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Relevant bibliographies by topics / Ceva's theorem

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Academic literature on the topic 'Ceva's theorem'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 April 2022

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Journal articles on the topic "Ceva's theorem"

1

Contreras, José N. "Discovering, Applying, and Extending Ceva's Theorem." Mathematics Teacher 108, no. 8 (April 2015): 632–37. http://dx.doi.org/10.5951/mathteacher.108.8.0632.

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Hoehn, Larry. "73.21 A Simple Generalisation of Ceva's Theorem." Mathematical Gazette 73, no. 464 (June 1989): 126. http://dx.doi.org/10.2307/3619672.

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Landy, Steven. "A Generalization of Ceva's Theorem to Higher Dimensions." American Mathematical Monthly 95, no. 10 (December 1988): 936. http://dx.doi.org/10.2307/2322390.

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Landy, Steven. "A Generalization of Ceva's Theorem to Higher Dimensions." American Mathematical Monthly 95, no. 10 (December 1988): 936–39. http://dx.doi.org/10.1080/00029890.1988.11972122.

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Koichu, Boris, and Abraham Berman. "3-D Dynamic Geometry: Ceva's Theorem in Space." International Journal of Computers for Mathematical Learning 9, no. 1 (2004): 95–108. http://dx.doi.org/10.1023/b:ijco.0000038277.75552.65.

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Soydan, Gökhan, Yusuf Doğru, and Umut Arslandoğan. "On the ratio of directed lengths on the plane with generalized absolute value metric and related properties." Filomat 26, no. 1 (2012): 119–29. http://dx.doi.org/10.2298/fil1201119s.

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In this paper, we show that a point of division divides a related line segment in the same ratio on the plane with generalized absolute value metric and Euclidean plane. Then the coordinates of the division point can be determined by the same formula as in the Euclidean plane. In the latter parts of the work, we give Ceva's and Menelaus'es theorems and the theorem of directed lines on the plane with generalized absolute value metric.

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Byrkit, Donald R., and Timothy L. Dixon. "A Corollary to Ceva's Theorem and Some of Its Consequences." School Science and Mathematics 90, no. 8 (December 1990): 683–93. http://dx.doi.org/10.1111/j.1949-8594.1990.tb12047.x.

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Annersih, Nevi, Mashadi Mashadi, and M. D. H. Gamal. "PENGEMBANGAN TEOREMA CEVA PADA SEGILIMA." JURNAL MATHEMATIC PAEDAGOGIC 3, no. 1 (July 10, 2018): 47. http://dx.doi.org/10.36294/jmp.v3i1.309.

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Abstract This paper discusses the development of the Ceva’s theorem on the pentagon in various cases including for the convex pentagon and the nonconvent pentagon. The Ceva’s theorem discusses the case of one-point concurrent in the pentagon. The proofing process is done in a simple way that is by using wide comparison. The results obtained from this paper are the existence of five lines from each vertex on the pentagon intersected at one point (concurrent) ie point P. Keywords: Ceva theorem, Ceva’s theorem on the pentagon, concurrent AbstrakTulisan ini membahas tentang pengembangan teorema Ceva pada segilima dalam berbagai kasus antara lain untuk segilima konveks dan segilima nonkonveks. Teorema Ceva segilima membahas kasus kekonkurenan satu titik yang berada pada segilima. Proses pembuktian dilakukan dengan cara sederhana yaitu dengan menggunakan perbandingan luas. Hasil yang diperoleh dari tulisan ini adalah eksistensi lima buah garis dari masing-masing titik sudut pada segilima berpotongan di satu titik (konkuren) yaitu titik P. Kata kunci: teorema Ceva, teorema Ceva pada segilima, konkurensi

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Coghetto, Roland. "Altitude, Orthocenter of a Triangle and Triangulation." Formalized Mathematics 24, no. 1 (March 1, 2016): 27–36. http://dx.doi.org/10.1515/forma-2016-0003.

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Summary We introduce the altitudes of a triangle (the cevians perpendicular to the opposite sides). Using the generalized Ceva’s Theorem, we prove the existence and uniqueness of the orthocenter of a triangle [7]. Finally, we formalize in Mizar [1] some formulas [2] to calculate distance using triangulation.

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Jupri, Al, Siti Fatimah, and Dian Usdiyana. "Dampak Perkuliahan Geometri Pada Penalaran Deduktif Mahasiswa: Kasus Pembelajaran Teorema Ceva." AKSIOMA : Jurnal Matematika dan Pendidikan Matematika 11, no. 1 (July 15, 2020): 93–104. http://dx.doi.org/10.26877/aks.v11i1.6011.

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Geometry is one of branches of mathematics that can develop deductive thinking ability for anyone, including students of prospective mathematics teachers, who learning it. This deductive thinking ability is needed by prospective mathematics teachers for their future careers as mathematics educators. This research therefore aims to investigate the influence of the learning process of a geometry course toward deductive reasoning ability of students of prospective mathematics teachers. To do so, this qualitative research was carried out through an observation of the learning process and assessment of the geometry course, involving 56 students of prospective mathematics teachers, in one of mathematics education program, in one of state universities in Bandung. A geometry topic observed in the learning process was the Ceva’s theorem, and the assessment was in the form of an individual written test on the application of the Ceva’s theorem in a proving process. The results showed that the learning process emphasizes on proving of theorems and mathematical statements. In addition, the test revealed that ten students are able to use the Ceva’s theorem in a proving process and different strategies of proving are found, including the use of properties of similarity between triangles and of the concept of trigonometry. This indicates a creativity of student deductive thinking in proving process. In conclusion, the geometry course that emphasizes on proving of theorems and mathematical statements has influenced on filexibility of student deductive thinking in proving processes.

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Dissertations / Theses on the topic "Ceva's theorem"

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Baker, Charla Bezdek András. "Triangle centers and Kiepert's hyperbola." Auburn, Ala., 2006. http://repo.lib.auburn.edu/2006%20Fall/Theses/BAKER_CHARLA_6.pdf.

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Karaca, Ozen. "The Theme Of Jewish Conspiracy In Turkish Nationalism: The Case Of Cevat Rifat Atilhan." Master's thesis, METU, 2008. http://etd.lib.metu.edu.tr/upload/12609505/index.pdf.

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This study analyzes the discourse of Cevat Rifat Atilhan, a leading anti-Semite figure and a conspiracy theorist in Turkish politics. The principal aim of this analysis is to shed light on Atilhan&rsquo
s conspiratorial mindset which has a considerable influence on anti-Semitism in contemporary Turkey. To this aim, conspiracy theories and anti-Semitism, two main components of Atilhan&rsquo
s discourse are examined in relation to each other from the perspective of nationalist discourse. This study argues that conspiracy theories in Atilhan'
s discourse which explain social antagonism as a Jewish plot can be considered as instruments to the reproduction of anti-Semitism. Accordingly, the inherent mechanisms of conspiracy theories which rest on the racist and xenophobic brand of nationalism represent the society on the basis of dichotomies. In Atilhan&rsquo
s discourse, this dichotomization is based on the positioning of the Jews vis-à
-vis Turkish nation. To the extent that the Jews are represented as enemies vis-à
-vis Turkish nation, anti-Semitism becomes likely to be reproduced. The theme of Jewish conspiracy in Atilhan&rsquo
s discourse is better explained by his different positions within Turkish nationalism ranging from Kemalism to racism, from racism to Islamism and conservative tones of nationalism. When his changing positions is examined in relation to the theme of Jewish conspiracy in his discourse, it is realized that Atilhan&rsquo
s discourse have a considerable influence on the discourse of ultra-nationalist, conservative nationalist and Islamist circles whose way of thinking is dominated by conspiracy theories.

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Marina, Milićević. "Formalni sistemi za dokazivanje teorema incidencije." Phd thesis, Univerzitet u Novom Sadu, Fakultet tehničkih nauka u Novom Sadu, 2020. https://www.cris.uns.ac.rs/record.jsf?recordId=114829&source=NDLTD&language=en.

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U ovoj tezi razvijen je formalni sistem za dokazivanje teoremaincidencije u projektivnoj geometiji. Osnova sistema je Čeva/Menelajmetod za dokazivanje teorema incidencije. Formalizacija o kojoj jeovdje riječ izvedena je korišćenjem Δ-kompleksa, pa su tako udisertaciji spojene oblasti logike, geometrije i algebarsketopologije. Aksiomatski sekventi proizilaze iz 2-ciklova Δ-kompleksa.Definisana je Euklidska i projektivna interpretacija sekvenata idokazana je saglasnost i odlučivost sistema. Dati su primjeriiščitavanja teorema incidencije iz dokazivih sekvenata sistema. Utezi je data i procedura za provjeru da li je skup od n šestorki tačakaaksiomatski sekvent.
In this thesis, a formal sequent system for proving incidence theorems inprojective geometry is introduced. This system is based on theCeva/Menelaus method for proving theorems. This formalization is performedusing Δ-complexes, so the areas of logic, geometry and algebraic topologyare combined in the dissertation. The axiomatic sequents of the system stemfrom 2-cycles of Δ-complexes. The Euclidean and projective interpretations ofthe sequents are defined and the decidability and soundness of the systemare proved. Patterns for extracting formulation and proof of the incidenceresult from derivable sequents of system are exemplified. The procedure fordeciding if set of n sextuples represent an axiomatic sequent is presentedwithin the thesis.

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MÍKOVÁ, Lucie. "Vybrané problémy z planimetrie." Master's thesis, 2017. http://www.nusl.cz/ntk/nusl-381442.

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This diploma thesis is focused on Selected problems in planimetry. The aim of this diploma thesis is description not only planimetric problems and their verification in a dynamic mathematical program GeoGebra, but also presentation of the author after whom it is called. The thesis is illustrated with pictures, which can help the reader to understand the problem and verification. This thesis can be used as a supplement the curriculum in secondary schools, where using dynamic program GeoGebra and subsequent verification may reach a better understanding of the topic.

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Book chapters on the topic "Ceva's theorem"

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Bottema, O., and Reinie Erne. "Ceva’s Theorem." In Topics in Elementary Geometry, 1–5. New York, NY: Springer New York, 2008. http://dx.doi.org/10.1007/978-0-387-78131-0_2.

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"Ceva’s Theorem." In Beautiful Geometry, 105–7. Princeton University Press, 2014. http://dx.doi.org/10.2307/j.ctt4cgb6n.36.

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"Ceva’s Theorem." In Exploring Advanced Euclidean Geometry with GeoGebra, 63–76. Providence, Rhode Island: American Mathematical Society, 2013. http://dx.doi.org/10.5948/9781614441113.010.

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"32. Ceva’s Theorem." In Beautiful Geometry, 105–7. Princeton University Press, 2014. http://dx.doi.org/10.1515/9781400848331-033.

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Adesso, Maria Giuseppina, Roberto Capone, Oriana Fiore, and Francesco Saverio Tortoriello. "Walking through the history of geometry teaching by Cevian and orthic triangles and quadrilaterals." In “DIG WHERE YOU STAND” 6. Proceedings of the Sixth International Conference on the History of Mathematics Education, 343–54. WTM-Verlag Münster, 2020. http://dx.doi.org/10.37626/ga9783959871686.0.26.

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The history of geometry teaching in Italy, in the period from the final years of the 19th century to the first half of the 20th century, is analysed here, taking into account the influence of both school reforms and the “New geometry of the triangle”, first introduced in France in 1873. Specifically, we refer to some theorems, about Cevian and orthic triangles, which may be included in the “New geometry of the triangle”, although they have been discovered in Italy before 1873. Some Italian booklets and textbooks have been analysed, to show the influence of these factors on the geometric teaching. Keywords: geometry teaching, New geometry of the triangle, Ceva’s theorem, orthic triangles, Cevian quadrilaterals, Fagnano’s problem

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Conference papers on the topic "Ceva's theorem"

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Pendar, Hodjat, Hajir Roozbehani, Hoda Sadeghian, and Hassan Zohoor. "Analysis of Singularities of a 3DOF Parallel Manipulator Based on a Novel Geometrical Method." In ASME 8th Biennial Conference on Engineering Systems Design and Analysis. ASMEDC, 2006. http://dx.doi.org/10.1115/esda2006-95592.

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In this article singular points of a parallel manipulator are obtained based on a novel geometrical method. Here we introduce the constrained plain method (CPM) and some of its application in parallel mechanism. Given the definition of constraint plane (CP) and infinite constraint plane (ICP) the dependency conditions of constraints is achieved with the use of a new theorem based on the Ceva geometrical theorem. The direction of angular velocity of a body is achieved by having three ICPs with the use of another theorem. Finally, with the use of the above two novel theorems singularities of the 3UPF_PU mechanism are obtained. It should be emphasized that this method is completely geometrical, involving no complex or massive calculations. In the previous methods based on the Grassmann Geometry, the mechanism needs to be statically analyzed at first, so that the Inverse Jacobian Matrix is achieved, and then the Plucker-Vector is derived. This task is somewhat inconvenient and in the end there are plenty of conditions remained to be pondered in order to obtain the singularity conditions, while the novel method introduced here, involves no tiring calculations neither the analysis of numerous conditions and yields the answer quickly.

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Zhang, M. J., Ran Zhang, Liguo Weng, Wenchuan Cai, Christ Doss, and Y. D. Song. "Robust and Adaptive Autolanding Control Strategies for Crew Exploration Vehicles (CEVs)." In 2007 Thirty-Ninth Southeastern Symposium on System Theory. IEEE, 2007. http://dx.doi.org/10.1109/ssst.2007.352372.

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Pendar, Hodjat, Maryam Mahnama, and Hassan Zohoor. "A Novel Method on Singularity Analysis in Parallel Manipulators." In ASME 8th Biennial Conference on Engineering Systems Design and Analysis. ASMEDC, 2006. http://dx.doi.org/10.1115/esda2006-95447.

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A parallel manipulator is a closed loop mechanism in which a moving platform is connected to the base by at least two serial kinematic chains. The main problem engaged in these mechanisms, is their restricted working space as a result of singularities. In order to tackle these problems, many methods have been introduced by scholars. However, most of the mentioned methods are too much time consuming and need a great amount of computations. They also in most cases do not provide a good insight to the existence of singularity for the designer. In this paper a novel approach is introduced and utilized to identify singularities in parallel manipulators. By applying the new method, one could get a better understanding of geometrical interpretation of singularities in parallel mechanisms. Here we have introduced the Constraint Plane Method (CPM) and some of its applications in parallel mechanisms. The main technique used here, is based on Ceva Theorem.

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