Relevant bibliographies by topics / Angle trisection

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

Academic literature on the topic 'Angle trisection'

Author: Grafiati
Published: 4 June 2021
Last updated: 25 April 2022

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Journal articles on the topic "Angle trisection"

1

De Catalina, Emiliano. "Angle Trisection, Bhaskara’s Proof, and Pythagorean Theorem." Recoletos Multidisciplinary Research Journal 9, no. 1 (June 3, 2021): 1–11. http://dx.doi.org/10.32871/rmrj2109.01.01.

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This paper deals with 1) angle trisection, 2) Bhaskara’s first proof, and 3) Pythagorean theorem. The purpose of this paper is threefold. First, to show a new, direct method of trisecting the 900 angle using unmarked straight edge and compass; secondly, to show Bhaskara’s first proof of the Pythagorean theorem (c2 = a2 + b2) as embedded in this new, direct trisection of the 900 angle; lastly, to show the derivation of the Pythagorean theorem from this trisection of the 900 angle. This paper employs the direct dissection method. It concludes by presenting four points: a) the concept of trisectability as distinct from concept of constructability; b) the trisection of the 900 angle as really a new, different method; c) Bhaskara’s first proof of the Pythagorean theorem as truly embedded in this trisection of the 900 angle and; d) another way of deriving Pythagorean theorem from this trisection of the 900 angle.
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Husyan Pour Shad, Mehryar. "Angle Trisection." JOURNAL OF ADVANCES IN MATHEMATICS 17 (September 16, 2019): 165–231. http://dx.doi.org/10.24297/jam.v17i0.8412.

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We seek to increase the development of science, but there are several fundamental questions about what is. Without solving the question is a false reflection of the history of science and the beginning of cognition. We know that their investigation and resolution, with the exception of rooting and knowledge of morphophonemic, do not come. Research on certain natural or pure mathematical phenomena is an example of my fundamental research that will lead to the definition of general principles and scientific theories.
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3

Rediske, Arthur Clair. "The Trisection of an Arbitrary Angle." JOURNAL OF ADVANCES IN MATHEMATICS 14, no. 2 (April 18, 2018): 7640–69. http://dx.doi.org/10.24297/jam.v14i2.7402.

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This paper presents an elegant classical geometric solution to the ancient Greek's problem of angle trisection. Its primary objective is to provide a provable construction for resolving the trisection of an arbitrary angle, based on the restrictions governing the problem. The angle trisection problem is believed to be unsolvable for compass-straightedge construction. As stated by Pierre Laurent Wantzel (1837), the solution of the angle trisection problem corresponds to an implicit solution of the cubic equation x cubed minus 3x minus 1 equals 0, which is algebraically irreducible, and so is the geometric solution of the angle trisection problem. The goal of the presented solution is to show the possibility to solve the trisection of an arbitrary angle using the traditional Greek's tools of geometry (a classical compass and straightedge) by changing the problem from the algebraic impossibility classification to a solvable plane geometrical problem. Fundamentally, this novel work is based on the fact that algebraic irrationality is not a geometrical impossibility. The exposed methods of proof have been reduced to the Euclidean postulates of classical geometry.
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Muench, Donald L. "An Iterative Angle Trisection." College Mathematics Journal 38, no. 2 (March 2007): 82–84. http://dx.doi.org/10.1080/07468342.2007.11922222.

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5

Bowring, B. R. "TRISECTION OF AN ANGLE." Survey Review 31, no. 244 (April 1992): 354–56. http://dx.doi.org/10.1179/sre.1992.31.244.354.

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Leung, S. C. "TRISECTION OF AN ANGLE." Survey Review 31, no. 246 (October 1992): 493. http://dx.doi.org/10.1179/sre.1992.31.246.493.

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7

Ananthapadmanabhan, S. "Trisection of an angle." International Journal of Mathematical Education in Science and Technology 19, no. 6 (November 1988): 907–19. http://dx.doi.org/10.1080/0020739880190618.

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8

Alex, Kimuya M. "The Angle Trisection Solution (A Compass-Straightedge (Ruler) Construction)." JOURNAL OF ADVANCES IN MATHEMATICS 13, no. 4 (August 4, 2017): 7308–32. http://dx.doi.org/10.24297/jam.v13i4.6175.

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This paper is devoted to exposition of a provable classical solution for the ancient Greeks classical geometric problem of angle trisection [3]. (Pierre Laurent Wantzel, 1837),presented an algebraic proof based on ideas from Galois field showing that, the angle trisection solution correspond to an implicit solution of the cubic equation; , which he stated as geometrically irreducible [23]. The primary objective of this novel work is to show the possibility to solve the trisection of an arbitrary angle using the traditional Greeks tools of geometry, and refutethe presented proof of angle trisection impossibility statement. The exposedproof of the solution is theorem , which is based on the classical rules of Euclidean geometry, contrary to the Archimedes proposition of usinga marked straightedge construction [4], [11].
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9

Lamb, John F. "Trisecting an Angle—Almost." Mathematics Teacher 81, no. 3 (March 1988): 220–22. http://dx.doi.org/10.5951/mt.81.3.0220.

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Trisecting an angle with Euclidean tools, a straightedge and compass, has been proved to be impossible. However, many people today are still fascinated by the problem, and some even try to do it in spite of the proof to the contrary. The National Council of Teachers of Mathematics published a book on the subject titled The Trisection Problem (Yates 1971) that contains several methods proposed over the years. One method in particular, given by d'Ocagne, is easy and produces an angle that looks very close to the correct size, so close that only a proof that it fails will convince stubborn believers. The proof presented here uses only algebra and trigonometry and hopefully will show students how the three areas of algebra, trigonometry, and geometry can be interrelated.
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Lamb, John F. "Trisecting an Angle—Almost, Part 2." Mathematics Teacher 84, no. 1 (January 1991): 20–23. http://dx.doi.org/10.5951/mt.84.1.0020.

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When students study constructions in high school geometry, they usually make the following conjecture: Since it is easy to bisect a line segment, easy to bisect an angle, and not too difficult to trisect a line segment, there ought to be a way to trisect an angle. The students may even devise ways that they think will accomplish the task. The errors in these methods are sometimes hard to detect. This article highlights one way that has been discovered that comes very close to trisecting an angle with Euclidean tools. Several ways are discussed in one of the books in the Classics in Mathematics Education series published by the National Council of Teachers of Mathematics titled The Trisection Problem (Yates 1971). One of the methods discovered by d'Ocagne was examined in “Trisecting an Angle—Almost” (Lamb 1988). His method was very easy to do, but it was not as accurate as some of the other methods. One of those methods that is also relatively easy to do and gives a much better approximation than the d'Ocagne method for angles between 0 degrees and 90 degrees was discovered by Karajordanoff in 1928 (Yates 1971). The procedure is as follows.
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Dissertations / Theses on the topic "Angle trisection"

1

Passaroni, Luiz Claudio de Sousa. "Construções geométricas por dobradura (ORIGAMI): Aplicações ao ensino básico." Universidade do Estado do Rio de Janeiro, 2015. http://www.bdtd.uerj.br/tde_busca/arquivo.php?codArquivo=9178.

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A presente dissertação tem o objetivo de mostrar a arte Origami sob um contexto matemático, apresentando um pequeno resumo dos aspectos história e o desenvolvimento do Origami ao longo do tempo e dando maior destaque às suas aplicações na matemática, com o emprego dos axiomas de Huzita e a proposta de ampliação deste conjunto de axiomas com a inclusão da circunferência no papel Origami. Com o uso das técnicas de dobraduras, este trabalho mostra várias aplicações do Origami na matemática, tais como: a solução de alguns problemas clássicos, a construção de polígonos, a demonstração da soma dos ângulos internos de um triângulo, cálculo de algumas áreas, a solução de alguns problemas de máximos e mínimos, seguidos dos conceitos matemático envolvidos em cada um deles. E a inclusão da circunferência no plano Origami permitiu ainda, o estudo das construções das cônicas por dobraduras
This work aims to demonstrate the Origami art in a mathematical context, with a brief summary of the historical aspects and its development over time, giving more prominence to applications in mathematics, with the use of the axioms of Huzita and proposal to expand this set of axioms to include the circle in Origami paper. As the use of folding techniques, this work shows various applications of Origami in mathematics, such as the solution of some classical problems; the construction of polygons; the demonstration of the sum of the interior angles of a triangle; the calculation of some areas and the solution of some problems of maximum and minimum, followed by mathematical concepts involved in each of them. The inclusion of the circle in Origami plan allowed also to study the constructions of conic by folding
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2

Sabir, Tanveer, and Aamir Muneer. "Geometrical Constructions : Trisecting the Angle, Doubling the Cube, Squaring the Circle and Construction of n-gons." Thesis, Växjö University, School of Mathematics and Systems Engineering, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:vxu:diva-5401.

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Fabián, Tomáš. "Algebraické křivky v historii a ve škole." Master's thesis, 2016. http://www.nusl.cz/ntk/nusl-346770.

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TITLE: Agebraic Curves in History and School AUTHOR: Bc. Tomáš Fabián DEPARTMENT: The Department of mathematics and teaching of mathematics SUPERVISOR: prof. RNDr. Ladislav Kvasz, Dr. ABSTRACT: The thesis includes a series of exercises for senior high school students and the first year of university students. In these exercises, students will increase their knowledge about conics, especially how to draw them. Furthermore, students can learn about two unfamiliar curves: Conchoid and Quadratrix. All these curves are afterwards used for solving other problems - some Apollonius's problems, Three impossible constructions etc. Most of the construction is done in GeoGebra software. All the tasks are designed for students to learn how to work with this software. The subject discussed is put into historical context, and therefore the exercises are provided with historical commentary. The thesis also includes didactic notes, important or interesting solutions of exercises, possible issues, mistakes and another relevant notes. KEYWORDS: conic, circle, ellipse, parabola, hyperbole, conchoid, quadratrix, trisecting an angle, squaring the circle, rectification of the circle, doubling a cube, Apollonius's problem, GeoGebra
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Fabián, Tomáš. "Algebraické křivky v historii a ve škole." Master's thesis, 2015. http://www.nusl.cz/ntk/nusl-349422.

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TITLE: Agebraic Curves in History and School AUTHOR: Bc. Tomáš Fabián DEPARTMENT: The Department of mathematics and teaching of mathematics SUPERVISOR: prof. RNDr. Ladislav Kvasz, Dr. ABSTRACT: The thesis includes a series of exercises for senior high school students and the first year of university students. In these exercises, students will increase their knowledge about conics, especially how to draw them. Furthermore, students can learn about two unfamiliar curves: Conchoid and Quadratrix. All these curves are afterwards used for solving other problems - some Apollonius's problems, Three impossible constructions etc. Most of the construction is done in GeoGebra software. All the tasks are designed for students to learn how to work with this software. The subject discussed is put into historical context, and therefore the exercises are provided with historical commentary. The thesis also includes didactic notes, important or interesting solutions of exercises, possible issues, mistakes and another relevant notes. KEYWORDS: conic, circle, ellipse, parabola, hyperbole, conchoid, quadratrix, trisecting an angle, squaring the circle, rectification of the circle, doubling a cube, Apollonius's problem, GeoGebra
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Books on the topic "Angle trisection"

1

A budget of trisections. New York: Springer-Verlag, 1987.

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New theory of trisection: Solved the most difficult math problem for centuries in the history of mathematics. Alexandria, Va: International School Math & Sciences Institute, 1999.

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3

Underwood, Dudley, and Mathematical Association of America, eds. The trisectors. 2nd ed. [Washington, D.C.]: Mathematical Association of America, 1994.

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4

Accurate trisection and other "impossible" subdivisions of angles for practical people: Geometric constructions for the division of arbitrary angles by natural numbers to any required degree of accuracy. [Ballinasloe, Co. Galway]: [J W Cahill], 2011.

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5

Sina, R. Plato and the Delian problem. Montreuil, France: R. Sina, 1992.

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6

Rubino, Anthony G. The trisection of angles. New York: Vantage Press, 1990.

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The trisection of any reclined angle. Ottawa: Mortimer, 1996.

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8

The trisection of any rectilineal angle. Ottawa: Copeland-Chatterton-Crain Press, 1996.

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9

Chen, Fen. Regular Polygons: Applied New Theory of Trisection to Construct a Regular Heptagon for Centuries in the History of Mathematics. International School Math & Sciences Institut, 2001.

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Klein, Felix. FAMOUS PROBLEMS OF ELEMENTARY GEOMETRY: The Duplication of the Cube, the Trisection of an Angle, the Quadrature of the Circle. Cosimo Classics, 2007.

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Book chapters on the topic "Angle trisection"

1

Sefrin-Weis, Heike. "Angle Trisection." In Pappus of Alexandria: Book 4 of the Collection, 277–91. London: Springer London, 2010. http://dx.doi.org/10.1007/978-1-84996-005-2_9.

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Knorr, Wilbur Richard. "The Angle Trisection by al-Sijzī." In Textual Studies in Ancient and Medieval Geometry, 293–300. Boston, MA: Birkhäuser Boston, 1989. http://dx.doi.org/10.1007/978-1-4612-3690-0_14.

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Knorr, Wilbur Richard. "The Angle Trisection by Ahmad ibn Müsä." In Textual Studies in Ancient and Medieval Geometry, 267–75. Boston, MA: Birkhäuser Boston, 1989. http://dx.doi.org/10.1007/978-1-4612-3690-0_12.

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Knorr, Wilbur Richard. "The Angle Trisection by Thābit ibn Qurra." In Textual Studies in Ancient and Medieval Geometry, 277–91. Boston, MA: Birkhäuser Boston, 1989. http://dx.doi.org/10.1007/978-1-4612-3690-0_13.

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Knorr, Wilbur Richard. "The Cube Duplication and Angle Trisection by Abū Sahl al-Qūhī." In Textual Studies in Ancient and Medieval Geometry, 301–9. Boston, MA: Birkhäuser Boston, 1989. http://dx.doi.org/10.1007/978-1-4612-3690-0_15.

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Mycka, Jerzy, Francisco Coelho, and José Félix Costa. "The Euclid Abstract Machine: Trisection of the Angle and the Halting Problem." In Lecture Notes in Computer Science, 195–206. Berlin, Heidelberg: Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/11839132_16.

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Floyd, Juliet. "On Saying What You Really Want to Say: Wittgenstein, Gödel, and the Trisection of the Angle." In From Dedekind to Gödel, 373–425. Dordrecht: Springer Netherlands, 1995. http://dx.doi.org/10.1007/978-94-015-8478-4_15.

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Meskens, Ad, and Paul Tytgat. "Trisecting an angle." In Compact Textbooks in Mathematics, 55–74. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-42863-5_5.

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Knorr, Wilbur Richard. "Angle Trisections in Pappus and Arabic Parallels." In Textual Studies in Ancient and Medieval Geometry, 213–24. Boston, MA: Birkhäuser Boston, 1989. http://dx.doi.org/10.1007/978-1-4612-3690-0_9.

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"Trisection of the Angle." In Spectrum, 342–48. Providence, Rhode Island: American Mathematical Society, 2019. http://dx.doi.org/10.1090/spec/004/56.

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Conference papers on the topic "Angle trisection"

1

Chen, Yaping, Cong Dong, and Jiafeng Wu. "Shell Side Flow and Heat Transfer Performances of Trisection Helical Baffle Heat Exchangers." In ASME 2013 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/imece2013-65697.

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The flow and heat transfer performances of three trisection helical baffle heat exchangers with different baffle shapes and assembly configurations, and a continuous helical baffle scheme with approximate spiral pitch were numerically simulated. The four schemes are two trisection helical baffle schemes of baffle incline angle of 20° with a circumferential overlap baffle scheme (20°TCO) and a end-to-end helical baffle scheme (20°TEE), a trisection mid-overlap helical baffle scheme with baffle incline angle of 36.2° (36.2°TMO), and a continuous helical baffle scheme with baffle helix angle of 16.8° (18.4°CH). The pressure or velocity nephograms with superimposed velocity vectors for meridian slice M1, transverse slices f and f1, and unfolded concentric hexagonal slices H2 and H3 are presented. The Dean vortex secondary flow field, which is one of the key mechanisms of enhancing heat transfer in heat exchangers, is clearly depicted showing a single vortex is formed in each baffle pitch cycle. The leakage patterns are demonstrated clearly on the unfolded concentric hexagonal slices. The results show that the 20°TCO and 18.4°CH schemes rank the first and second in shell-side heat transfer coefficient and comprehensive indexes ho/Δpo and ho/Δpo1/3. The 20°TEE scheme without circumferential overlap is considerably inferior to the 20°TCO scheme. The 36.2°TMO scheme is the worst in both shell-side heat transfer coefficient and comprehensive index ho/Δpo1/3.
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Chen, Yaping, Ruibing Cao, Jiafeng Wu, Cong Dong, and Yanjun Sheng. "Experimental Study on Shell Side Heat Transfer Performance of Circumferential Overlap Trisection Helical Baffle Heat Exchangers." In ASME 2011 International Mechanical Engineering Congress and Exposition. ASMEDC, 2011. http://dx.doi.org/10.1115/imece2011-63254.

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A set of experiments were conducted on the circumferential overlap trisection helical baffle heat exchangers with inclined angles of 20°, 24°, 28° and 32° single-thread and inclined angle of 32° dual-thread one, and a segmental baffle heat exchanger as a contrast scheme. The cylinder case of the testing heat exchanger is a common shell, while the tube bundle core could be replaced. The shell side heat transfer coefficient ho is obtained by subtract tube-side convection thermal resistance and tube wall conduction resistance from the overall heat transfer coefficient K. The curves of shell side heat transfer coefficient ho, pressure drop Δpo, Nusselt number Nuo, and axial Euler number Euz,o are presented versus axial Reynolds number Rez,o. A comprehensive performance index Nuo/Euz,o is suggested to demonstrate the integral properties of both heat transfer and flow resistance of different schemes, and the curves of Nuo/Euz,o versus Rez,o of the different schemes are presented. The results show that the scheme with inclined angle 20° performs better than other schemes, and the scheme with inclined angle 24° ranks the second, however the segment scheme ranks the last. The curves of Nuo/Euz,o of both schemes with inclined angle 32° of single-thread and dual-thread are almost coincident, even though their heat transfer coefficient and pressure drop curves are quite different. The results indicate also that for the circumferential overlap trisection helical baffle schemes the optimal inclined angle is around 20° instead of around 40° as rated by many literatures for the quadrant helical baffle schemes.
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