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Journal articles on the topic 'Quadrilateral'

Author: Grafiati

Published: 4 June 2021

Last updated: 2 February 2022

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1

Josefsson, Martin. "Properties of bisect-diagonal quadrilaterals." Mathematical Gazette 101, no. 551 (June 15, 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 only two books where any theorems on such quadrilaterals are studied. In each of the books, one necessary and sufficient condition for such quadrilaterals is proved (see Theorem 1 and 2 in the next section). The purpose of this paper is to investigate basic properties ofconvexbisecting quadrilaterals, but we have chosen to give them a slightly different name. Let us first remind the reader that a quadrilateral whose diagonals have equal lengths is called an equidiagonal quadrilateral and one whose diagonals are perpendicular is called an orthodiagonal quadrilateral.

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2

Choudhry, Ajai. "Brahmagupta quadrilaterals with equal perimeters and equal areas." International Journal of Number Theory 16, no. 03 (October 2, 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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3

Mammana, Maria Flavia, and Biagio Micale. "Quadrilaterals of triangle centres." Mathematical Gazette 92, no. 525 (November 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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4

RAMASWAMI, SUNEETA, MARCELO SIQUEIRA, TESSA SUNDARAM, JEAN GALLIER, and JAMES GEE. "CONSTRAINED QUADRILATERAL MESHES OF BOUNDED SIZE." International Journal of Computational Geometry & Applications 15, no. 01 (February 2005): 55–98. http://dx.doi.org/10.1142/s0218195905001609.

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We introduce a new algorithm to convert triangular meshes of polygonal regions, with or without holes, into strictly convex quadrilateral meshes of small bounded size. Our algorithm includes all vertices of the triangular mesh in the quadrilateral mesh, but may add extra vertices (called Steiner points). We show that if the input triangular mesh has t triangles, our algorithm produces a mesh with at most [Formula: see text] quadrilaterals by adding at most t+2 Steiner points, one of which may be placed outside the triangular mesh domain. We also describe an extension of our algorithm to convert constrained triangular meshes into constrained quadrilateral ones. We show that if the input constrained triangular mesh has t triangles and its dual graph has h connected components, the resulting constrained quadrilateral mesh has at most [Formula: see text] quadrilaterals and at most t+3h Steiner points, one of which may be placed outside the triangular mesh domain. Examples of meshes generated by our algorithm, and an evaluation of the quality of these meshes with respect to a quadrilateral shape quality criterion are presented as well.

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5

GROSSMAN, PINHAS, and MASAKI IZUMI. "CLASSIFICATION OF NONCOMMUTING QUADRILATERALS OF FACTORS." International Journal of Mathematics 19, no. 05 (May 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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6

Josefsson, Martin. "Further characterisations of tangential quadrilaterals." Mathematical Gazette 101, no. 552 (October 16, 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 = b + d [1, pp. 64-67]. If you want to have more background information about characterisations of tangential quadrilaterals, then we recommend you to check out the lovely papers [2, 3, 4], as well as our previous contributions on the subject [5, 6, 7]. These six papers together include about 30 characterisations that are either proved or reviewed there with references.

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7

Fraivert, David. "Pascal-points quadrilaterals inscribed in a cyclic quadrilateral." Mathematical Gazette 103, no. 557 (June 6, 2019): 233–39. http://dx.doi.org/10.1017/mag.2019.54.

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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)

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8

IZADI, FARZALI, FOAD KHOSHNAM, DUSTIN MOODY, and ARMAN SHAMSI ZARGAR. "ELLIPTIC CURVES ARISING FROM BRAHMAGUPTA QUADRILATERALS." Bulletin of the Australian Mathematical Society 90, no. 1 (April 10, 2014): 47–56. http://dx.doi.org/10.1017/s0004972713001172.

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AbstractA Brahmagupta quadrilateral is a cyclic quadrilateral whose sides, diagonals and area are all integer values. In this article, we characterise the notions of Brahmagupta, introduced by K. R. S. Sastry [‘Brahmagupta quadrilaterals’, Forum Geom. 2 (2002), 167–173], by means of elliptic curves. Motivated by these characterisations, we use Brahmagupta quadrilaterals to construct infinite families of elliptic curves with torsion group $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\mathbb{Z}/2\mathbb{Z}\times \mathbb{Z}/2\mathbb{Z}$ having ranks (at least) four, five and six. Furthermore, by specialising we give examples from these families of specific curves with rank nine.

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9

Bao, Yuan, Zhaoliang Meng, and Zhongxuan Luo. "AC0-nonconforming quadrilateral finite element for the fourth-order elliptic singular perturbation problem." ESAIM: Mathematical Modelling and Numerical Analysis 52, no. 5 (September 2018): 1981–2001. http://dx.doi.org/10.1051/m2an/2018033.

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In this paper, aC0nonconforming quadrilateral element is proposed to solve the fourth-order elliptic singular perturbation problem. For each convex quadrilateralQ, the shape function space is the union ofS21(Q*) and a bubble space. The degrees of freedom are defined by the values at vertices and midpoints on the edges, and the mean values of integrals of normal derivatives over edges. The local basis functions of our element can be expressed explicitly by a new reference quadrilateral rather than by solving a linear system. It is shown that the method converges uniformly in the perturbation parameter. Lastly, numerical tests verify the convergence analysis.

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10

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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11

Sharp, Robert V., and John L. Saxton. "Three-dimensional records of surface displacement on the Superstition Hills fault zone associated with the earthquakes of 24 November 1987." Bulletin of the Seismological Society of America 79, no. 2 (April 1, 1989): 376–89. http://dx.doi.org/10.1785/bssa0790020376.

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Abstract Seven quadrilaterals, constructed at broadly distributed points on surface breaks within the Superstition Hills fault zone, were repeatedly remeasured after the pair of 24 November 1987 earthquakes to monitor the growing surface displacement. Changes in the dimensions of the quadrilaterals are recalculated to right-lateral and extensional components at millimeter resolution, and vertical components of change are resolved at 0.2 mm precision. The displacement component data for four of the seven quadrilaterals record the complete fault movement with respect to an October 1986 base. These data fit with remarkable agreement the power law U ( t ) = U f ( B t 1 + B t ) c , where U(t) is a displacement component at time t after the second main shock and Uf, B, and c are constants. This power law permits estimation of the final displacement, Uf, from the data obtained within the period of observation. Data from one quadrilateral, located near the epicenter of the second main shock and northeast-trending conjugate faults, allow that about 5 cm of right-lateral slip may have been associated with the first main shock there. Data from the other quadrilaterals confirm that the surface faulting on most of the Superstition Hills fault zone did initiate at the time of the second main shock of the 1987 earthquakes. The three-dimensional motion vectors all describe nearly linear trajectories throughout the observation period, and they indicate smooth shearing on their respective fault surfaces. The inclination of the shear surfaces is generally nearly vertical, except near the south end of the Superstition Hills fault zone where two strands dip northeastward at about 70°. Surface displacement on these strands is right reverse. Another kind of deformation, superimposed on the fault displacements, has been recorded at all quadrilateral sites. It consists of a northwest-southeast contraction or component of contraction that ranged from 0 to 0.1 per cent of the quadrilateral lengths between November 1987 and April 1988.

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12

Buchholz, R. H., and J. A. MacDougall. "Heron quadrilaterals with sides in arithmetic or geometric progression." Bulletin of the Australian Mathematical Society 59, no. 2 (April 1999): 263–69. http://dx.doi.org/10.1017/s0004972700032883.

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We study triangles and cyclic quadrilaterals which have rational area and whose sides form geometric or arithmetic progressions. A complete characterisation is given for the infinite family of triangles with sides in arithmetic progression. We show that there are no triangles with sides in geometric progression. We also show that apart from the square there are no cyclic quadrilaterals whose sides form either a geometric or an arithmetic progression. The solution of both quadrilateral cases involves searching for rational points on certain elliptic curves.

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13

Josefsson, Martin. "Metric relations in crossed trapezia." Mathematical Gazette 102, no. 554 (June 18, 2018): 264–69. http://dx.doi.org/10.1017/mag.2018.57.

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The trapezium (trapezoid in American English) is one of the seven most well-known quadrilaterals that is studied in school geometry. However, it is always assumed that it is convex. In this note we shall derive metric formulas for the most important quantities incrossedtrapezia and compare them to the similar formulas for convex trapezia. The corresponding investigation regarding crossed cyclic quadrilaterals was conducted in [1]. Any crossed quadrilateral has a pair of opposite sides intersecting and both of its diagonals are outside of itself.

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14

Barutu, Fabelia Andani, Mashadi Mashadi, and Sri Gemawati. "Pengembangan Teorema Morley pada Segiempat." Journal of Medives : Journal of Mathematics Education IKIP Veteran Semarang 2, no. 1 (January 1, 2018): 41. http://dx.doi.org/10.31331/medives.v2i1.526.

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Pada umumnya teorema Morley diberlakukan pada segitiga, dalam tulisan ini akan dikembangkan ide teorema Morley untuk bangun datar dengan sisi yang lebih banyak (dalam hal ini segi empat) dan menentukan rumus panjang sisi segiempat Morley tersebut. Segiempat yang dibahas yakni persegi, persegi panjang, belah ketupat, layang-layang, dan trapesium sama kaki. Pembuktian dalam tulisan ini menggunakan cara yang lebih sederhana dengan konsep kesebangunan dan konsep trigonometri. Kata kunci: Teorema Morley, konsep kekongruenan, trigonometri. ABSTRACT Morley’s Theorem generally applies in triangle. This paper applied Morley’s Theorem in quadrilateral to determine the side lenght of Morley’s quadrilateral. Quadrilaterals discussed in this paper are square, rectangle rhombus, kite, and isoscelestrapezium. Simpler way is used to prove by applying congruence and trigonometric concepts. Keywords: Morley’s Theorem, congruence concept, trigonometry.

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15

Mansuri, Akhlak, Rohit Mehta, and R. S. Chandel. "Central Graph of Quadrilateral Snakes with Chromatic Number." Journal of the Indonesian Mathematical Society 27, no. 1 (March 31, 2021): 1–8. http://dx.doi.org/10.22342/jims.27.1.948.1-8.

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This article shows the study about the harmonious coloring and to investigate the harmonious chromatic number of the central graph of quadrilateral snake, double quadrilateral snake, triple quadrilateral snake, k-quadrilateral snake, alternate quadrilateral snake, double alternate quadrilateral snake, triple alternate quadrilateral snake and k-alternate quadrilateral snake, denoted by C(Qn), C(DQn), C(TQn), C(kQn), C(AQn), C(D(AQn)), C(T(AQn)), C(k(AQn)) respectively.

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16

MING, PINGBING, and ZHONGCI SHI. "QUADRILATERAL MESH." Chinese Annals of Mathematics 23, no. 02 (April 2002): 235–52. http://dx.doi.org/10.1142/s0252959902000237.

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17

Lai, Ming-Jun, and Larry L. Schumaker. "Quadrilateral Macroelements." SIAM Journal on Mathematical Analysis 33, no. 5 (January 2002): 1107–16. http://dx.doi.org/10.1137/s0036141000377134.

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18

Fraivert, David. "New points that belong to the nine-point circle." Mathematical Gazette 103, no. 557 (June 6, 2019): 222–32. http://dx.doi.org/10.1017/mag.2019.53.

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In the present paper, we show that the point of intersection of the bimedians of a cyclic quadrilateral belongs to the nine-point circle (Euler’s circle) of the triangle with one vertex at the point of intersection of the quadrilateral’s diagonals and the other vertices at the points of intersection of the extensions of its pairs of opposite sides.

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19

Firmansah, Fery. "Pelabelan Harmonis Ganjil pada Graf Bunga Double Quadrilateral." JURNAL ILMIAH SAINS 20, no. 1 (March 10, 2020): 12. http://dx.doi.org/10.35799/jis.20.1.2020.27278.

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Graf harmonis ganjil adalah graf yang memenuhi sifat-sifat pelabelan harmonis ganjil. Tujuan dari penelitian ini adalah mendapatkan kelas graf baru yang merupakan graf harmonis ganjil. Metode penelitian yang digunakan terdiri dari beberapa tahapan yaitu konstruksi definisi, formulasi fungsi pelabelan dan pembuktian teorema. Hasil dari penelitian ini adalah konstruksi graf bunga double quadrilateral dengan dan graf bunga variasi double quadrilateral dengan yang merupakan pengembangan dari graf double quadrilateral dan graf variasi double quadrilateral . Lebih lanjut telah dibuktikan bahwa graf dan adalah graf harmonis ganjil.Kata Kunci: graf double quadrilateral, graf bunga, graf harmonis ganjil, pelabelan graf Odd Harmonious Labelling on The Flower Double Quadrilateral Graphs ABSTRACTOdd harmonious graphs are graphs that have odd harmonious labeling properties. The purpose of this study is to get a new class of graphs which are odd harmonious graphs. The research method used consists of several stages, namely construction of definitions, formulation of labeling functions and proof of theorems. The results of this study is to get a graph construction will be given, namely the flower quadrilateral graphs with and the flower variation of quadrilateral graphs with , which are the development of double quadrilateral graphs and variation double quadrilateral graphs . It has further been proven that and are odd harmonious graphs.Keywords: double quadrilateral graph, flower graph, labeling graph, odd harmonious graph

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20

Locher, Paul J., and Pieter Jan Stappers. "Factors Contributing to the Implicit Dynamic Quality of Static Abstract Designs." Perception 31, no. 9 (September 2002): 1093–107. http://dx.doi.org/10.1068/p3299.

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Participants rated the dynamic quality of a set of twelve-element nonrepresentational or abstract visual designs each composed of one of four types of triangles or four types of quadrilaterals. We investigated the contribution to the perceived or implicit dynamics of the design of the four factors edge alignment of compositional elements, physical weight distribution about the horizontal axis, activity directions within the designs, and type of compositional element. It was found that edge alignment of elements was the most influential factor contributing to the dynamics both of triangle and of quadrilateral designs. In addition, dynamics was found to be positively correlated with the number of perceived activity directions within both types of stimuli. Triangle designs, but not quadrilateral ones, with greater structural weight above the horizontal axis were rated as more dynamic. Results suggest that implicit dynamics of nonrepresentational designs arises from a percept based on a global spatial analysis of the stimulus characteristics studied.

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21

T, Pathinathan, and Santhoshkumar S. "Quadrilateral Fuzzy Number." International Journal of Engineering & Technology 7, no. 4.10 (October 2, 2018): 1018. http://dx.doi.org/10.14419/ijet.v7i4.10.26661.

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Fuzzy numbers are used to represent uncertainty. Various types of fuzzy numbers are used in practical applications. In this paper we define Perfect Pentagonal Fuzzy Number (PPFN), Quadrilateral Fuzzy Number (QNF) and Left skewed Quadrilateral Fuzzy Number and Right skewed Quadrilateral Fuzzy Number. We study their algebraic properties with numerical examples.

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22

Pambuccian, Victor, and Michael Wolterman. "Saccheri Quadrilateral: 11004." American Mathematical Monthly 112, no. 1 (January 1, 2005): 88. http://dx.doi.org/10.2307/30037398.

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23

Daniels, Joel, Claudio T. Silva, and Elaine Cohen. "Localized Quadrilateral Coarsening." Computer Graphics Forum 28, no. 5 (July 2009): 1437–44. http://dx.doi.org/10.1111/j.1467-8659.2009.01520.x.

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24

Panozzo, Daniele. "Demystifying Quadrilateral Remeshing." IEEE Computer Graphics and Applications 35, no. 2 (March 2015): 88–95. http://dx.doi.org/10.1109/mcg.2015.26.

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25

Zurkiya, Omar, and T. Gregory Walker. "Quadrilateral Space Syndrome." Journal of Vascular and Interventional Radiology 25, no. 2 (February 2014): 229. http://dx.doi.org/10.1016/j.jvir.2013.10.016.

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26

Manske, Robert C., Afton Sumler, and Jodi Runge. "Quadrilateral Space Syndrome." Athletic Therapy Today 14, no. 2 (March 2009): 45–47. http://dx.doi.org/10.1123/att.14.2.45.

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27

Ming, Pingbing, and Zhong-Ci Shi. "Quadrilateral mesh revisited." Computer Methods in Applied Mechanics and Engineering 191, no. 49-50 (December 2002): 5671–82. http://dx.doi.org/10.1016/s0045-7825(02)00471-1.

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28

Hoogenboom, Pierre C. J., and Johan Blaauwendraad. "Quadrilateral shear panel." Engineering Structures 22, no. 12 (December 2000): 1690–98. http://dx.doi.org/10.1016/s0141-0296(99)00061-9.

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29

Brown, Sherry-Ann N., Derrick A. Doolittle, Carol J. Bohanon, Arjun Jayaraj, Sailendra G. Naidu, Eric A. Huettl, Kevin J. Renfree, et al. "Quadrilateral Space Syndrome." Mayo Clinic Proceedings 90, no. 3 (March 2015): 382–94. http://dx.doi.org/10.1016/j.mayocp.2014.12.012.

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30

Chong, J. Kenneth. "Quadrilateral space syndrome." Plastic and Reconstructive Surgery 76, no. 4 (October 1985): 662. http://dx.doi.org/10.1097/00006534-198510000-00063.

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31

Daniels, Joel, Cláudio T. Silva, Jason Shepherd, and Elaine Cohen. "Quadrilateral mesh simplification." ACM Transactions on Graphics 27, no. 5 (December 2008): 1–9. http://dx.doi.org/10.1145/1409060.1409101.

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32

Sederberg, Thomas W., and Jianmin Zheng. "Birational quadrilateral maps." Computer Aided Geometric Design 32 (January 2015): 1–4. http://dx.doi.org/10.1016/j.cagd.2014.11.001.

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33

Di Paolo, Rocco J., Chris Philip, Anthony L. Maganzini, and John D. Hirce. "Quadrilateral analysis revisited." American Journal of Orthodontics 88, no. 5 (November 1985): 442. http://dx.doi.org/10.1016/0002-9416(85)90072-7.

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34

Kaura, Vinay. "India’s Quadrilateral conundrum." India Review 20, no. 3 (May 27, 2021): 322–47. http://dx.doi.org/10.1080/14736489.2021.1931750.

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35

Josefsson, Martin. "On the classification of convex quadrilaterals." Mathematical Gazette 100, no. 547 (March 2016): 68–85. http://dx.doi.org/10.1017/mag.2016.9.

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We live in a golden age regarding the opportunities to explore Euclidean geometry. The access to dynamic geometry computer programs for everyone has made it very easy to study complex configurations in a way that has never been possible before. This is especially apparent in the study of triangle geometry, where the flow of new problems, properties, and papers is probably the highest it has ever been in the history of mathematics. Even though it has increased a bit in recent years, the interest in quadrilateral geometry is significantly lower. Why are triangles so much more popular than quadrilaterals? In fact, we think it would be more logical if the situation were reversed, since there are so many classes of quadrilaterals to explore. This is the primary reason we think that quadrilaterals are a lot more interesting to study than triangles.

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36

Amelia, Rista, and Ismail Ismail. "PEMAHAMAN KONSEP SEGIEMPAT SISWA DITINJAU DARI TIPE KEPRIBADIAN EKSTROVERT-INTROVERT DAN JENIS KELAMIN." MATHEdunesa 9, no. 1 (June 29, 2020): 231–40. http://dx.doi.org/10.26740/mathedunesa.v9n1.p231-240.

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Understanding the concept is one important factor in the purpose of learning mathematics. Understanding concepts is the ability of students in mastering a concept both in explaining and applying a concept in problem solving or problem solving. Personality plays a role in the learning process of students this is because the attitude of each individual in making decisions is influenced by habits. Personality and gender differences can allow differences in understanding of concepts. This research is a qualitative descriptive study with the aim to describe the understanding of the quadrilateral concept of students in terms of extrovert-introvert personality types and gender. In this study four junior high school students were chosen as subjects determined by extrovert-introvert personality types and gender. Data collection instruments used consisted of mathematics ability tests, MBTI personality questionnaires, quadrilateral understanding of concept material tests and interview guidelines. The results of this study indicate (a) Extroverted male students are less able to restate the quadrilateral concept, and less able to use and utilize and choose procedures or operations to solve quadrilateral problems (b) Extroverted female students are less able to restate the quadrilateral concept, less able to calcify quadrilateral based on appropriate traits, and less able to use and utilize and choose procedures or operations to solve quadrilateral problems (c) Introverted male students are less able to restate the quadrilateral concept, less able to calcify rectangles based on appropriate traits, ( d) Introverted female students are less able to calcify quadrilateral based on appropriate traits. The implication of the results of this study is the understanding of the concepts in each personality of both men and women need to be considered. Keywords: Understanding of concepts, quadrilateral, ekstrovert-introvert and gender.

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Rogério César dos Santos, Ana Clara Oliveira Comby, and Ramires Vargas da Silva. "A Curious Property of Octagons." Scientific Inquiry and Review 3, no. 2 (June 5, 2019): 01–07. http://dx.doi.org/10.32350/sir.32.01.

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The famous theorem of Van Aubel for quadrilaterals postulates that if squares are built externally on the sides of any quadrilateral, then the two segments that join the opposing centers of these squares are congruent and orthogonal. Inspired by this result and also by the results of Krishna, in this article we will prove the following result of plane geometry: each octagon is associated with a parallelogram, in some cases the parallelogram in question can be degenerate at a point or a segment. This is possible because of complex numbers and basics of analytical geometry.

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38

Yamakawa, Soji, and Kenji Shimada. "Quad-Layer: Layered Quadrilateral Meshing of Narrow Two-Dimensional Domains by Bubble Packing and Chordal Axis Transformation." Journal of Mechanical Design 124, no. 3 (August 6, 2002): 564–73. http://dx.doi.org/10.1115/1.1486014.

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This paper presents a computational method for quadrilateral meshing of a thin, or narrow, two-dimensional domain for finite element analysis. The proposed method creates a well-shaped single-layered, multi-layered, or partially multi-layered quadrilateral mesh. Element sizes can be uniform or graded. A high quality, layered quadrilateral mesh is often required for finite element analysis of a narrow two-dimensional domain with a large deformation such as in the analysis of rubber deformation or sheet metal forming. Fully automated quadrilateral meshing is performed in two stages: (1) extraction of the skeleton of a given domain by discrete chordal axis transformation, and (2) discretization of the chordal axis into a set of line segments and conversion of each of the line segments to a single quadrilateral element or multiple layers of quadrilateral elements. In each step a physically-based computational method called bubble packing is applied to discretize a curve into a set of line segments of specified sizes. Experiments show that the accuracy of a large-deformation FEM analysis can be significantly improved by using a well-shaped quadrilateral mesh created by the proposed method.

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39

Beardon, A. F. "Pitot's theorem, dynamic geometry and conics." Mathematical Gazette 105, no. 562 (February 17, 2021): 52–60. http://dx.doi.org/10.1017/mag.2021.7.

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It is well known that a convex quadrilateral is a cyclic quadrilateral if, and only if, the sum of each pair of opposite angles is π. This result (which gives a necessary and sufficient condition for the existence of a circle which circumscribes a given quadrilateral) is beautifully complemented by Pitot’s theorem which says that a given convex quadrilateral has an inscribed circle if, and only if, the sum of the lengths of one pair of opposite edges is the same as the sum for the other pair. Henri Pitot, a French engineer, noticed the easy part of this result in 1725 (see Figure 1), and the converse was first proved by J-B Durrande in 1815. Accordingly, we shall say that a convex quadrilateral is a Pitot quadrilateral if, and only if, the sum of the lengths of one pair of opposite edges is the same as the sum for the other pair.

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Sen, Ramesh K., Gaurav Saini, Sagar Kadam, and Neha Raman. "Anatomical quadrilateral plate for acetabulum fractures involving quadrilateral surface: A review." Journal of Clinical Orthopaedics and Trauma 11, no. 6 (November 2020): 1072–81. http://dx.doi.org/10.1016/j.jcot.2020.10.013.

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Chen, Hamilton, and Vincent Reginald Narvaez. "Ultrasound-Guided Quadrilateral Space Block for the Diagnosis of Quadrilateral Syndrome." Case Reports in Orthopedics 2015 (2015): 1–4. http://dx.doi.org/10.1155/2015/378627.

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Quadrilateral space syndrome (QSS) is a rare nerve entrapment disorder that occurs when the axillary nerve and posterior circumflex humeral artery (PCHA) become compressed in the quadrilateral space. QSS presents as vague posterolateral shoulder pain that is exacerbated upon the abduction and external rotation of the shoulder. Diagnosis of QSS is difficult because of the vague presentation of QSS. In addition, even though MRI and MR angiography can be used in QSS diagnosis, there is currently no “gold standard” diagnostic imaging studies for QSS. In this case report, we describe a novel ultrasound-guided technique for a diagnostic quadrilateral space block and present a case where the diagnostic block was used to diagnose QSS. We believe that a diagnostic block of the quadrilateral space is a useful adjunct in the evaluation of patients with suspected QSS, especially in cases where examination findings and other diagnostic modalities are indeterminate.

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Cen, Song, Xiao-Ming Chen, and Xiang-Rong Fu. "Quadrilateral membrane element family formulated by the quadrilateral area coordinate method." Computer Methods in Applied Mechanics and Engineering 196, no. 41-44 (September 2007): 4337–53. http://dx.doi.org/10.1016/j.cma.2007.05.004.

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Beardon, A. F. "What is the most symmetric quadrilateral?" Mathematical Gazette 96, no. 536 (July 2012): 207–12. http://dx.doi.org/10.1017/s0025557200004435.

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What is the most symmetric quadrilateral you can think of? Most people would say ‘a square’, but having given this (or any other) answer, can you create your own definition of a ‘quadrilateral’, and of ‘most symmetric’, so that you can justify your answer as a rigorous piece of mathematics? This is a challenging investigation because the answer may not be the obvious one.Often the main difficulty in solving a problem lies in finding appropriate definitions; here we must first consider the questions ‘what is a quadrilateral?’, and ‘what is a symmetry of a quadrilateral?’.

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Shi, G., Y. Liu, and X. Wang. "Accurate, Efficient, and Robust Q4-Like Membrane Elements Formulated in Cartesian Coordinates Using the Quasi-Conforming Element Technique." Mathematical Problems in Engineering 2015 (2015): 1–14. http://dx.doi.org/10.1155/2015/198390.

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By using the quasi-conforming element technique, two four-node quadrilateral membrane elements with 2 degrees of freedom at each node (Q4-like membrane element) are formulated in rectangular Cartesian coordinates. One of the four-node quadrilateral membrane elements is based on the assumed strain field with only five independent strain parameters and accounting for the Poisson effect explicitly. There are no independent internal parameters and numerical integration involved in the evaluation of the strain parameters in these four-node quadrilateral membrane elements, and their element stiffness matrices are computed explicitly in Cartesian coordinates. Consequently, the formulation of these four-node quadrilateral membrane elements is extremely simple, and the resulting elements are very computationally efficient. These two quasi-conforming quadrilateral membrane elements pass the patch test and are free from shear locking and insensitive to the element distortion in the range of practical application. The numerical result comparison with other four-node quadrilateral membrane elements, including Q4-like plane elements with drilling degrees of freedom and the Q6-type isoparametric elements with very complicated nonconforming modes, shows that the present quasi-conforming quadrilateral membrane elements are not only reliable and robust, but also very accurate in both displacement and stress evaluations in the analysis of practical plane elasticity problems.

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Jeyakarthikeyan, P. V., R. Yogeshwaran, and Karthikk Sridharan. "An Efficient Method to Generate Element Stiffness Matrix of Quadrilateral Elements in Closed Form on Application of Vehicle Analysis." Applied Mechanics and Materials 852 (September 2016): 582–87. http://dx.doi.org/10.4028/www.scientific.net/amm.852.582.

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This paper presents about generating elemental stiffness matrix for quadrilateral elements in closed form solution method for application on vehicle analysis which is convenient and simple as long as Jacobian is matrix of constant. The interpolation function of the field variable to be found can integrate explicitly once for all, which gives the constant universal matrices A, B and C. Therefore, stiffness matrix is no longer integration of the given functional, it is simple calculation of universal matrices and local co-ordinates of the element. So time taken for generation of element stiffness can be reduced considerably compared to Gauss numerical integration method. For effective use of quadrilateral elements hybrid grid generation is recommended that contains all interior element edges are parallel to each other (rectangle or square elements) and outer boundary elements are quadrilaterals with distortion. So in the Proposed method, the closed form and Gauss numerical method is used explicitly for interior elements and outer elements respectively. The time efficiency of proposed method is compared with conventional Gauss quadrature that is used for entire domain. It is found that the proposed method is much efficient than Gauss Quadrature.

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McLean, K. Robin. "Conics and convexity." Mathematical Gazette 98, no. 542 (July 2014): 266–72. http://dx.doi.org/10.1017/s0025557200001303.

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In [1], W. D. Munn proved the following result.Theorem 1: Infinitely many ellipses pass through the four vertices of a given convex quadrilateral.Much of the geometry that I studied as an undergraduate in the 1950s concerned complex projective space, in which convexity plays no part. So I found Theorem 1 especially piquant and sought to understand it better. This article is the result. After examining the convexity of quadrilaterals in general, especially those inscribed in conics, I consider the following problem. Let P be a variable point in the plane, distinct from the vertices of a given convex quadrilateral ABCD. It is well known that there is a unique conic, S (P), through the five points A, B, C, D and P. How does the nature of this conic depend on the position of P? As a spin-off, we get a very short proof of Theorem 1. Finally I look at what happens when the quadrilateral ABCD is not convex. In this case, S (P) is always a hyperbola, but the distribution of A, B, C and D on its branches is still of interest.

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Pereira-Mendoza, Lionel. "What Is a Quadrilateral?" Mathematics Teacher 86, no. 9 (December 1993): 774–76. http://dx.doi.org/10.5951/mt.86.9.0774.

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Valinoti, Joseph R. "Re: The quadrilateral analysis." American Journal of Orthodontics 88, no. 3 (September 1985): 264–65. http://dx.doi.org/10.1016/s0002-9416(85)90222-2.

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Orton, D. J. "69.41 A Circumscribing Quadrilateral." Mathematical Gazette 69, no. 450 (December 1985): 295. http://dx.doi.org/10.2307/3617581.

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Bishop, Christopher J. "Quadrilateral Meshes for PSLGs." Discrete & Computational Geometry 56, no. 1 (March 14, 2016): 1–42. http://dx.doi.org/10.1007/s00454-016-9771-9.

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