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Relevant bibliographies by topics / Quadrilaterals

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Academic literature on the topic 'Quadrilaterals'

Author: Grafiati

Published: 4 June 2021

Last updated: 27 July 2024

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Journal articles on the topic "Quadrilaterals"

1

Josefsson, Martin. "Properties of bisect-diagonal quadrilaterals." Mathematical Gazette 101, no. 551 (2017): 214–26. http://dx.doi.org/10.1017/mag.2017.61.

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The general class of quadrilaterals where one diagonal is bisected by the other diagonal has appeared very rarely in the geometrical literature, but they have been named several times in connection with quadrilateral classifications. Günter Graumann strangely gave these objects two different names in [1, pp. 192, 194]: sloping-kite and sliding-kite. A. Ramachandran called them slant kites in [2, p. 54] and Michael de Villiers called them bisecting quadrilaterals in [3, pp. 19, 206]. The latter is a pretty good name, although a bit confusing: what exactly is bisected?We have found no papers and

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Josefsson, Martin. "New characterisations of bicentric quadrilaterals." Mathematical Gazette 106, no. 567 (2022): 414–26. http://dx.doi.org/10.1017/mag.2022.114.

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A bicentric quadrilateral is a convex quadrilateral that can have both an incircle (it is tangential) and a circumcircle (it is cyclic), see Figure 1. We know of only a dozen characterisations of bicentric quadrilaterals published before. In all of them the starting point is either a tangential or a cyclic quadrilateral, which then must satisfy some condition in order also to be of the other type. Before we proceed to prove seven new such necessary and sufficient conditions for bicentric quadrilaterals, we review one characterisation and one property of tangential quadrilaterals that we will a

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Mammana, Maria Flavia, and Biagio Micale. "Quadrilaterals of triangle centres." Mathematical Gazette 92, no. 525 (2008): 466–75. http://dx.doi.org/10.1017/s0025557200183664.

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Let Q be a convex quadrilateral ABCD. We denote by TA, TB, Tc, TD, the four triangles BCD, CDA, DAB, ABC, respectivelyThe barycentres (or centroids), orthocentres, incentres and circumcentres of such triangles determine other quadrilaterals in their turn that we call the quadrilateral of the barycentres, of the orthocentres, of the incentres and of the circumcentres, respectively. We denote these quadrilaterals by Qb, Q0, Qi, Qc, respectively.

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Na, Hyeonseok, Seonghwan Jin, Eunsung Jung, Gunwoo Han, and Youngmin Cho. "A Study on the Macbeath inconic of Convex Quadrilaterals and Orthic inconic of Convex Quadrilaterals." Korean Science Education Society for the Gifted 15, no. 3 (2023): 483–93. http://dx.doi.org/10.29306/jseg.2023.15.3.483.

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This study was based on the research results conducted as an R&E project for gifted students with financial support from the Korea Foundation for the Advancement of Science and Creativity. In this study, the Macbeath inconic and Orthic inconic defined in triangles are expanded to convex quadrilateral to study the Macbeath inconic of convex quadrilaterals and the Orthic inconic of convex quadrilaterals. Through this study, the following research results are obtained. First, it is discovered that the condition for a quadrilateral in which the Macbeath inconic of a convex quadrilateral exists

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Ekawati, Rooselyna, Ahmad Wachidul Kohar, Tatag Yuli Eko Siswono, Agung Lukito, Kai-Lin Yang, and Khoirun Nisa. "Mathematics teacher educators’ noticing of pedagogical content knowledge on hierarchical classification of quadrilateral." Infinity Journal 12, no. 2 (2023): 261–74. http://dx.doi.org/10.22460/infinity.v12i2.p261-274.

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This study aims to investigate mathematics teacher educators’ (MTE) knowledge in noticing preservice teachers’ pedagogical content knowledge (PCK) on the hierarchical classification of the quadrilateral. A multiple case study was conducted to analyze the responses of ten MTEs in an online moderated-forum group discussion (M-FGD) from their written work on the MTE-PCK test completed prior to the M-FGD. The PCK test consisted of two tasks: the task that examines MTEs’ knowledge to predict pre-service teachers’ reason in representing the hierarchical classification of quadrilateral in Venn diagra

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Choudhry, Ajai. "Brahmagupta quadrilaterals with equal perimeters and equal areas." International Journal of Number Theory 16, no. 03 (2019): 523–35. http://dx.doi.org/10.1142/s1793042120500268.

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A cyclic quadrilateral is called a Brahmagupta quadrilateral if the lengths of its four sides and two diagonals, and the area are all given by integers. In this paper, we consider the hitherto unsolved problem of finding two Brahmagupta quadrilaterals with equal perimeters and equal areas. We obtain two parametric solutions of the problem — the first solution generates examples in which each quadrilateral has two equal sides while the second solution gives quadrilaterals all of whose sides are unequal. We also show how more parametric solutions of the problem may be obtained.

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Josefsson, Martin. "Further characterisations of tangential quadrilaterals." Mathematical Gazette 101, no. 552 (2017): 401–11. http://dx.doi.org/10.1017/mag.2017.122.

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Tangential quadrilaterals are defined to be quadrilaterals in which a circle can be inscribed that is tangent to all four sides. It is well known and easy to prove that a convex quadrilateral is tangential if, and only if, the angle bisectors of all four vertex angles are concurrent at a point, which is the centre of the inscribed circle (incircle). The most well-known and in problem solving useful characterisation of tangential quadrilaterals is Pitot's theorem, which states that a convex quadrilateral is tangential if and only if its consecutive sides a, b, c, d satisfy the relation a + c =

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Chairunnisa Inayatusufi and Tian Abdul Aziz. "Design of Quadrilateral Learning with RME Approach for Junior High School Students." JURNAL RISET PEMBELAJARAN MATEMATIKA SEKOLAH 5, no. 2 (2021): 1–13. http://dx.doi.org/10.21009/jrpms.052.01.

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The purpose of this study is to provide alternative learning options, with a realistic mathematics education learning design or RME on quadrilaterl material for Junior High School students. This writing uses instructional design to develop a learning model. Learning development is done by analyzing needs and learners. Performance objectives and learning outcomes are discussed in detail and adapted to instructional objectives. The results of this study indicate that a quadrilateral learning design by applying the RME approach is recommended for educators in conducting quadrilateral learning. Th

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GROSSMAN, PINHAS, and MASAKI IZUMI. "CLASSIFICATION OF NONCOMMUTING QUADRILATERALS OF FACTORS." International Journal of Mathematics 19, no. 05 (2008): 557–643. http://dx.doi.org/10.1142/s0129167x08004807.

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A quadrilateral of factors is an irreducible inclusion of factors N ⊂ M with intermediate subfactors P and Q such that P and Q generate M and the intersection of P and Q is N. We investigate the structure of a noncommuting quadrilateral of factors with all the elementary inclusions P ⊂ M, Q ⊂ M, N ⊂ P, and N ⊂ Q 2-supertransitive. In particular, we classify noncommuting quadrilaterals with the indices of the elementary subfactors less than or equal to 4. We also compute the angles between P and Q for quadrilaterals coming from α-induction and asymptotic inclusions.

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Bao, Hui, and Xingdi Chen. "A New Hyperbolic Area Formula of a Hyperbolic Triangle and Its Applications." Journal of Mathematics 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/838497.

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We study some characterizations of hyperbolic geometry in the Poincaré disk. We first obtain the hyperbolic area and length formula of Euclidean disk and a circle represented by its Euclidean center and radius. Replacing interior angles with vertices coordinates, we also obtain a new hyperbolic area formula of a hyperbolic triangle. As its application, we give the hyperbolic area of a Lambert quadrilateral and some geometric characterizations of Lambert quadrilaterals and Saccheri quadrilaterals.

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Dissertations / Theses on the topic "Quadrilaterals"

1

Yu, Paul W. Presmeg Norma C. Barrett Jeffrey Edward. "Prototype development and discourse among middle school students in a dynamic geometric environment." Normal, Ill. Illinois State University, 2004. http://wwwlib.umi.com/cr/ilstu/fullcit?p3172886.

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Thesis (Ph. D.)--Illinois State University, 2004.<br>Title from title page screen, viewed November 22, 2005. Dissertation Committee: Norma C. Presmeg, Jeffrey E. Barrett (co-chairs), Sherry L. Meier. Includes bibliographical references (leaves 186-194) and abstract. Also available in print.

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Banerjee, Nirjhar. "Random obtuse triangles and convex quadrilaterals." Thesis, Massachusetts Institute of Technology, 2009. http://hdl.handle.net/1721.1/54212.

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Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2009.<br>This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.<br>Cataloged from student submitted PDF version of thesis.<br>Includes bibliographical references (p. 83-85).<br>We intend to discuss in detail two well known geometrical probability problems. The first one deals with finding the probability that a random triangle is obtuse in nature. We initially discuss the various ways of choosing a ran

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Darch, Melissa. "Characterizing Classes of Quadrilaterals and Hexagons." Thesis, Southern Illinois University at Edwardsville, 2018. http://pqdtopen.proquest.com/#viewpdf?dispub=10793876.

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<p> The purpose of this thesis is to investigate possibly interesting classes of polygons within quadrilaterals and hexagons. We utilize zero sets of polynomials using the vertices of these polygons to find characteristics of two new quadrilateral classes and four hexagon classes. We will refer to the polynomials as “forms”. These forms are invariant under translation and rotation and scaled by a factor under dilation. We define three functions: X- a reflection across the <i> x</i>-axis, <i>&fcy;</i>- a relabeling of vertices across the <i> AC</i> diagonal (or in a hexagon, across

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Lynch, Keith. "On triangles and quadrilaterals of groups." Diss., Virginia Tech, 1995. http://hdl.handle.net/10919/38574.

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This dissertation demonstrates the existence of a pair of algebraic and geometric structures on triangles of groups and on quadrilaterals of groups. These structures are an automatic and biautomatic structure. In addition, this paper also discusses the growth function for the quadrilaterals. We show that these groups have these desired structures and discuss what they are. We also give an extraordinary example of a pair of quadrilaterals of groups that are defined nearly identically but do not behave alike.<br>Ph. D.

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StClair, Jessica Lindsey. "Geometry of Spaces of Planar Quadrilaterals." Diss., Virginia Tech, 2011. http://hdl.handle.net/10919/26887.

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The purpose of this dissertation is to investigate the geometry of spaces of planar quadrilaterals. The topology of moduli spaces of planar quadrilaterals (the set of all distinct planar quadrilaterals with fixed side lengths) has been well-studied [5], [8], [10]. The symplectic geometry of these spaces has been studied by Kapovich and Millson [6], but the Riemannian geometry of these spaces has not been thoroughly examined. We study paths in the moduli space and the pre-moduli space. We compare intraplanar paths between points in the moduli space to extraplanar paths between those same points

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Park, Yee-han. "Primary mathematics teachers' pedagogical content knowledge of the teaching of quadrilaterals." Click to view the E-thesis via HKUTO, 2003. http://sunzi.lib.hku.hk/hkuto/record/B31963481.

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Fraiji, Nicolas. "Illuminating triangles, quadrilaterals and convex polygons with vertex floodlights." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape7/PQDD_0029/MQ67822.pdf.

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Park, Yee-han, and 白綺嫻. "Primary mathematics teachers' pedagogical content knowledge of the teaching of quadrilaterals." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2003. http://hub.hku.hk/bib/B31963481.

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Ng, Dicky. "Investigating Elementary Teachers’ Mathematical Knowledge for TeachingGeometry: The Case of Classification of Quadrilaterals." Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 440 - 444, 2012. https://slub.qucosa.de/id/qucosa%3A1793.

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This paper examines the mathematical knowledge for teaching (MKT) in Indonesia, specifically in school geometry content. A translated and adapted version of the MKT measures developed by the Learning Mathematics for Teaching (LMT) project was administered to 210 Indonesian primary and junior high teachers. Psychometric analyses revealed that items related to classification of quadrilaterals were difficult for these teachers. Further interactions with teachers in a professional development setting confirmed that teachers held a set of exclusive definitions of quadrilaterals.

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Ng, Dicky. "Investigating Elementary Teachers’ Mathematical Knowledge for Teaching Geometry: The Case of Classification of Quadrilaterals." Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-80730.

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This paper examines the mathematical knowledge for teaching (MKT) in Indonesia, specifically in school geometry content. A translated and adapted version of the MKT measures developed by the Learning Mathematics for Teaching (LMT) project was administered to 210 Indonesian primary and junior high teachers. Psychometric analyses revealed that items related to classification of quadrilaterals were difficult for these teachers. Further interactions with teachers in a professional development setting confirmed that teachers held a set of exclusive definitions of quadrilaterals.

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Books on the topic "Quadrilaterals"

1

Leech, Bonnie Coulter. Quadrilaterals. PowerKids Press, 2007.

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Smoothey, Marion. Quadrilaterals. Marshall Cavendish, 1993.

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Smoothey, Marion. Quadrilaterals. Marshall Cavendish, 1993.

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Smoothey, Marion. Quadrilaterals. Marshall Cavendish, 1993.

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5

Robinson, John. Distortion measures for quadrilaterals with curved boundaries. NAFEMS, 1987.

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Jennifer, Griffin, Witonsky David, and Willmore Edwin, eds. The classification of quadrilaterals: A study of definition. Information Age Pub., 2008.

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Baum, Rex L. Measurement of slope deformation using quadrilaterals: A description of a new method for measuring displacement at the boundaries of a landslide and strain and tilt at the surface of a landslide. Dept. of the Interior, 1988.

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Baum, Rex L. Measurement of slope deformation using quadrilaterals: A description of a new method for measuring displacement at the boundaries of a landslide and strain and tilt at the surface of a landslide. U.S. G.P.O., 1988.

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9

Blaisdell, Molly. If you were a quadrilateral. Picture Window Books, 2010.

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Papamichael, Nicholas. A domain decomposition method for approximating the conformal modules of long quadrilaterals. Brunel University, Department of Mathematics and Statistics, 1991.

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Book chapters on the topic "Quadrilaterals"

1

Hochberg, Robert, and Glenn Hurlbert. "Pythagorean Quadrilaterals." In Applications of Fibonacci Numbers. Springer Netherlands, 2004. http://dx.doi.org/10.1007/978-0-306-48517-6_12.

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Horwitz, Alan. "Bielliptic Quadrilaterals." In Ellipses Inscribed in, and Circumscribed about, Quadrilaterals. Chapman and Hall/CRC, 2024. http://dx.doi.org/10.1201/9781003474890-13.

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Mitrinović, D. S., J. E. Pečarić, and V. Volenec. "Inequalities for Quadrilaterals." In Recent Advances in Geometric Inequalities. Springer Netherlands, 1989. http://dx.doi.org/10.1007/978-94-015-7842-4_14.

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Johnson, Dana T., Marguerite M. Mason, and Jill Adelson. "Properties of Quadrilaterals." In Polygons Galore! Routledge, 2021. http://dx.doi.org/10.4324/9781003237204-10.

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Horwitz, Alan. "Midpoint Diagonal Quadrilaterals." In Ellipses Inscribed in, and Circumscribed about, Quadrilaterals. Chapman and Hall/CRC, 2024. http://dx.doi.org/10.1201/9781003474890-5.

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Grigorieva, Ellina. "Quadrilaterals and Other Polygons." In Methods of Solving Complex Geometry Problems. Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-00705-2_2.

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Hanks, Mary-Lyons Walk, Jennifer K. Lampert, and Katherine Plum. "Apply Properties of Quadrilaterals." In William & Mary's Center for Gifted Education Thinking Like a Mathematician GRADE 3. Routledge, 2021. http://dx.doi.org/10.4324/9781003239079-25.

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Maehara, Hiroshi. "On Acute Triangulations of Quadrilaterals." In Discrete and Computational Geometry. Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/3-540-47738-1_22.

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Horwitz, Alan. "Dynamics of Ellipses Inscribed in Quadrilaterals." In Ellipses Inscribed in, and Circumscribed about, Quadrilaterals. Chapman and Hall/CRC, 2024. http://dx.doi.org/10.1201/9781003474890-7.

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Ramasubramanian, K., Takao Hayashi, Clemency Montelle, and S. G. Dani. "Mensuration of quadrilaterals in the Līlāvatī." In Sources and Studies in the History of Mathematics and Physical Sciences. Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-13-6034-3_7.

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Conference papers on the topic "Quadrilaterals"

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Keaton, Jeffrey R., and Richard W. Gailing. "Monitoring Slope Deformation With Quadrilaterals for Pipeline Risk Management." In 2004 International Pipeline Conference. ASMEDC, 2004. http://dx.doi.org/10.1115/ipc2004-0197.

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Ground displacements, strains, and tilts can be calculated by repeated measurements of the lengths of six chords and relative elevations of an array of four points, known as a quadrilateral. Quadrilateral measurements allow ground-surface deformation and strain to be calculated. Typically, soil-pipeline interaction results in pipeline strain being less than ground strain. Strain gauges traditionally have been used on pipelines in landslide areas to aid in managing pipeline risk. Quadrilaterals may be economical alternatives to placing strain gauges on existing pipelines in areas of active or p

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Shengelia, Ioane. "Computation on conformal moduli of Quadrilaterals." In RDP online workshop "Recent Advances in Mathematical Physics". Sissa Medialab, 2021. http://dx.doi.org/10.22323/1.394.0016.

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Lubiw, Anna. "Decomposing polygonal regions into convex quadrilaterals." In the first annual symposium. ACM Press, 1985. http://dx.doi.org/10.1145/323233.323247.

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Ariska, Mashadi, and Leli Deswita. "Modification of the Varignon theorem on quadrilaterals." In 2ND INTERNATIONAL CONFERENCE ON ADVANCED INFORMATION SCIENTIFIC DEVELOPMENT (ICAISD) 2021: Innovating Scientific Learning for Deep Communication. AIP Publishing, 2023. http://dx.doi.org/10.1063/5.0106508.

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Mota-Gutierrez, Sergio A., Victor Ayala-Ramirez, and Raul E. Sanchez-Yanez. "Recognizing hand-drawn quadrilaterals using genetic algorithms." In 2009 III Conference of University of Guanajuato IEEE Students Chapter (IEEExPO). IEEE, 2009. http://dx.doi.org/10.1109/ieeexpo.2009.5422870.

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Connell, Stuart D., D. Graham Holmes, and Mark E. Braaten. "Adaptive Unstructured 2D Navier-Stokes Solutions on Mixed Quadrilateral/Triangular Meshes." In ASME 1993 International Gas Turbine and Aeroengine Congress and Exposition. American Society of Mechanical Engineers, 1993. http://dx.doi.org/10.1115/93-gt-099.

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This paper presents a solution adaptive scheme for solving the Navier-Stokes equations on an unstructured mixed grid of triangles and quadrilaterals. The solution procedure uses an explicit Runge-Kutta finite volume time marching scheme with an adaptive blend of second and fourth order smoothing. The governing equations are solved in a 2D, axisymmetric or quasi-3D form. In viscous regions quadrilateral elements are used to facilitate the one dimensional refinement required for the efficient resolution of boundary layers and wakes. The effect of turbulence is incorporated through using either a

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Brady, Michael H., and Steven W. Peterson. "A Derivation of the Pole Curve Equations in the Projective Plane." In ASME 1992 Design Technical Conferences. American Society of Mechanical Engineers, 1992. http://dx.doi.org/10.1115/detc1992-0270.

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Abstract The traditional four-position method of mechanism synthesis focuses on the poles corresponding to four displacements. From these poles arise equations for the center-points and circle-points of possible four-bar linkages. However, if one of the poles is infinite (the associated displacement is a pure translation), the established derivations for the pole curve equation break down. This problem is rectified by expressing the pole curve equation in the projective plane, because all points, including points at infinity, have finite homogeneous coordinates. In Part I of this paper, this f

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Xiao, Yumin, and R. S. Amano. "A New Development of Multi-to-One Cell-Matching Method and Its Application in VOF Interface Tracking." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-84897.

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A new algorithm—multi-to-one cell matching method for interface tracking in volume-of-fluid (VOF) calculation is presented. This method is based upon unstructured grid and implemented on cells having quadrilaterals or hexahedrons origin. This method utilizes the geometrical characteristic of each vertex in an arbitrary cell to classify the vertex type and to group faces into four (two dimensional) or six (three dimensional) groups. The final regrouped arbitrary cells have the similar geometric information and VOF distributions as that of quadrilaterals or hexahedrons. Convective flux to solve

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Suzuki, Hirotaka. "Skew quadrilateral membrane folding for lampshade design." In The 13th International Conference on Engineering and Computer Graphics BALTGRAF-13. Vilnius Gediminas Technical University, 2015. http://dx.doi.org/10.3846/baltgraf.2015.016.

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Historically, Japanese traditional lampstand 'Andon', was manufactured from paper. And paper folding method was adopted into some Andon or western lampshade design. For example, Yoshimura/Diamond pattern, known as a structure of crashed cylinder, or a structure of building roof, that has been of beneficial use in commercial lampshade products. Yoshimura pattern structure includes a set of skew quadrilaterals which are not on a plane surface and each quadrilateral is constructed with 2 planar triangles. Development of Yoshimura pattern is constructed by one set of horizontal parallel lines at e

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Bhagath, Parabattina, and Pradip K. Das. "Quadrilaterals based phoneme segmentation technique for low resource spoken languages." In TENCON 2022 - 2022 IEEE Region 10 Conference (TENCON). IEEE, 2022. http://dx.doi.org/10.1109/tencon55691.2022.9977455.

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Reports on the topic "Quadrilaterals"

1

D`Azevedo, E. F. Are bilinear quadrilaterals better than linear triangles? Office of Scientific and Technical Information (OSTI), 1993. http://dx.doi.org/10.2172/10179134.

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D'Azevedo, E. F. Are Bilinear Quadrilaterals Better Than Linear Triangles? Office of Scientific and Technical Information (OSTI), 1993. http://dx.doi.org/10.2172/814567.

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Asvestas, John S. Calculation of Moment Matrix Elements for Bilinear Quadrilaterals and Higher-Order Basis Functions. Defense Technical Information Center, 2016. http://dx.doi.org/10.21236/ad1001926.

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Mitchell, John Anthony. Mean curl formulation on quadrilaterals with application to implicit magnetics diffusion equations in Alegra 2D. Office of Scientific and Technical Information (OSTI), 2012. http://dx.doi.org/10.2172/1057253.

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Santos, H. A., J. A. Evans, and T. J. Hughes. Generalization of the Twist-Kirchhoff Theory of Plate Elements to Arbitrary Quadrilaterals and Assessment of Convergence. Defense Technical Information Center, 2011. http://dx.doi.org/10.21236/ada555338.

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Babuska, I., T. Strouboulis, S. K. Gangaraj, and C. S. Upadhyay. Eta%-Superconvergence in the Interior of Locally Refined Meshes of Quadrilaterals: Superconvergence of the Gradient in Finite Element Solutions of Laplace's and Poisson's Equations. Defense Technical Information Center, 1994. http://dx.doi.org/10.21236/ada277242.

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Babuska, I., T. Strouboulis, C. S. Upadhyay, and S. K. Gangaraj. A Model Study of Element Residual Estimators for Linear Elliptic Problems: The Quality of the Estimators in the Interior of Meshes of Triangles and Quadrilaterals. Defense Technical Information Center, 1994. http://dx.doi.org/10.21236/ada282849.

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D'Azevedo, E. On Optimal Bilinear Quadrilateral Meshes. Office of Scientific and Technical Information (OSTI), 2000. http://dx.doi.org/10.2172/814808.

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Merrington, Louise. The India–US–China–Pakistan strategic quadrilateral. East Asian Bureau of Economic Research, 2012. http://dx.doi.org/10.59425/eabc.1334181602.

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Blacker, T., and M. Stephenson. Paving: A new approach to automated quadrilateral mesh generation. Office of Scientific and Technical Information (OSTI), 1990. http://dx.doi.org/10.2172/7184374.

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