in a series of hexahedral meshes, used in finite difference method analysis, are illustrated. To evaluate the quality of the obtained results, a degree of uniformity is calculated and a comparative study of the improvement obtained in each zone of the hexahedral mesh is conducted. The proposed method permits the marking out of the portions of mesh in which a Laplacian smoothening fails to improve the mesh quality, therefore, requiring the use of other methods in which inserted mesh points are taken into account.

Hybrid Finite Element and Volume Integral Methods for Scattering Using Parametric Geometry

In this paper we address several topics relating to the development and implementation of volume integral and hybrid finite element methods for electromagnetic modeling. Comparisons with the finite elementboundary integral method are given in terms of accuracy and computing resources. We also discuss preconditioning, parallelization of the multilevel fast multipole method and propose higher-order basis for curvilinear quadrilaterals and volumetric basis functions for curvilinear hexahedra. The latter have the desirable property of vanishing divergence within the element but non-zero curl. In addition, a new domain decomposition is introduced for solving array problems involving involving several million degrees of freedom. Three orders of magnitude CPU reduction is demonstrated for such applications. keyword: Radar scattering, magnetic materials, volume integral equations, finite-element boundary-integral method, fast multipole method, parallelization, antenna radiation, preconditioning, curvilinear elements, higherorder basis functions.

Hemispheric differences in the recognition of possible and impossible objects

Three experiments using a visual half‐field technique were conducted to address the question of lateralised processing of three‐dimensional aspects of visual stimuli. We used drawings of “possible” and “impossible” triangles and quadri laterals. In one condition subjects had to decide whether these stimuli were possible (i.e., the depicted figures could exist in the three‐dimensional world) whereas in the second condition the task was to distinguish between triangular and quadrangular shapes. All experiments revealed an interaction of task and visual field on discrimination indices (d′) suggesting a dissociation of the processing of two‐ and three‐dimensional aspects of visual stimuli. These results are discussed with respect to known perceptual differences between the cerebral hemispheres.

88.20 Pythagoras' theorem for quadrilaterals

88.20 Pythagoras' theorem for quadrilaterals