Relevant bibliographies by topics / Triangle identities

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Triangle identities'

Author: Grafiati
Published: 2 June 2025
Last updated: 31 July 2025

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Journal articles on the topic "Triangle identities"

1

Clarke, Robert. "Some Triangle Identities." Mathematical Gazette 70, no. 453 (1986): 211. http://dx.doi.org/10.2307/3615680.

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Sh.L.Ermatov. "TRIGONOMETRIC IDENTITIES OF THE QUADRILATERAL." ACADEMIC RESEARCH IN MODERN SCIENCE 2, no. 10 (2023): 72–73. https://doi.org/10.5281/zenodo.7793925.

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It is known that there are many trigonometric identities regarding the Triangle. These mirrors represent the trigonometric relationship between the inner corners of a triangle, the trigonometric relationship between the inner corners of the Triangle and its main elements (surface, perimeter, sides, radius of the inner and outer drawn circle, bisector, median, height).
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Coghetto, Roland. "Some Facts about Trigonometry and Euclidean Geometry." Formalized Mathematics 22, no. 4 (2014): 313–19. http://dx.doi.org/10.2478/forma-2014-0031.

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Summary We calculate the values of the trigonometric functions for angles: [XXX] , by [16]. After defining some trigonometric identities, we demonstrate conventional trigonometric formulas in the triangle, and the geometric property, by [14], of the triangle inscribed in a semicircle, by the proposition 3.31 in [15]. Then we define the diameter of the circumscribed circle of a triangle using the definition of the area of a triangle and prove some identities of a triangle [9]. We conclude by indicating that the diameter of a circle is twice the length of the radius
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Gutiérrez, J. M., M. A. Hernández, P. J. Miana, and N. Romero. "New identities in the Catalan triangle." Journal of Mathematical Analysis and Applications 341, no. 1 (2008): 52–61. http://dx.doi.org/10.1016/j.jmaa.2007.09.073.

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Zhang, Zhizheng, and Bijun Pang. "Several identities in the Catalan triangle." Indian Journal of Pure and Applied Mathematics 41, no. 2 (2010): 363–78. http://dx.doi.org/10.1007/s13226-010-0022-0.

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KULOĞLU, BAHAR, and ENGİN ÖZKAN. "NEW NARAYANA TRIANGLE." Journal of Science and Arts 22, no. 3 (2022): 563–70. http://dx.doi.org/10.46939/j.sci.arts-22.3-a04.

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In this paper, inspiring Hosoya’s triangle, we define a new Narayana triangle. Then, we represent this Narayana triangle geometrically on the plane. In addition, we give some identities and properties of the new Narayana triangle.
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AU-YANG, HELEN, and JACQUES H. H. PERK. "STAR-TRIANGLE EQUATIONS AND IDENTITIES IN HYPERGEOMETRIC SERIES." International Journal of Modern Physics B 16, no. 14n15 (2002): 1853–65. http://dx.doi.org/10.1142/s0217979202011561.

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In this paper, we introduce the cyclic basic hypergeometric series p + 1Φp with q → ω where ωN = 1. This is a terminating series with N terms, whose summand has period N. We show how the Fourier transform of the weights of the integrable chiral Potts model are related to the 2Φ1, which is summable. We show that 3Φ2 satisfies certain transformation formulae. We then show that the Saalschützian 4Φ3 series is summable at argument z = ω. This then gives the simplest proof of the star-triangle relation in the chiral Potts model. Finally, we let N → ∞, where the star-triangle equation becomes a two-
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Amrouche, Said, and Hacène Belbachir. "Asymmetric extension of Pascal-Delannoy triangles." Applicable Analysis and Discrete Mathematics, no. 00 (2022): 28. http://dx.doi.org/10.2298/aadm200411028a.

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In this paper, we give a generalization of the Pascal triangle called the quasi s-Pascal triangle. For this, consider a set of lattice path, which is a dual approach to the definition of Ramirez and Sirvent: A Generalization of the k-bonacci Sequence from Riordan Arrays. The electronic journal of combinatorics, 22(1) (2015), 1-38. We give the recurrence relation for the sum of elements lying over finite ray of the quasi s-Pascal triangle, then, we establish a q-analogue of the coefficient of this triangle. Some identities are also given.
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WOSPAKRIK, H. J. "DISPERSIVE DERIVATION OF THE TRIANGLE ANOMALY." Modern Physics Letters A 01, no. 06 (1986): 403–7. http://dx.doi.org/10.1142/s0217732386000506.

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The convergence properties of the invariant form factors dispersion integrals corresponding to the VVA triangle diagram are examined. It is found that there is a particular Lorentz decomposition of the VVA 3-point function where one of its invariant form factors diverges logarithmically. This is rendered convergent by introducing one substraction constant that turns out to be proportional to the anomalous term of the vector Ward identities.
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Panagiotis, Chr Stefanides. "Golden Root Geometry Structuring the Polyhedra and other Forms Via Plato’s Triangles. Quadrature of Circle." DIALOGO 1, no. 1 (2014): 37–42. http://dx.doi.org/10.51917/dialogo.2014.1.1.4.

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Under Golden Root Geometry Structuring the Polyhedra and other Forms Via Plato’s Triangles, we refer to the basic geometric configurations which, as this theory contemplates, are necessary for the progressive mode of formation of the five polyhedral and the geometries involved in their sections and related circles and further to logarithms, via lines, areas and volumes. Basis of all these structures is a very special Scalene Orthogonal Triangle “Plato’s Most Beautiful” [F25], together with his Orthogonal Isosceles one. Structural Forms are identified bearing in common these triangular identiti
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Dissertations / Theses on the topic "Triangle identities"

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Trégourès, Loïc. "Jeu en triangle : Football, politique et identités dans l'espace post-yougoslave des années 1980 à nos jours." Thesis, Lille 2, 2017. http://www.theses.fr/2017LIL20003/document.

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La transformation de supporters de football serbes, bosniaques et croates en soldats dès 1991, la présence de supporters en première ligne contre la police dans la chute du régime de Milošević et dans l’opposition au président croate Franjo Tuđman, la mobilisation violente de supporters contre la tenue de gay pride, la prise d’assaut de l’ambassade des Etats-Unis à Belgrade, sont autant de faits qui s’inscrivent au croisement du football par les acteurs en jeu, du politique par la portée de leurs actes, et de l’identitaire comme fondement légitimateur à agir. C’est donc à partir de ces faits p
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Bergaglio, Cecilia. "Identités et stratégies politiques du PCI et du PCF : une comparaison entre le Triangolo Industriale en italie et la région industrielle du Rhônes - Alpes en France." Thesis, Université Grenoble Alpes (ComUE), 2015. http://www.theses.fr/2015GREAL029.

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Les objectifs du projet de recherche ont leur fondement dans la tentative de répondre à quelques questions essentielles concernant l'identité du Parti Communiste italien et du Parti Communiste français en tant que sujets politiques complexes, multiformes et dynamiques.On a d'abord crée deux laboratoires d'analyse, l'un en Italie, le deuxième en France, en tant que lieux d'observation, d'étude et de dénouement des thèmes les plus significatifs liés à l'identité, la stratégie et la culture communiste.En ce qui concerne l'Italie, on a tout naturellement choisi le Triangle Industriel qui constitue
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Books on the topic "Triangle identities"

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White, Christopher Schwaner Christopher. Some Sine and Cosine Identities Obtained from Pascal's Triangle. Dorrance Publishing, 2012.

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2

Master math: Trigonometry : including everything from trigonometric functions, equations, triangle, and graphs to identities, coordinate systems, and complex numbers. Thomson/Delmar Learning, 2002.

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Book chapters on the topic "Triangle identities"

1

Radin, Michael A. "Pascal’s Triangle Identities." In Introduction to Recognition and Deciphering of Patterns. Chapman and Hall/CRC, 2020. http://dx.doi.org/10.1201/9780367808747-4.

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Radin, Michael A. "Pascal's Triangle Identities." In Introduction to Math Olympiad Problems. Chapman and Hall/CRC, 2021. http://dx.doi.org/10.1201/9781003089469-5.

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Shin, Gi-Wook. "National Identities, Historical Memories, and Reconciliation in Northeast Asia." In Asia’s Alliance Triangle. Palgrave Macmillan US, 2015. http://dx.doi.org/10.1057/9781137541710_16.

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Wieviorka, Michel. "The Ethnicity Triangle." In Negotiating Identities. BRILL, 1995. http://dx.doi.org/10.1163/9789004652002_004.

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Vishwakarma, Suryaprakash, and Seema Purohit. "RASCAL TRIANGLE." In Futuristic Trends in Contemporary Mathematics & Applications Volume 3 Book 2. Iterative International Publishers, Selfypage Developers Pvt Ltd, 2024. http://dx.doi.org/10.58532/v3bkcm2p6ch2.

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In Combinatorics use of Pascal Triangle techniques and identities is well known when it comes to deriving Binomial Coefficients, Fibonacci Numbers, Interesting Numbers Patterns. Literature shows though not much efforts are being done to generate the Pascal like pattens, a decade ago in 2010, Pascal like triangles are generated by three middle school students using their own alternate ways, without knowing what Pascal Triangle is about. They coined the name “Rascal Triangle” for the new number patterns generated by them. In this Chapter, researchers tried to regenerate the generalizations of Ra
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Van Brummelen, Glen. "4. Identities, and more identities." In Trigonometry: A Very Short Introduction. Oxford University Press, 2020. http://dx.doi.org/10.1093/actrade/9780198814313.003.0004.

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The world of trigonometry is full of identities: some of them extremely useful, others beautiful, and a few that are simply bizarre. ‘Identities, and more identities’ takes a tour of the menagerie of identities, viewing a little from each of these categories. The first two examples are known as triangle identities, because they refer to angles and lengths in a given triangle. The Law of Sines and the Law of Cosines are discussed, along with Mollweide’s formulas, the Law of Tangents, Morrie’s Law, and the introduction of logarithms, which became the preferred computing tool in mathematical astr
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"2. Blurred Identities: Representing Modern Life." In The Triangle of Representation. Columbia University Press, 2000. http://dx.doi.org/10.7312/pren12090-003.

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Van Brummelen, Glen. "The Modern Approach: Right-Angled Triangles." In Heavenly Mathematics. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691175997.003.0005.

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This chapter discusses the modern approach to solving right-angled triangles. After a brief background on John Napier's trigonometric work, in which he referred mostly to right-angled spherical triangles, the chapter describes the theorems for right triangles. It then considers an oblique triangle split into two right triangles and the ten fundamental identities of a right-angled spherical triangle, how the locality principle can be applied to derive the Pythagorean Theorem, and how to find a ship's direction of travel using the theorem. It also looks at Napier's work on logarithms which was d
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Marler, Regina. "The Bloomsbury Love Triangle." In Queer Bloomsbury. Edinburgh University Press, 2016. http://dx.doi.org/10.3366/edinburgh/9781474401692.003.0008.

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In this essay, Marler shows how queer connections and fluid identities served to foster more lasting bonds among the Bloomsberries, making lifelong loving and working partnerships possible where by stricter definitions no such connection could have been made. While the young group of friends may have launched into love triangles experimentally, or as the expected outcome of romantic rivalries, the triangle would often prove to complicate but bolster the original dyads. At a time when sodomy was a felony, primary heterosexual relationships also nicely concealed homosexual relationships. Or the
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Vălcan, Teodor Dumitru. "DEDUCTIBILITY AND ANALOGY IN THE STUDY OF SOME TRIANGLES (I) - general results." In Education, Society, Family. Interdisciplinary Perspectives and Analyses. Eikon Publishing House, 2021. http://dx.doi.org/10.56177/epvl.ch9.2021.en.

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In this paper we propose, using the relations of logical deductibility and the analogy method, to present some interesting results in the Geometry of the triangle. Thus, we consider a triangle ABC and three cevians, which intersect at point K and intersect the sides of the given triangle at points A, B and C, and the circle circumscribed to the triangle ABC in A1, B1 and C1. Then we will call the triangle ABC the triangle K-cevian attached to the triangle ABC and the point K, and the triangle A1B1C1 we will call the triangle K-circumcevian attached to the triangle ABC and the point K. Us
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Conference papers on the topic "Triangle identities"

1

AU-YANG, HELEN, and JACQUES H. H. PERK. "STAR-TRIANGLE EQUATIONS AND IDENTITIES IN HYPERGEOMETRIC SERIES." In Proceedings of APCTP-NANKAI Joint Symposium. WORLD SCIENTIFIC, 2002. http://dx.doi.org/10.1142/9789812776358_0001.

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