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Journal articles on the topic 'Triangle'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Mui, Grace, and Jennifer Mailley. "A tale of two triangles: comparing the Fraud Triangle with criminology’s Crime Triangle." Accounting Research Journal 28, no. 1 (2015): 45–58. http://dx.doi.org/10.1108/arj-10-2014-0092.

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Purpose – This paper aims to propose the application of the Crime Triangle of Routine Activity Theory to fraud events as a complement to the universally accepted Fraud Triangle. Design/methodology/approach – The application of the Crime Triangle is illustrated using scenarios of asset misappropriations by type of perpetrator: external perpetrator, employee, management and the board and its governing bodies. Findings – The Crime Triangle complements the Fraud Triangle’s perpetrator-centric focus by examining the environment where fraud occurs and the relevant parties that play their role in pre

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2

Odehnal, Boris. "Two Convergent Triangle Tunnels." KoG, no. 22 (2018): 3–11. http://dx.doi.org/10.31896/k.22.1.

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A semi-orthogonal path is a polygon inscribed into a given polygon such that the $i$-th side of the path is orthogonal to the $i$-th side of the given polygon. Especially in the case of triangles, the closed semi-orthogonal paths are triangles which turn out to be similar to the given triangle. The iteration of the construction of semi-orthogonal paths in triangles yields infinite sequences of nested and similar triangles. We show that these two different sequences converge towards the bicentric pair of the triangle's Brocard points. Furthermore, the relation to discrete logarithmic spirals al

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Jurkin, Ema. "Poncelet Porisms and Loci of Centers in the Isotropic Plane." Mathematics 12, no. 4 (2024): 618. http://dx.doi.org/10.3390/math12040618.

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Any triangle in an isotropic plane has a circumcircle u and incircle i. It turns out that there are infinitely many triangles with the same circumcircle u and incircle i. This one-parameter family of triangles is called a poristic system of triangles. We study the trace of the centroid, the Feuerbach point, the symmedian point, the Gergonne point, the Steiner point and the Brocard points for such a system of triangles. We also study the traces of some further points associated with the triangles of the poristic family, and we prove that the vertices of the contact triangle, tangential triangle

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4

Norihiro, Someyama. "Qualitative Properties on Bulging Triangles and Their Original Triangles." Journal of Advanced Studies in Topology 12, no. 1-2 (2022): 57–65. https://doi.org/10.5281/zenodo.7458250.

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We consider bulging triangles introduced by the author \cite{So1} and study their qualitative properties. We focus on the triangle consisting of edge-centers of a bulging triangle, ``edge-central triangle.'' In addition, we investigate the similarity to bulging triangles and centroids of their original triangles and edge-central triangles.

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Hikmatovich, Ibragimov Husniddin. "Connection Between A Right Triangle And An Equal Side Triangle." American Journal of Interdisciplinary Innovations and Research 02, no. 11 (2020): 105–14. http://dx.doi.org/10.37547/tajiir/volume02issue11-20.

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There is some evidence that a right triangle and an equilateral triangle are related. Information about Pythagorean numbers is given. The geometric meaning of the relationship between right triangles and equilateral triangles is shown. The geometric meaning of the relationship between an equilateral triangle and an equilateral triangle is shown.

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6

Wysiadecki, Grzegorz, Maciej Radek, R. Shane Tubbs, et al. "Microsurgical Anatomy of the Inferomedial Paraclival Triangle: Contents, Topographical Relationships and Anatomical Variations." Brain Sciences 11, no. 5 (2021): 596. http://dx.doi.org/10.3390/brainsci11050596.

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The inferomedial triangle is one of the two surgical triangles in the paraclival subregion of the skull base. It is delineated by the posterior clinoid process, the dural entrance of the trochlear nerve and the dural entrance of the abducens nerve. The aim of the present article is to describe the anatomical variations within the inferomedial triangle. Measurements of the triangle’s borders and area were supplemented by detailed observations of the topographical anatomy and various arrangements of its contents. Nine adult cadaveric heads (18 sides) and 28 sagittal head sections were studied. T

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7

Čerin, Zvonko. "On Napoleon triangles and propeller theorems." Mathematical Gazette 87, no. 508 (2003): 42–50. http://dx.doi.org/10.1017/s0025557200172092.

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In this paper we shall consider two situations in triangle geometry when equilateral triangles appear and then show that they are closely related.In the first (known as the Napoleon theorem) equilateral triangles BCAT, CABT, and ABCT, are built on the sides of an arbitrary triangle ABC and their centroids are (almost always) vertices of an equilateral triangle ANBNCN (known as a Napoleon triangle of ABC; see Figure 1).

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Kodrnja, Iva, and Helena Koncul. "The Loci of Vertices of Nedian Triangles." KoG, no. 21 (2017): 19–25. http://dx.doi.org/10.31896/k.21.5.

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In this article we observe nedians and nedian triangles of ratio $\eta$ for a given triangle. The locus of vertices of the nedian triangles for $\eta\in\mathbb{R}$ is found and its correlation with isotomic conjugates of the given triangle is shown. Furthermore, the curve on which lie vertices of a nedian triangle for fixed $\eta$, when we iterate nedian triangles, is found.

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9

ISMAIL, SHAHRINA. "PERFECT TRIANGLES ON THE CURVE." Journal of the Australian Mathematical Society 109, no. 1 (2019): 68–80. http://dx.doi.org/10.1017/s144678871900003x.

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A Heron triangle is a triangle that has three rational sides $(a,b,c)$ and a rational area, whereas a perfect triangle is a Heron triangle that has three rational medians $(k,l,m)$. Finding a perfect triangle was stated as an open problem by Richard Guy [Unsolved Problems in Number Theory (Springer, New York, 1981)]. Heron triangles with two rational medians are parametrized by the eight curves $C_{1},\ldots ,C_{8}$ mentioned in Buchholz and Rathbun [‘An infinite set of heron triangles with two rational medians’, Amer. Math. Monthly 104(2) (1997), 106–115; ‘Heron triangles and elliptic curves’

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Hidayatin, Nur, and Frida Murtinasari. "Generalisasi Ketaksamaan Sinus pada Segitiga." Jurnal Axioma : Jurnal Matematika dan Pembelajaran 7, no. 1 (2022): 72–78. http://dx.doi.org/10.56013/axi.v7i1.1195.

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This study aims to find a generalization of the sine inequality of any triangles. This generalization is the general form of the sine inequality in a triangle when the angles given are not angles of the triangle, i.e. when the sum of the three angles is not equal to . The sine inequality that will be studied focuses on the inequalities of the sum and multiplication of sine in triangles. In the process, qualitative research methods are carried out in the form of literature review, namely studying the sum and the multiplication inequalities of sine in triangles which will then be developed and o

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Kolar Šuper, Ružica. "Some Properties of Special Hyperbolas in the Isotropic Plane." Sarajevo Journal of Mathematics 18, no. 2 (2024): 211–16. http://dx.doi.org/10.5644/sjm.18.02.03.

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In this paper we consider special hyperbolas circumscribed to the symmetral triangle of a given triangle. Considering some special cases of these hyperbolas we get equations of some special conics related to the triangles associated to a given triangle as e.g., the Jeˇrabek hyperbola of the tangential triangle of the given triangle and the circumscribed circle of the symmetral triangle which is also the polar circle of the given triangle. We investigate some other interesting properties of special hyperbolas circumscribed to the symmetral triangle of a given triangle.

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12

ZHANG, XIN-MIN, L. RICHARD HITT, BIN WANG, and JIU DING. "SIERPIŃSKI PEDAL TRIANGLES." Fractals 16, no. 02 (2008): 141–50. http://dx.doi.org/10.1142/s0218348x08003934.

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We generalize the construction of the ordinary Sierpiński triangle to obtain a two-parameter family of fractals we call Sierpiński pedal triangles. These fractals are obtained from a given triangle by recursively deleting the associated pedal triangles in a manner analogous to the construction of the ordinary Sierpiński triangle, but their fractal dimensions depend on the choice of the initial triangles. In this paper, we discuss the fractal dimensions of the Sierpiński pedal triangles and the related area ratio problem, and provide some computer-generated graphs of the fractals.

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13

Parry, C. F., and Clark Kimberling. "Triangle Centers and Central Triangles." Mathematical Gazette 85, no. 502 (2001): 172. http://dx.doi.org/10.2307/3620531.

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Leversha, Gerry, and Clark Kimberling. "Triangle Centers and Central Triangles." Mathematical Gazette 85, no. 502 (2001): 173. http://dx.doi.org/10.2307/3620532.

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15

Delahaye, Jean-Paul. "Découper un triangle en triangles." Pour la Science N° 500 - juin, no. 6 (2019): 82–87. http://dx.doi.org/10.3917/pls.500.0082.

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16

Montoro, Carlos, and Regine Hampel. "CALL: A triangle of triangles." EuroCALL Review 20, no. 1 (2012): 126. http://dx.doi.org/10.4995/eurocall.2012.16204.

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Institutional investment in technology and infrastructure for the provision of new online and self-access language learning opportunities is not always accompanied by the necessary changes in the practices of learners, practitioners and managers in higher education (Wertsch, 2002). As a result, feelings of frustration, helplessness and confusion in individuals can begin to emerge soon after the initial excitement and novelty wear off. A large investment project that has little or no overall impact may give rise to questions about the adequate use of resources and ultimately lead to abandoning,

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17

Garstang, R. H. "70.38 Triangles in a Triangle." Mathematical Gazette 70, no. 454 (1986): 288. http://dx.doi.org/10.2307/3616187.

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18

Dolan, Stan. "Triangles around a given triangle." Mathematical Gazette 99, no. 546 (2015): 432–43. http://dx.doi.org/10.1017/mag.2015.80.

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19

Lester, June A. "Triangles III: Complex triangle functions." Aequationes Mathematicae 53, no. 1-2 (1997): 4–35. http://dx.doi.org/10.1007/bf02215963.

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Lester, June A. "Triangles II: Complex triangle coordinates." Aequationes Mathematicae 52, no. 1 (1996): 215–45. http://dx.doi.org/10.1007/bf01818341.

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21

Volenec, Vladimir, Zdenka Kolar-Begović, and Ružica Kolar-Šuper. "On Some Properties of the First Brocard Triangle in the Isotropic Plane." Mathematics 10, no. 9 (2022): 1381. http://dx.doi.org/10.3390/math10091381.

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In this paper we introduce the first Brocard triangle of an allowable triangle in the isotropic plane and derive the coordinates of its vertices in the case of a standard triangle. We prove that the first Brocard triangle is homologous to the given triangle and that these two triangles are parallelogic. We consider the relationships between the first Brocard triangle and the Steiner axis, the Steiner point, and the Kiepert parabola of the triangle. We also investigate some other interesting properties of this triangle and consider relationships between the Euclidean and the isotropic case.

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22

Perng, Cherng-tiao. "On Yiu’s Equilateral Triangles Associated with a Kiepert Hyperbola." Geometry 2, no. 3 (2025): 10. https://doi.org/10.3390/geometry2030010.

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In 2014, Paul Yiu constructed two equilateral triangles inscribed in a Kiepert hyperbola associated with a reference triangle. It was asserted that each of the equilateral triangles is triply perspective with the reference triangle, and in each case, the corresponding three perspectors are collinear. In this note, we provide proof of his assertions. Furthermore, as an analogue of Lemoine’s problem, we formulated and answered the question of how to recover the reference triangle given a Kiepert hyperbola, one of the two Fermat points and one vertex of the reference triangle.

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23

SZILARD, ANDRAS, and SANDOR NAGYDOBAI KISS. "An area formula for the triangle of residual centroids and its generalizations." Creative Mathematics and Informatics 30, no. 1 (2021): 11–18. http://dx.doi.org/10.37193/cmi.2021.01.02.

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In this paper we consider an inscribed triangle XY Z to a triangle ABC and we establish a relation between the area of these two triangles and the area of the triangle determined by the centroids of the residual triangles AZY, BXZ and CY X. Moreover we generalize this relation to the case of a general barycenter instead of centroid and also to quadrilaterals.

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24

Su, Xuzhong, and Xinjin Liu. "Theoretical research of spinning triangle division on spun yarn torque." International Journal of Clothing Science and Technology 31, no. 6 (2019): 839–55. http://dx.doi.org/10.1108/ijcst-01-2019-0004.

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Purpose The purpose of this paper is to theoretically study the effects of ring spinning triangle division on spun yarn torques. Design/methodology/approach The case that the spinning triangle is divided into two parts, primary triangles and final triangle, is investigated. Theoretical model of yarn torque was given by linking the fiber tension in the spinning triangle to yarn torque under the assumption that the arrangement of fibers (substrands) in the substrands (yarn) is hexagonal close packing. Then, as an application of the proposed method, 14.6tex cotton yarns were taken as an example f

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Volenec, Vladimir, Zdenka Kolar–Begović, and Ružica Kolar–Šuper. "Kiepert Triangles in an Isotropic Plane." Sarajevo Journal of Mathematics 7, no. 1 (2024): 81–90. http://dx.doi.org/10.5644/sjm.07.1.08.

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In this paper the concept of the Kiepert triangle of an allowable triangle in an isotropic plane is introduced. The relationships between the areas and the Brocard angles of the standard triangle and its Kiepert triangle are studied. It is also proved that an allowable triangle and any of its Kiepert triangles are homologic. In the case of a standard triangle the expressions for the center and the axis of this homology are given. 2000 Mathematics Subject Classification. 51N25

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26

Rodríguez-Hernández, Ana, and Michael T. Lawton. "Anatomical triangles defining surgical routes to posterior inferior cerebellar artery aneurysms." Journal of Neurosurgery 114, no. 4 (2011): 1088–94. http://dx.doi.org/10.3171/2010.8.jns10759.

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Object Surgical routes to posterior inferior cerebellar artery (PICA) aneurysms are opened between the vagus (cranial nerve [CN] X), accessory (CN XI), and hypoglossal (CN XII) nerves for safe clipping, but these routes have not been systematically defined. The authors describe 3 anatomical triangles and their relationships with PICA aneurysms, routes for surgical clipping, outcomes, and angiographically demonstrated anatomy. Methods The vagoaccesory triangle is defined by CN X superiorly, CN XI laterally, and the medulla medially. It is divided by CN XII into the suprahypoglossal triangle (ab

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27

Read, Emrys. "On the class of an integer triangle." Mathematical Gazette 106, no. 566 (2022): 291–99. http://dx.doi.org/10.1017/mag.2022.69.

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Any mathematics student who has ever used the cosine rule to investigate simple properties of an integer triangle will immediately have realised that the cosine of each angle of the triangle must be a rational number. It is clear, however, that the same is not in general true for the sines. In [1], it is shown how to use a property of the sines of the angles of an integer triangle to categorise the triangle as being of a particular class. In this article, we develop some of the concepts and results of [1] to derive a method for generating integer triangles of a given class. Finally, we apply o

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Rešić, Sead, Alma Šehanović, and Amila Osmić. "ISOSCELES TRIANGLES ON THE SIDES OF A TRIANGLE." Journal Human Research in Rehabilitation 9, no. 1 (2019): 123–30. http://dx.doi.org/10.21554/hrr.041915.

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Famous construction of Fermat-Toricelly point of a triangle leads to the question is there a similar way to construct other isogonic centers of a triangle in a similar way. For a purpose we remember that Fermat-Torricelli point of a triangle ΔABC is obtained by constructing equilateral triangles outwardly on the sides AB,BC and CA. If we denote thirth vertices of those triangles by C1 ,A1 and B1 respectively, then the lines AA1 ,BB1 and CC1 concurr at the Fermat-Torricelli point of a triangle ΔABC (Van Lamoen, 2003). In this work we present the condition for the concurrence, of the lines AA1 ,

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Liu, Xinjin, and Xuzhong Su. "Theoretical study of Solospun yarn torque." International Journal of Clothing Science and Technology 27, no. 5 (2015): 628–39. http://dx.doi.org/10.1108/ijcst-04-2014-0050.

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Purpose – Solospun technology is one of the most important new spinning methods, which is implemented by dividing Ring spinning triangle into several small primary triangles and one final triangle by a Solospun roller. That is, there are two parts of spinning triangle in the Solospun technology, including primary triangles part and final triangle part. In the general case, the primary triangles are much smaller than final triangle. Therefore, the purpose of this paper is to present theoretical study of Solospun yarn torqueby linking the fiber tension in the spinning triangle to yarn torque und

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YUSTER, RAPHAEL. "Dense Graphs With a Large Triangle Cover Have a Large Triangle Packing." Combinatorics, Probability and Computing 21, no. 6 (2012): 952–62. http://dx.doi.org/10.1017/s0963548312000235.

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It is well known that a graph with m edges can be made triangle-free by removing (slightly less than) m/2 edges. On the other hand, there are many classes of graphs which are hard to make triangle-free, in the sense that it is necessary to remove roughly m/2 edges in order to eliminate all triangles.We prove that dense graphs that are hard to make triangle-free have a large packing of pairwise edge-disjoint triangles. In particular, they have more than m(1/4+cβ) pairwise edge-disjoint triangles where β is the density of the graph and c ≥ is an absolute constant. This improves upon a previous m

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Rafiqa, Dewi. "EVALUASI MEMBANGKITKAN FUNGSI KEANGGOTAAN PADA FUZZY MODEL MAMDANI." Jurasik (Jurnal Riset Sistem Informasi dan Teknik Informatika) 1, no. 1 (2016): 41–45. https://doi.org/10.5281/zenodo.546760.

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This paper discusses the comparison of two forms in raising function membership. Determining the membership functions through an isosceles triangle will scores declined in the triangle. While the right-angled triangle, after the peak of the triangle there is no possibility of value decrease. So that the value obtained an ascending grades and dropped out after the peak of the triangle. calculated by Mamdani models, the output value calculated by the isosceles triangle has a value lower compared with those produced by a right-angled triangle. This matter due to a right triangle does not have the

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M, Mahalakshmi, Kannan J, Deepshika A, and Kaleeswari K. "Existence and Non - Existence of Exponential Diophantine Triangles Over Triangular Numbers." Indian Journal of Science and Technology 16, no. 41 (2023): 3599–604. https://doi.org/10.17485/IJST/v16i41.2338.

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Abstract <strong>Objectives:</strong> The specified problem addressed here is the existence and non-existence of Exponential Diophantine triangles over triangular numbers ( ). <strong>Methods:</strong> An Exponential Diophantine triangle over triangular numbers is defined as a triangle with sides and where and are non - negative integers such that . To prove the existence of such triangles, negative Pell’s equation and its solutions are used along with some basic number theoretic concepts. To verify the non-existence, the well-known Catalan’s conjecture, binomial exp

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M, Mahalakshmi, Kannan J, Deepshika A, and Kaleeswari K. "Existence and Non - Existence of Exponential Diophantine Triangles Over Triangular Numbers." Indian Journal of Science and Technology 16, no. 41 (2023): 3599–604. https://doi.org/10.17485/IJST/v16i41.2338.

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Abstract <strong>Objectives:</strong> The specified problem addressed here is the existence and non-existence of Exponential Diophantine triangles over triangular numbers ( ). <strong>Methods:</strong> An Exponential Diophantine triangle over triangular numbers is defined as a triangle with sides and where and are non - negative integers such that . To prove the existence of such triangles, negative Pell’s equation and its solutions are used along with some basic number theoretic concepts. To verify the non-existence, the well-known Catalan’s conjecture, binomial exp

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M, Mahalakshmi, Kannan J, Deepshika A, and Kaleeswari K. "Existence and Non - Existence of Exponential Diophantine Triangles Over Triangular Numbers." Indian Journal of Science and Technology 16, no. 41 (2023): 3599–604. https://doi.org/10.17485/IJST/v16i41.2338.

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Abstract <strong>Objectives:</strong> The specified problem addressed here is the existence and non-existence of Exponential Diophantine triangles over triangular numbers ( ). <strong>Methods:</strong> An Exponential Diophantine triangle over triangular numbers is defined as a triangle with sides and where and are non - negative integers such that . To prove the existence of such triangles, negative Pell’s equation and its solutions are used along with some basic number theoretic concepts. To verify the non-existence, the well-known Catalan’s conjecture, binomial exp

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M, Mahalakshmi, Kannan J, Deepshika A, and Kaleeswari K. "Existence and Non - Existence of Exponential Diophantine Triangles Over Triangular Numbers." Indian Journal of Science and Technology 16, no. 41 (2023): 3599–604. https://doi.org/10.17485/IJST/v16i41.2338.

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Abstract <strong>Objectives:</strong> The specified problem addressed here is the existence and non-existence of Exponential Diophantine triangles over triangular numbers ( ). <strong>Methods:</strong> An Exponential Diophantine triangle over triangular numbers is defined as a triangle with sides and where and are non - negative integers such that . To prove the existence of such triangles, negative Pell’s equation and its solutions are used along with some basic number theoretic concepts. To verify the non-existence, the well-known Catalan’s conjecture, binomial exp

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M, Mahalakshmi, Kannan J, Deepshika A, and Kaleeswari K. "Existence and Non - Existence of Exponential Diophantine Triangles Over Triangular Numbers." Indian Journal of Science and Technology 16, no. 41 (2023): 3599–604. https://doi.org/10.17485/IJST/v16i41.2338.

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Abstract <strong>Objectives:</strong> The specified problem addressed here is the existence and non-existence of Exponential Diophantine triangles over triangular numbers ( ). <strong>Methods:</strong> An Exponential Diophantine triangle over triangular numbers is defined as a triangle with sides and where and are non - negative integers such that . To prove the existence of such triangles, negative Pell’s equation and its solutions are used along with some basic number theoretic concepts. To verify the non-existence, the well-known Catalan’s conjecture, binomial exp

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Xia, Yuyang, Yixiang Fang, and Wensheng Luo. "Efficiently Counting Triangles in Large Temporal Graphs." Proceedings of the ACM on Management of Data 3, no. 1 (2025): 1–27. https://doi.org/10.1145/3709688.

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In many real-world applications (e.g., email networks, social networks, and phone call networks), the relationships between entities can be modeled as a temporal graph, in which each edge is associated with a timestamp representing the interaction time. As a fundamental task in temporal graph analysis, triangle counting has received much attention, and several triangle models have been developed, including δ-temporal triangle, sliding-window triangle, and (δ 1,3 , δ 1,2 , δ 2,3 )-temporal triangle. In particular, the δ-temporal triangle, requiring the gap of timestamps of any two edges within

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Dr., R. Sivaraman. "TRIANGLE OF TRIANGULAR NUMBERS." TRIANGLE OF TRIANGULAR NUMBERS 9, no. 10 (2021): 2390–94. https://doi.org/10.47191/ijmcr/v9i10.01.

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Among several interesting number triangles that exist in mathematics, Pascal’s triangle is one of the best triangle possessing rich mathematical properties. In this paper, I will introduce a number triangle containing triangular numbers arranged in particular fashion. Using this number triangle, I had proved five interesting theorems which help us to generate Pythagorean triples as well as establish bijection between whole numbers and set of all integers.

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Bicua, Levi L., Precious R. Tayaben, and Abraham P. Racca. "An Iterative Process Applied to Equilateral Triangles Resulting to the Identity 1/3+1/9+1/27+…=1/2." Abstract Proceedings International Scholars Conference 6, no. 1 (2019): 146. http://dx.doi.org/10.35974/isc.v6i1.1207.

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In this paper, we define a particular iterative process and apply it to triangles. It was shown that the process results to self-similar triangles if and only if the generator triangle is an equilateral triangle. Furthermore, the identity 1/3+1/9+1/27+...=1/2 resulted from the process.

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Read, Emrys. "Integer triangles with integer circumradii." Mathematical Gazette 107, no. 569 (2023): 241–48. http://dx.doi.org/10.1017/mag.2023.55.

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When studying properties of the circumcircle of an integer triangle, it quickly becomes evident that the radius of such a circle (circumradius) need not itself be an integer. When it is not an integer, the circumradius can still be rational but it can also be irrational, as exemplified in the following examples. It is left to the reader to verify that the triangle with sides 10, 24, 26 has circumradius 13, and that the corresponding values for the triangles with sides 13, 14, 15 and 1, 1, 1 are 65/8 and respectively. It is shown in Theorem 1 below that a necessary condition for the circumradiu

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Hansen, David W. "On Inscribed and Escribed Circles of Right Triangles, Circumscribed Triangles, and the Four-Square, Three-Square Problem." Mathematics Teacher 96, no. 5 (2003): 358–64. http://dx.doi.org/10.5951/mt.96.5.0358.

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For more than twenty years, I have been studying the fascinating relationships between right triangles and their inscribed and escribed circles. An inscribed circle is one that is tangent to all three sides of a triangle and whose center lies inside the triangle. An escribed circle is one that is tangent to one of the sides of the triangle and to the extensions of the other two sides and whose center lies outside the triangle. Every triangle has one inscribed and three escribed circles, as shown in figure 1.

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Mannion, David. "A Markov chain of triangle shapes." Advances in Applied Probability 20, no. 2 (1988): 348–70. http://dx.doi.org/10.2307/1427394.

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The process of choosing a random triangle inside a compact convex region, K, may be iterated when K itself is a triangle. In this way successive generations of random triangles are created. Properties of scale, location and orientation are filtered out, leaving only the shapes of the triangles as the objects of study. Various simulation investigations indicate quite clearly that, as n increases, the nth-generation triangle shape converges to collinearity. In this paper we attempt to establish such convergence; our results fall slightly short of a complete proof.

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Mannion, David. "A Markov chain of triangle shapes." Advances in Applied Probability 20, no. 02 (1988): 348–70. http://dx.doi.org/10.1017/s0001867800017018.

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The process of choosing a random triangle inside a compact convex region, K, may be iterated when K itself is a triangle. In this way successive generations of random triangles are created. Properties of scale, location and orientation are filtered out, leaving only the shapes of the triangles as the objects of study. Various simulation investigations indicate quite clearly that, as n increases, the nth-generation triangle shape converges to collinearity. In this paper we attempt to establish such convergence; our results fall slightly short of a complete proof.

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McKay, Angela. "An Analogue of Napoleon’s Theorem in the Hyperbolic Plane." Canadian Mathematical Bulletin 44, no. 3 (2001): 292–97. http://dx.doi.org/10.4153/cmb-2001-029-3.

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AbstractThere is a theorem, usually attributed to Napoleon, which states that if one takes any triangle in the Euclidean Plane, constructs equilateral triangles on each of its sides, and connects the midpoints of the three equilateral triangles, one will obtain an equilateral triangle. We consider an analogue of this problem in the hyperbolic plane.

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Dr., R. Sivaraman. "LUCAS NUMBERS TRIANGLE." International Journal of Applied and Advanced Scientific Research (IJAASR) 6, no. 2 (2021): 39–44. https://doi.org/10.5281/zenodo.5758677.

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Among several number triangles that exist in mathematics, Pascal’s triangle is well known for its extra-ordinary combinatorial properties and applications. It is well known that stacking entries of Pascal’s triangle in a particular fashion and adding them in North – East diagonal direction, we can generate Fibonacci numbers. In this paper, I will introduce a number triangle constructed similar to Pascal’s triangle through which I have proved eight interestingand new mathematical properties and also have generated Lucas numbers which is connected with Golden Ratio.

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Liu, Hongmin, Hongya Zhang, Zhiheng Wang, and Yiming Zheng. "Feature Matching Based on Triangle Guidance and Constraints." International Journal of Pattern Recognition and Artificial Intelligence 32, no. 08 (2018): 1855014. http://dx.doi.org/10.1142/s0218001418550145.

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For images with distortions or repetitive patterns, the existing matching methods usually work well just on one of the two kinds of images. In this paper, we present novel triangle guidance and constraints (TGC)-based feature matching method, which can achieve good results on both kinds of images. We first extract stable matched feature points and combine these points into triangles as the initial matched triangles, and triangles combined by feature points are as the candidates to be matched. Then, triangle guidance based on the connection relationship via the shared feature point between the

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Khabibah, Siti. "PEWARNAAN PADA GRAF BINTANG SIERPINSKI." Jurnal Ilmiah Matematika dan Pendidikan Matematika 9, no. 1 (2017): 37. http://dx.doi.org/10.20884/1.jmp.2017.9.1.2853.

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This paper discuss about Sierpinski star graph , which its construction based on the Sierpinski triangle. Vertex set of Sierpinski star graph is a set of all triangles in Sierpinski triangle; and the edge set of Sierpinski star graph is a set of all sides that are joint edges of two triangles on Sierpinski triangle. From the vertex and edge coloring of Sierpinski star graph, it is found that the chromatic number on vertex coloring of graph is 1 for n = 1 and 2 for ; while the chromatic number on edge coloring of graf is 0 for n = 1 and for

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Ferreira, Luis Dias. "Arithmetic Triangle." Journal of Mathematics Research 9, no. 2 (2017): 100. http://dx.doi.org/10.5539/jmr.v9n2p100.

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The product of the first $n$ terms of an arithmetic progression may be developed in a polynomial of $n$ terms. Each one of them presents a coefficient $C_{nk}$ that is independent from the initial term and the common difference of the progression. The most interesting point is that one may construct an "Arithmetic Triangle'', displaying these coefficients, in a similar way one does with Pascal's Triangle. Moreover, some remarkable properties, mainly concerning factorials, characterize the Triangle. Other related `triangles' -- eventually treated as matrices -- also display curious facts, in th

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CALVO, T., G. MAYOR, J. TORRENS, J. SUÑER, M. MAS, and M. CARBONELL. "GENERATION OF WEIGHTING TRIANGLES ASSOCIATED WITH AGGREGATION FUNCTIONS." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 08, no. 04 (2000): 417–51. http://dx.doi.org/10.1142/s0218488500000290.

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In this work, we present several ways to obtain different types of weighting triangles, due to these types characterize some interesting properties of Extended Ordered Weighted Averaging operators, EOWA, and Extended Quasi-linear Weighted Mean, EQLWM, as well as of their reverse functions. We show that any quantifier determines an EOWA operator which is also an Extended Aggregation Function, EAF, i.e., the weighting triangle generated by a quantifier is always regular. Moreover, we present different results about generation of weighting triangles by means of sequences and fractal structures. F

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Yin, Haozhe, Kai Wang, Wenjie Zhang, Ying Zhang, Ruijia Wu, and Xuemin Lin. "Efficient Computation of Hyper-Triangles on Hypergraphs." Proceedings of the VLDB Endowment 18, no. 3 (2024): 729–42. https://doi.org/10.14778/3712221.3712238.

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Hypergraphs, which use hyperedges to capture groupwise interactions among different entities, have gained increasing attention recently for their versatility in effectively modeling real-world networks. In this paper, we study the problem of computing hyper-triangles (formed by three fully-connected hyperedges), which is a basic structural unit in hypergraphs. Although existing approaches can be adopted to compute hyper-triangles by exhaustively examining hyperedge combinations, they overlook the structural characteristics distinguishing different hyper-triangle patterns. Consequently, these a

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