Relevant bibliographies by topics / Circumcenter

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

Academic literature on the topic 'Circumcenter'

Author: Grafiati
Published: 4 June 2021
Last updated: 19 February 2022

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Journal articles on the topic "Circumcenter"

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Rubillo, James M. "Illustrating the Euler Line." Mathematics Teacher 80, no. 5 (1987): 389–93. http://dx.doi.org/10.5951/mt.80.5.0389.

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In 1765 the Swiss mathematician Leon-hard Euler proved that the centroid of a triangle trisects the line segment joining its circumcenter to its orthocenter. Thus the circumcenter, the centroid, and the ortho-center are collinear and form the Euler line of the triangle. The definition of each of these points is presented in table 1.
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Walker, Peter, and Tom Zerger. "The Centroid-Circumcenter Distance: 10948." American Mathematical Monthly 111, no. 1 (2004): 65. http://dx.doi.org/10.2307/4145028.

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Jiang, Xiao Wei, Yu Hu, Yue Ting Yang, and Tian Luan. "Look the Partial Equilibrium with the Global Optimum from the Problem of the Shortest Circuit for Three Villages." Advanced Materials Research 989-994 (July 2014): 2377–80. http://dx.doi.org/10.4028/www.scientific.net/amr.989-994.2377.

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We explore the relationship between the partial equilibrium and the global optimum from the problem of the shortest circuit for three villages (PSCTV). Using the related properties of Fermat point and the circumcenter of the triangle, we can come to the conclusion that the partial equilibrium sometimes brings into correspondence with the global optimum but there is a great deal of difference between the two by analysing the difference between the sum of distances from Fermat point to all vertices and the ones from circumcenter to all vertices.
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Khatimah, Husnul, Mashadi Mashadi, and Sri Gemawati. "PENGEMBANGAN TEOREMA DAO PADA ENAM CIRCUMCENTER." Euclid 5, no. 1 (2018): 21. http://dx.doi.org/10.33603/e.v5i1.514.

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Tabachnikov, Serge, and Emmanuel Tsukerman. "Remarks on the Circumcenter of Mass." Arnold Mathematical Journal 1, no. 2 (2015): 101–12. http://dx.doi.org/10.1007/s40598-015-0009-3.

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Colindres, Carlos A. Mejía. "Thunder and Lightning: Understanding Equidistance." Mathematics Teacher 108, no. 6 (2015): 454–60. http://dx.doi.org/10.5951/mathteacher.108.6.0454.

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Akopyan, Arseniy V. "Some Remarks on the Circumcenter of Mass." Discrete & Computational Geometry 51, no. 4 (2014): 837–41. http://dx.doi.org/10.1007/s00454-014-9596-3.

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Tabachnikov, Serge, and Emmanuel Tsukerman. "Circumcenter of Mass and Generalized Euler Line." Discrete & Computational Geometry 51, no. 4 (2014): 815–36. http://dx.doi.org/10.1007/s00454-014-9597-2.

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Coghetto, Roland. "Circumcenter, Circumcircle and Centroid of a Triangle." Formalized Mathematics 24, no. 1 (2016): 17–26. http://dx.doi.org/10.1515/forma-2016-0002.

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Summary We introduce, using the Mizar system [1], some basic concepts of Euclidean geometry: the half length and the midpoint of a segment, the perpendicular bisector of a segment, the medians (the cevians that join the vertices of a triangle to the midpoints of the opposite sides) of a triangle. We prove the existence and uniqueness of the circumcenter of a triangle (the intersection of the three perpendicular bisectors of the sides of the triangle). The extended law of sines and the formula of the radius of the Morley’s trisector triangle are formalized [3]. Using the generalized Ceva’s Theorem, we prove the existence and uniqueness of the centroid (the common point of the medians [4]) of a triangle.
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Martínez, Sonia. "Practical multiagent rendezvous through modified circumcenter algorithms." Automatica 45, no. 9 (2009): 2010–17. http://dx.doi.org/10.1016/j.automatica.2009.05.013.

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Dissertations / Theses on the topic "Circumcenter"

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JÃnior, Antonio Sinval Bezerra. "Pontos notÃveis de um triÃngulo : uma abordagem geomÃtrica e analÃtica." Universidade Federal do CearÃ, 2014. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=11765.

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Nesse trabalho, comeÃaremos com um pouco da histÃria dos centros notÃveis do triÃngulo, com foco nos quatro pontos notÃveis: Baricentro, Incentro, Ortocentro e circuncentro, alÃm da Reta de Euler. Em seguida abordaremos alguns resultados clÃssicos associados ao triÃngulo e as coordenadas de pontos no plano cartesiano que serÃo Ãteis para auxiliar nas demonstraÃÃes dos capÃtulos que seguem. Nestes capÃtulos sÃo apresentados os pontos notÃveis do triÃngulo e algumas de suas caracterÃsticas, bem como o Ponto de Speiker e a de Reta de Euler de dois aspectos: do ponto de vista da Geometria Euclidiana e do ponto de vista da Geometria AnalÃtica.<br>In this work, we start with a little history of notable centers of the triangle, focusing on the four notable points: Centroid, Incentro, orthocenter and circumcenter, besides Straight Euler.Then discuss some classical results associated with the triangle and the coordinates of points on the Cartesian plane that will be useful to assist in the statements of the chapters that follow.These chapters are presented the outstanding points of the triangle and some of its characteristics as well as the Point Speiker and Reta Euler two aspects: the point of view of Euclidean geometry and the point of view of analytic geometry.
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Kitaoka, Alessandra de Carvalho. "O uso de tecnologias como ferramenta de apoio às aulas de geometria." Universidade Federal de São Carlos, 2013. https://repositorio.ufscar.br/handle/ufscar/5942.

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Made available in DSpace on 2016-06-02T20:29:23Z (GMT). No. of bitstreams: 1 5405.pdf: 3455845 bytes, checksum: 749a1a7ca8b7d3b9399b8de99a655175 (MD5) Previous issue date: 2013-08-16<br>Financiadora de Estudos e Projetos<br>This project's main goal is propose the application of a Teaching Sequence about how finding the notable points of a triangle, in particular, the circumcenter. Introducing in the sequence geometric objects primaries of Euclidean geometry with the axioms and the theorems necessary to construct the circumcenter. The geometric objects will be built through educational software Geogebra. The teaching of geometry, often present to the end of the textbook, is faced with the difficulty of the students to manipulate instruments as ruler, protractor and compass. On the other hand, the fascination of students by computers facilitates the use of geometric softwares. The sum of these factors, have inspired this project. Based on the methodology of the didactic engineering I intend to show the construction steps of mathematical knowing from the student's research experimenting, visualizing, conjecturing, generalizing even demonstrating the mathematical basement in this context.<br>O presente trabalho objetiva relatar a aplicação de uma Sequência Didática sobre como encontrar os pontos notáveis de um triângulo, em particular o circuncentro, apresento na sequência entes geométricos primários da geometria euclidiana plana junto aos axiomas e teoremas necessários para a construção do circuncentro. Os objetos geométricos serão construídos através do software educacional Geogebra. O ensino da geometria, muitas vezes relegado ao final do livro didático, se depara com a dificuldade que os alunos têm em manipular instrumentos como régua, transferidor e compasso. Por outro lado, o fascínio dos estudantes por computadores facilita a utilização de softwares da Geometria dinâmica. A soma desses fatores, inspirou esse trabalho. Baseado na metodologia da engenharia didática, pretendo mostrar etapas da construção do conhecimento matemático a partir da investigação do aluno, experimentando, visualizando, conjecturando, generalizando e até mesmo demonstrando todo embasamento matemático envolvido nesse contexto.
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Felício, Adriano César. "A determinação dos pontos notáveis de um triângulo utilizando o software GeoGebra." Universidade Federal de São Carlos, 2013. https://repositorio.ufscar.br/handle/ufscar/5938.

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Made available in DSpace on 2016-06-02T20:29:22Z (GMT). No. of bitstreams: 1 5363.pdf: 6155796 bytes, checksum: 5fcc940d5e974f06e05cfe033a89fcd9 (MD5) Previous issue date: 2013-08-19<br>Financiadora de Estudos e Projetos<br>In this paper, I intend to report the experience of implementing an activity in some classes in a public school of the city of Ribeirão Preto, state of São Paulo, where it was made an approach to the subject "Notable Points of a Triangle" by using the software GeoGebra like as a tool for teaching and learning. The aim is to analyze students' reactions and the interaction of the same at the presentation of the content using this software. Also a comparison of the progress is made with regard to student learning through the production and execution of activities, consisting of scripts/walkthroughs. The methodology used is the didactic engineering. Working in pairs, due to the limited amount of computers in the computer lab of the school, improved academic relations between some students, arising naturally an exchange of ideas and awakening a spirit of collaboration in a very healthy learning space. At the end of the study the author concluded that activities using computing resources as an educational tool optimizes the process of teaching and learning.<br>Neste trabalho, pretendo relatar a experiência de aplicação de uma atividade em algumas aulas, em uma escola municipal da prefeitura de Ribeirão Preto, estado de São Paulo, onde foi feita a abordagem do assunto Pontos Notáveis de um Triângulo utilizando o software GeoGebra como ferramenta de ensino e aprendizagem. O objetivo é analisar as reações dos alunos e a interação dos mesmos, por ocasião da apresentação do conteúdo utilizando este software. Também é feita uma comparação dos avanços obtidos no tocante à aprendizagem dos alunos através das produções e da execução de atividades, constituídas de roteiros/instruções passo a passo. A metodologia utilizada é a engenharia didática. O trabalho em duplas, por conta da quantidade limitada de computadores existentes no laboratório de informática da escola, estreitou as relações acadêmicas entre alguns alunos, fazendo surgir naturalmente uma troca de ideias e despertando um espírito de colaboração muito saudáveis num espaço de aprendizagem. Ao final da pesquisa o autor concluiu que atividades utilizando recursos computacionais como ferramenta educativa otimizam o processo de ensino e aprendizagem.
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Tein-Jen, Chiang. "A Circumcenter of Triangle Location Estimation in UWB." 2004. http://www.cetd.com.tw/ec/thesisdetail.aspx?etdun=U0009-0112200611320786.

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Chiang, Tein-Jen, and 江天仁. "A Circumcenter of Triangle Location Estimation in UWB." Thesis, 2005. http://ndltd.ncl.edu.tw/handle/77733405431542300468.

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碩士<br>元智大學<br>資訊工程學系<br>93<br>We propose a novel location estimation algorithm based on the circumstance center of a triangle and time of arrival method. The estimated result is superior to the other existing method. In fact, on average the circumcenter of triangle (COT) approach can improve the accuracy about 26% when it is compared with other methods. Additionally, we also propose a weighting method, on various positioning methods. The accuracy of the weighted Line of Position (LOP) approach can be improved by 22%, of the Weighted TDOA approach by 24%, and of the Weighted COT approach can be improved by 31%. Keywords : Ultra-wideband、Circumcenter of Triangle、Line of Position
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Weng, Min-Chieh, and 翁敏傑. "Effects of Context Integration on Circumcenter, Incenter and Centroid of a Triangle." Thesis, 2016. http://ndltd.ncl.edu.tw/handle/74583801262928534986.

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碩士<br>國立交通大學<br>理學院科技與數位學習學程<br>104<br>Abstract This study was mainly employed by digital tools. In order to explore the learners’ learning achievements and the differences of their cognitive load, we adopted a teaching research about the unit “Circumcenter, Incenter and Centroid of Triangle” in Grade 1-9 Curriculum of mathematics. This was a quasi-experiment study by using Microsoft PowerPoint assisted with AMA (Activate Mind and Attention). The experimental group, based on the Cognitive Load Theory and adopted context integration model to teach .The control group, based on the narrative context of the textbook and adopted knowledge-oriented model to teach. The major results of this study are as following： 1. Aspects of students’ learning achievements： (1) There was significant difference between the pre-test and post-test scores of the experimental group and the control group on the Mathematical Learning Achievement Test. It might refer that both of the teaching materials were able to reach the purpose of effective teaching. (2) There was no significant difference between the experimental group and the control group in the post-test. However, there was significant difference in the delayed post-test. Through the design of the task- oriented teaching environment, it was helped to expand cognitive schemas. 2. Aspects of the cognitive load： (1) Through the teaching materials of cognitive load theory, it illustrates that we can increase students’ learning willingness and elevates the level of understanding; even reduce the loss of their spirit and the learning difficulties. (2) There was no significant difference between the experimental group and the control group in the cognitive load. An appropriate teaching materials can reduce the cognitive load, it is not affected by the teaching context. (3) Because of the task-oriented model used in the experimental group, the learners engaged in their learning more to increase the effective cognitive load and focused on their learning.
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Fu, Yi-Lun, and 傅一倫. "A Circumcenter-based Algorithm for Irregular Sensing Range Wireless Sensor Network Deployment." Thesis, 2007. http://ndltd.ncl.edu.tw/handle/89533743414208881065.

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碩士<br>國立成功大學<br>電腦與通信工程研究所<br>95<br>As the growing of Wireless Sensor Network, various kinds of relative topics have been broadly discussed. Among these topics, since “coverage” directly influent the performance of the network, it catches a lot of concentration. The proposed methods assume that the sensor has a fixed sensing ability in all directions, but experiments show that sensors may have various sensing ability in various directions. In other words, the coverage area of a sensor node will not be a circular disk. Under this situation, there will be a lot of holes so that the coverage rate cannot achieve as high as expected. This proposed paper holds the assumption of irregular sensing range and propose a sensor deployment algorithm. An irregular sensing model is used to present the unexpected holes caused by irregular sensing range. Deployed sensor nodes will be grouped through the Triangulation procedure. Because of the property of having same distance between the three vertices, the circum center of a triangle is a ideal position to put a node on. Moreover, the proposed algorithm does adjustments according to the status of grids around the circum center, the distance between the circum center and the vertices, and the distance between the circum centers. The algorithm terminates when there is not any new node to provide enough efficient coverage. A boundary enhancement scheme is included in this algorithm to solve the problem that the result of new node location seldom appears near the boundary and elevate the whole coverage rate. The experiment results show that the proposed algorithm can use sensor nodes efficiently and elevate the coverage rate up to 95% fast. In the opposite, the remaining holes will be bitty and dissipative so that lots of new nodes are needed to cover these holes with low benefits.
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Huang, Chien-Chin, and 黃建欽. "The Effects of Using Trigger-based Animation on Learning the Circumcenter of A Triangle." Thesis, 2009. http://ndltd.ncl.edu.tw/handle/55413034111305625005.

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Hong, Yun Quan, and 洪筠荃. "Development of tetrahedron circumcenter element and its applications to 3-D semiconductor device simulation." Thesis, 2017. http://ndltd.ncl.edu.tw/handle/as6uhv.

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碩士<br>國立中央大學<br>電機工程學系<br>105<br>In this thesis, in order to obtain an accurate simulation in the production process, we developed the 3-D tetrahedron circumcenter element to correct the error caused by the edge effect. So as to achieve the accuracy of mesh, we tested and verified the result by using the current density, special resistors and p-n diode. We also compared the estimated value with theoretical value to obtain the correct result from verification. We hope that we can develop the tetrahedral after this experiment. Unfortunately, the exposed right angle tetrahedron of circumcenter caused the error of the volume overlap. The hexahedral structure is a pity. Additionally, we developed a circular and spherical structure to obtain a 3-D mesh with a minimum grid points.
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CHUANG, SHU-YA, and 莊舒雅. "The Study Of Students’ Learning Satisfaction Of Geogebra Software Applied on Circumcenter, Incenter and Centroid of a Triangle." Thesis, 2017. http://ndltd.ncl.edu.tw/handle/03900404748676953930.

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碩士<br>吳鳳科技大學<br>應用數位媒體研究所<br>105<br>This study mainly discusses the influence of Geogebra software on the satisfaction of mathematics learning and the difference of learning background variables. Take the " Circumcenter, Incenter and Centroid of a Triangle " of the ninth grade geometric proof unit as an example. This study employed 122 of the ninth grade students in Chiayi County as subjects and a total of 116 samples were valid.The Experimental research method was adopted. To collect the research data, application of Geogebra software teaching, and learning satisfaction questionnaire was used. The results of this study are as follows: First, the students use geogebra to learn the Circumcenter, Incenter and Centroid of a Triangle towards satisfaction.“Teacher teaching” shows better impact on satisfaction. "Learning environment" has no significant impact on satisfaction. Second,background variables have no significant moderated effects between the factors(curriculum plan,learning environment,teacher teaching, interpersonal relationship) and satisfaction after using geogebra.
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Book chapters on the topic "Circumcenter"

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Rodríguez, Marc, Sere Abdoulaye, Gaëlle Largeteau-Skapin, and Eric Andres. "Generalized Perpendicular Bisector and Circumcenter." In Computational Modeling of Objects Represented in Images. Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-12712-0_1.

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Das, Sandip, Ayan Nandy, and Swami Sarvottamananda. "Radius, Diameter, Incenter, Circumcenter, Width and Minimum Enclosing Cylinder for Some Polyhedral Distance Functions." In Algorithms and Discrete Applied Mathematics. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-74180-2_24.

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Md Nasir, Paramartha Dutta, and Avishek Nandi. "Recognition of Change in Facial Expressions From Video Sequence Using Incenter-Circumcenter Pair Gradient Signature." In Advances in Intelligent Systems and Computing. Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-5400-1_73.

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Nandi, Avishek, Paramartha Dutta, and Md Nasir. "Recognizing Human Emotions from Facial Images by Landmark Triangulation: A Combined Circumcenter-Incenter-Centroid Trio Feature-Based Method." In Algorithms in Machine Learning Paradigms. Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-1041-0_9.

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Nasir, Md, Paramartha Dutta, and Avishek Nandi. "Recognition of Transforming Behavior of Human Emotions from Face Video Sequence: A Triangulation-Induced Circumradius-Incenter-Circumcenter Combined Approach." In Intelligence Enabled Research. Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-9290-4_9.

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"The Circumcentre, O. The Sine Rule." In Trigonometry. WORLD SCIENTIFIC, 2016. http://dx.doi.org/10.1142/9789813203129_0007.

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Conference papers on the topic "Circumcenter"

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Martinez, Sonia. "Practical rendezvous through modified circumcenter algorithms." In 2007 46th IEEE Conference on Decision and Control. IEEE, 2007. http://dx.doi.org/10.1109/cdc.2007.4434171.

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Verma, M., and K. K. Shukla. "Fuzzy constrained shortest path algorithm using circumcenter of centroids." In 2013 3rd IEEE International Advanced Computing Conference (IACC 2013). IEEE, 2013. http://dx.doi.org/10.1109/iadcc.2013.6514304.

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Abdullah, Lazim, and Fateen Najwa Azman. "Circumcenter of centroid in ranking fuzzy number: A case of generalized trapezoidal fuzzy numbers." In 2015 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE). IEEE, 2015. http://dx.doi.org/10.1109/fuzz-ieee.2015.7337941.

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Fazenda, A. L., and J. S. Travelho. "Bidimensional modeling for incompressible viscous flow using the Circumcenter Based Approach in an unstructured grid." In AFM 2010. WIT Press, 2010. http://dx.doi.org/10.2495/afm100101.

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