Relevant bibliographies by topics / Triangle Inequality

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

Academic literature on the topic 'Triangle Inequality'

Author: Grafiati
Published: 4 June 2021
Last updated: 25 July 2025

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Journal articles on the topic "Triangle Inequality"

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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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Hoehn, Larry. "Geometrical Inequalities via Bisectors." Mathematics Teacher 82, no. 2 (1989): 96–99. http://dx.doi.org/10.5951/mt.82.2.0096.

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The proofs of several theorems in secondary school mathematics that involve geometrical inequalities are more complicated than they really need to be. This article presents an easier-to-understand alternative to the usual proofs of inequalities in triangles. The only inequality with which we need to assume familiarity is the triangle inequality (i.e., the sum of any two sides of a plane triangle is greater than the third side).
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Yang, Zheng, Lirong Jian, Chenshu Wu, and Yunhao Liu. "Beyond triangle inequality." ACM Transactions on Sensor Networks 9, no. 2 (2013): 1–20. http://dx.doi.org/10.1145/2422966.2422983.

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Shevchishin, Vsevolod, and Gleb Smirnov. "Symplectic triangle inequality." Proceedings of the American Mathematical Society 148, no. 4 (2020): 1389–97. http://dx.doi.org/10.1090/proc/14842.

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Greenhoe, D. "Properties of distance spaces with power triangle inequalities." Carpathian Mathematical Publications 8, no. 1 (2016): 51–82. http://dx.doi.org/10.15330/cmp.8.1.51-82.

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Metric spaces provide a framework for analysis and have several very useful properties. Many of these properties follow in part from the triangle inequality. However, there are several applications in which the triangle inequality does not hold but in which we may still like to perform analysis. This paper investigates what happens if the triangle inequality is removed all together, leaving what is called a distance space, and also what happens if the triangle inequality is replaced with a much more general two parameter relation, which is herein called the "power triangle inequality". The pow
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Barnes, Benedict, E. D. J. O. Wusu-Ansah, S. K. Amponsah, and I. A. Adjei. "The Proofs of Triangle Inequality Using Binomial Inequalities." European Journal of Pure and Applied Mathematics 11, no. 1 (2018): 352–61. http://dx.doi.org/10.29020/nybg.ejpam.v11i1.3165.

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In this paper, we introduce the different ways of proving the triangle inequality ku − vk ≤ kuk + kvk, in the Hilbert space. Thus, we prove this triangle inequality through the binomial inequality and also, prove it through the Euclidean norm. The first generalized procedure for proving the triangle inequality is feasible for any even positive integer n. The second alternative proof of the triangle inequality establishes the Euclidean norm of any two vectors in the Hilbert space.
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Vu, Tuyen. "Spectral inequality for Dirac right triangles." Journal of Mathematical Physics 64, no. 4 (2023): 041502. http://dx.doi.org/10.1063/5.0147732.

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We consider a Dirac operator on right triangles, subject to infinite-mass boundary conditions. We conjecture that the lowest positive eigenvalue is minimized by the isosceles right triangle under the area or perimeter constraints. We prove this conjecture under extra geometric hypotheses relying on a recent approach of Briet and Krejčiřík [J. Math. Phys. 63, 013502 (2022)].
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Bencze, Mihaly, and GCHQ Problems Group. "A Triangle Inequality: 10644." American Mathematical Monthly 106, no. 5 (1999): 476. http://dx.doi.org/10.2307/2589167.

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Bailey, Herbert R., and Robert Bannister. "A Stronger Triangle Inequality." College Mathematics Journal 28, no. 3 (1997): 182. http://dx.doi.org/10.2307/2687521.

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Shahbari, Juhaina A., and Moshe Stupel. "106.13 A triangle inequality." Mathematical Gazette 106, no. 565 (2022): 138. http://dx.doi.org/10.1017/mag.2022.28.

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Dissertations / Theses on the topic "Triangle Inequality"

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Narreddy, Naga Sambu Reddy, and Tuğrul Durgun. "Clusters (k) Identification without Triangle Inequality : A newly modelled theory." Thesis, Uppsala universitet, Institutionen för informatik och media, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-183608.

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Cluster analysis characterizes data that are similar enough and useful into meaningful groups (clusters).For example, cluster analysis can be applicable to find group of genes and proteins that are similar, to retrieve information from World Wide Web, and to identify locations that are prone to earthquakes. So the study of clustering has become very important in several fields, which includes psychology and other social sciences, biology, statistics, pattern recognition, information retrieval, machine learning and data mining [1] [2].   Cluster analysis is the one of the widely used technique
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Berman, Andrew P. "Efficient content-based retrieval of images using triangle-inequality-based algorithms /." Thesis, Connect to this title online; UW restricted, 1999. http://hdl.handle.net/1773/6989.

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Hamilton, Jeremy. "An Exploration of the Erdös-Mordell Inequality." Youngstown State University / OhioLINK, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=ysu1287605197.

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OTSUBO, Shigeru, and Yumeka HIRANO. "Poverty-Growth-Inequality Triangle under Globalization: Time Dimensions and the Control Factors of the Impacts of Integration." 名古屋大学大学院国際開発研究科, 2012. http://hdl.handle.net/2237/16949.

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Wigren, Thomas. "The Cauchy-Schwarz inequality : Proofs and applications in various spaces." Thesis, Karlstads universitet, Avdelningen för matematik, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-38196.

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We give some background information about the Cauchy-Schwarz inequality including its history. We then continue by providing a number of proofs for the inequality in its classical form using various proof techniques, including proofs without words. Next we build up the theory of inner product spaces from metric and normed spaces and show applications of the Cauchy-Schwarz inequality in each content, including the triangle inequality, Minkowski's inequality and Hölder's inequality. In the final part we present a few problems with solutions, some proved by the author and some by others.
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Johnson, Timothy Kevin. "A reformulation of Coombs' Theory of Unidimensional Unfolding by representing attitudes as intervals." Thesis, The University of Sydney, 2004. http://hdl.handle.net/2123/612.

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An examination of the logical relationships between attitude statements suggests that attitudes can be ordered according to favourability, and can also stand in relationships of implication to one another. The traditional representation of attitudes, as points on a single dimension, is inadequate for representing both these relations but representing attitudes as intervals on a single dimension can incorporate both favourability and implication. An interval can be parameterised using its two endpoints or alternatively by its midpoint and latitude. Using this latter representation, the midpoin
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Johnson, Timothy Kevin. "A reformulation of Coombs' Theory of Unidimensional Unfolding by representing attitudes as intervals." University of Sydney. Psychology, 2004. http://hdl.handle.net/2123/612.

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An examination of the logical relationships between attitude statements suggests that attitudes can be ordered according to favourability, and can also stand in relationships of implication to one another. The traditional representation of attitudes, as points on a single dimension, is inadequate for representing both these relations but representing attitudes as intervals on a single dimension can incorporate both favourability and implication. An interval can be parameterised using its two endpoints or alternatively by its midpoint and latitude. Using this latter representation, the midpoin
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Hsu, Chih-Yung, and 許至勇. "Refinements of triangle inequality and Jensen’s inequality." Thesis, 2007. http://ndltd.ncl.edu.tw/handle/86930617569692611296.

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碩士<br>國立中央大學<br>數學研究所<br>95<br>In this thesis, we prove a sharp triangle inequality and its reverse inequality for strongly integrable functions with values in a Banach space X. This contains as a special case a recent result of Kato et al on sharp triangle inequality for n elements. We also discuss a generalized triangle inequality for Lp functions with values in X. It contains as a special case the triangle inequality of the second kind for two elements, which is implied by the Euler-Lagrange type identity. Besides, some properties related to a refined Jensen’s inequality are observed.
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Wang, Huan-Yu, and 王煥宇. "A Fast Similarity Algorithm for Personal Ontologies Using Triangle Inequality." Thesis, 2009. http://ndltd.ncl.edu.tw/handle/93888608461842522310.

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碩士<br>國立中興大學<br>資訊科學與工程學系所<br>97<br>The Personal Ontology Recommender System (PORE) currently operated in the library of National Chung Hsing University is a recommender system developed by our research team. The system consists of content-based recommendation model based on personal ontology and collaborative filtering recommendation model. For collaborative filtering, the recommender system needs to compute the similarity between any two users. That will incur lots of computations because the library currently has more than thirty thousands of users and three hundred thousands of collections
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CHING, HOU HSUEH, and 侯雪卿. "The Case Study of learning triangle inequality of Elementary School Students." Thesis, 2019. http://ndltd.ncl.edu.tw/handle/fqa7c6.

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博士<br>國立中正大學<br>教育學研究所<br>107<br>The purpose of this study is to investigate grade 4 students’ learning performance and learning outcomes in the topic of triangle inequality. This study uses a case study approach. Three grade 4 students in different achievement level attended in a sequence of learning activities in the investigative approach. The learning performance and learning outcomes are analyzed and interpreted by classroom observing, interviews, work sheets, pre- and post- assessment, and self-reflection of the instructor. The results show that:1.Grade 4 students are able to understand
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Books on the topic "Triangle Inequality"

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Socolovsky, Eduardo A. A dissimilarity measure for clustering high- and infinite dimensional data that satisfies the triangle inequality. Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 2002.

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Book chapters on the topic "Triangle Inequality"

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Denny, William Gozali, and Ruli Manurung. "SOM Training Optimization Using Triangle Inequality." In Advances in Self-Organizing Maps and Learning Vector Quantization. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-28518-4_5.

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Schubert, Erich. "A Triangle Inequality for Cosine Similarity." In Similarity Search and Applications. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-89657-7_3.

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Saito, Jun. "Why is inequality widening?" In Japan and the Growth-Equity-Small Government Impossible Triangle. Routledge, 2024. http://dx.doi.org/10.4324/9781003178897-2.

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Chandran, L. Sunil, and L. Shankar Ram. "Approximations for ATSP with Parametrized Triangle Inequality." In STACS 2002. Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/3-540-45841-7_18.

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Saito, Jun. "Wouldn't pursuing growth widen inequality?" In Japan and the Growth-Equity-Small Government Impossible Triangle. Routledge, 2024. http://dx.doi.org/10.4324/9781003178897-7.

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Nguyen, Vu-Linh, Toan Nguyen-Mau, and Van-Nam Huynh. "Accelerate K-Mode Algorithms Using The Triangle Inequality." In Lecture Notes in Computer Science. Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-76235-2_24.

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Manyem, Prabhu. "Constrained spanning, Steiner trees and the triangle inequality." In Springer Optimization and Its Applications. Springer New York, 2009. http://dx.doi.org/10.1007/978-0-387-98096-6_19.

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Kowalik, Łukasz, and Marcin Mucha. "Two Approximation Algorithms for ATSP with Strengthened Triangle Inequality." In Lecture Notes in Computer Science. Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-03367-4_41.

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Böckenhauer, Hans-Joachim, Karin Freiermuth, Juraj Hromkovič, Tobias Mömke, Andreas Sprock, and Björn Steffen. "The Steiner Tree Reoptimization Problem with Sharpened Triangle Inequality." In Lecture Notes in Computer Science. Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-13073-1_17.

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Lumezanu, Cristian, Randy Baden, Neil Spring, and Bobby Bhattacharjee. "Triangle Inequality and Routing Policy Violations in the Internet." In Lecture Notes in Computer Science. Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-00975-4_5.

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Conference papers on the topic "Triangle Inequality"

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Zhakubayev, Alibek, and Greg Hamerly. "Using Annealing to Accelerate Triangle Inequality k-means." In 2024 IEEE 11th International Conference on Data Science and Advanced Analytics (DSAA). IEEE, 2024. http://dx.doi.org/10.1109/dsaa61799.2024.10722770.

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Berman, Andrew P., and Linda G. Shapiro. "Triangle-inequality-based pruning algorithms with triangle tries." In Electronic Imaging '99, edited by Minerva M. Yeung, Boon-Lock Yeo, and Charles A. Bouman. SPIE, 1998. http://dx.doi.org/10.1117/12.333855.

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Acharyya, Sreangsu, Arindam Banerjee, and Daniel Boley. "Bregman Divergences and Triangle Inequality." In Proceedings of the 2013 SIAM International Conference on Data Mining. Society for Industrial and Applied Mathematics, 2013. http://dx.doi.org/10.1137/1.9781611972832.53.

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Lumezanu, Cristian, Randy Baden, Neil Spring, and Bobby Bhattacharjee. "Triangle inequality variations in the internet." In the 9th ACM SIGCOMM conference. ACM Press, 2009. http://dx.doi.org/10.1145/1644893.1644914.

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Wang, Guohui, Bo Zhang, and T. S. Eugene Ng. "Towards network triangle inequality violation aware distributed systems." In the 7th ACM SIGCOMM conference. ACM Press, 2007. http://dx.doi.org/10.1145/1298306.1298331.

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Kaafar, M. A., F. Cantin, B. Gueye, and G. Leduc. "Detecting Triangle Inequality Violations for Internet Coordinate Systems." In 2009 IEEE International Conference on Communications Workshops. IEEE, 2009. http://dx.doi.org/10.1109/iccw.2009.5207998.

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Ghamdi, Sami Al, and Giuseppe Di Fatta. "Efficient Parallel K-Means on MapReduce Using Triangle Inequality." In 2017 IEEE 15th Intl Conf on Dependable, Autonomic and Secure Computing, 15th Intl Conf on Pervasive Intelligence and Computing, 3rd Intl Conf on Big Data Intelligence and Computing and Cyber Science and Technology Congress(DASC/PiCom/DataCom/CyberSciTech). IEEE, 2017. http://dx.doi.org/10.1109/dasc-picom-datacom-cyberscitec.2017.163.

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He, Chunxia, Jinyi Chang, and Xiaoyun Chen. "Using the Triangle Inequality to Accelerate TTSAS Cluster Algorithm." In 2010 International Conference on Electrical and Control Engineering (ICECE 2010). IEEE, 2010. http://dx.doi.org/10.1109/icece.2010.620.

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Gentile, Camillo. "Distributed Sensor Location through Linear Programming with Triangle Inequality Constraints." In 2006 IEEE International Conference on Communications. IEEE, 2006. http://dx.doi.org/10.1109/icc.2006.255710.

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Zhang, Tongquan, and Ying Yin. "Travelling Production Line Problem on Digraphs with Parameterized Triangle Inequality." In 2010 International Conference on Computational Intelligence and Software Engineering (CiSE). IEEE, 2010. http://dx.doi.org/10.1109/cise.2010.5676930.

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Reports on the topic "Triangle Inequality"

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Verdisco, Aimee, Jennelle Thompson, and Santiago Cueto. Early Childhood Development: Wealth, the Nurturing Environment and Inequality First Results from the PRIDI Database. Inter-American Development Bank, 2016. http://dx.doi.org/10.18235/0011753.

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This paper presents findings from the Regional Project on Child Development Indicators, PRIDI for its acronym in Spanish. PRIDI created a new tool, the Engle Scale, for evaluating development in children aged 24 to 59 months in four domains: cognition, language and communication, socio-emotional and motor skills. It also captures and identifies factors associated with child development. The Engle Scale was applied in nationally representative samples in four Latin American countries: Costa Rica, Nicaragua, Paraguay and Peru. The results presented here are descriptive, but they offer new insigh
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