Relevant bibliographies by topics / Conic sections

Contents

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

Academic literature on the topic 'Conic sections'

Author: Grafiati
Published: 4 June 2021
Last updated: 29 July 2024

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Journal articles on the topic "Conic sections"

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Olmstead, Eugene A., and Arne Engebretsen. "Technology Tips: Exploring the Locus Definitions of the Conic Sections." Mathematics Teacher 91, no. 5 (May 1998): 428–34. http://dx.doi.org/10.5951/mt.91.5.0428.

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Conic sections were first studied in 350 B.C. by Menaechmus, who cut a circular conical surface at various angles. Early mathematicians who added to the study of conics include Apollonius, who named them in 220 B.C., and Archimedes, who studied their fascinating properties around 212 B.C. In previous articles in this journal, conic sections have been shown both as an algebraic, or parametric, representation (Vonder Embse 1997) and as a geometric, that is, a paper-folding, model (Scher 1996). Both articles offer important insights into the mathematical nature of the conic sections and into teaching methods that can integrate conics into our curriculum. Even though many textbooks discuss conic equations and their graphs, they do not fully develop locus definitions of conic sections.
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Laywine, Alison. "Kant on conic sections." Canadian Journal of Philosophy 44, no. 5-6 (December 2014): 719–58. http://dx.doi.org/10.1080/00455091.2014.977835.

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This paper tries to make sense of Kant’s scattered remarks about conic sections to see what light they shed on his philosophy of mathematics. It proceeds by confronting his remarks with the source that seems to have informed his thinking about conic sections: the Conica of Apollonius. The paper raises questions about Kant’s attitude towards mathematics and the way he understood the cognitive resources available to us to do mathematics.
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Germain-McCarthy, Yvelyne. "Circular Graphs: Vehicles for Conic and Polar Connections." Mathematics Teacher 88, no. 1 (January 1995): 26–28. http://dx.doi.org/10.5951/mt.88.1.0026.

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A unified treatment of conic sections and polar equations of conics can be found in most calculus books where the reciprocals of limafçons are shown to be conic sections. The treatment, however, is from an algebraic standpoint and does not refer to the inherent connection between polar graphs and the graphs of trigonometric functions and conics. Beginning with information gained from the graphs of circular functions of the form y = A + B sin x, students can be guided to graph conic sections on the polar plane without using a table of values. This approach helps students to appreciate the roles that both algebra and coordinate geometry play in weaving various sections of mathematics into a meaningful whole.
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.., Hamiyet, and Mohammad Abobala. "The Application of AH-Isometry in the Study of Neutrosophic Conic Sections." Galoitica: Journal of Mathematical Structures and Applications 2, no. 2 (2022): 18–22. http://dx.doi.org/10.54216/gjmsa.020203.

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One of the most important areas of analytic geometry involves the concept of conic sections. The objective of this paper is to introduce the concept of neutrosophic conic sections, so that each neutrosophic conic section represents two classic conic section in the general case. On the other hand, all special cases resulting from the expansion by moving to the neutrosophic systems will be discussed and handled.
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Li, Zhiguang. "Problem-solving teaching strategies from the perspective of dividing the core literacy of mathematical operations." BCP Education & Psychology 6 (August 25, 2022): 207–13. http://dx.doi.org/10.54691/bcpep.v6i.1791.

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Mathematical operation literacy is one of the six core literacy proposed in the new Chinese senior high school curriculum reform round. Based on the problem-solving teaching link of the high school mathematics conic section, this paper is based on the connotation and method of mathematical operation literacy cultivation. Combined with the problems that high school students have in the problem-solving of conic sections, we innovate the teaching strategies for solving conic sections, improve students' literacy of mathematical operations in classroom teaching, and help teachers teach conic sections better. To enable students to grasp the problem-solving method of the conic section better.
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Said, Arwan Mhd. "Menentukan Bentuk Kuadrat Bagian Kerucut Dan Permukaan Kuadratik dengan Menggunakan Matriks." Foramadiahi: Jurnal Kajian Pendidikan dan Keislaman 8, no. 1 (December 1, 2016): 47. http://dx.doi.org/10.46339/foramadiahi.v8i1.42.

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In determining quadratic forms by using the matrix, the way is to eliminate the tribe the product of a quadratic form, ie with how to change variables, and will use the results to assess the graph Conic sections (slices or cross-section of the cone, or conic section ).Problems in this study is how to determine the quadratic forms of conic sections and quadratic surfaces with using Matrix. From these results, it can be concluded that determine the shape of squares of conic sections and quadratic surfaces can be determined by using a matrix
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Siegel, Lauren. "Crafting Conic Sections." Math Horizons 29, no. 2 (November 8, 2021): 29. http://dx.doi.org/10.1080/10724117.2021.1978760.

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Dray, Tevian, and Corinne A. Manogue. "Electromagnetic conic sections." American Journal of Physics 70, no. 11 (November 2002): 1129–35. http://dx.doi.org/10.1119/1.1501115.

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Layton, William. "Regarding conic sections." Physics Teacher 52, no. 2 (February 2014): 68–69. http://dx.doi.org/10.1119/1.4862099.

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Korotkiy, Viktor. "Contact Conic Sections." Геометрия и графика 4, no. 3 (September 19, 2016): 36–45. http://dx.doi.org/10.12737/21532.

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Dissertations / Theses on the topic "Conic sections"

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Zharkov, Sergei. "Conic structures in differential geometry." Thesis, Connect to e-thesis, 2000. http://theses.gla.ac.uk/1005/.

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Thesis (Ph.D.) -- University of Glasgow, 2000.
Includes bibliographical references (p.86-88). Print version also available. Mode of access : World Wide Web. System requirements : Adobe Acrobat reader required to view PDF document.
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Naeve, Trent Phillip. "Conics in the hyperbolic plane." CSUSB ScholarWorks, 2007. https://scholarworks.lib.csusb.edu/etd-project/3075.

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An affine transformation such as T(P)=Q is a locus of an affine conic. Any affine conic can be produced from this incidence construction. The affine type of conic (ellipse, parabola, hyperbola) is determined by the invariants of T, the determinant and trace of its linear part. The purpose of this thesis is to obtain a corresponding classification in the hyperbolic plane of conics defined by this construction.
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Golipour-Koujali, M. "General rendering and antialiasing algorithms for conic sections : a GCE analysis." Thesis, London South Bank University, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.434558.

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McKinney, Colin Bryan Powell. "Conjugate diameters: Apollonius of Perga and Eutocius of Ascalon." Diss., University of Iowa, 2010. https://ir.uiowa.edu/etd/711.

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The Conics of Apollonius remains a central work of Greek mathematics to this day. Despite this, much recent scholarship has neglected the Conics in favor of works of Archimedes. While these are no less important in their own right, a full understanding of the Greek mathematical corpus cannot be bereft of systematic studies of the Conics. However, recent scholarship on Archimedes has revealed that the role of secondary commentaries is also important. In this thesis, I provide a translation of Eutocius' commentary on the Conics, demonstrating the interplay between the two works and their authors as what I call conjugate. I also give a treatment on the duplication problem and on compound ratios, topics which are tightly linked to the Conics and the rest of the Greek mathematical corpus. My discussion of the duplication problem also includes two computer programs useful for visualizing Archytas' and Eratosthenes' solutions.
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Khalfallah, Hazem. "Mordell-Weil theorem and the rank of elliptical curves." CSUSB ScholarWorks, 2007. https://scholarworks.lib.csusb.edu/etd-project/3119.

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The purpose of this thesis is to give a detailed group theoretic proof of the rank formula in a more general setting. By using the proof of Mordell-Weil theorem, a formula for the rank of the elliptical curves in certain cases over algebraic number fields can be obtained and computable.
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PENCHEL, RAFAEL ABRANTES. "Synthesis of Offset Reflector Antennas Using Conic Sections and Confocal Quadric Surfaces." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2014. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=24631@1.

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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO
COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR
CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO
O presente trabalho propõe técnicas numéricas para a síntese de antenas refletoras que utilizando seções de cônicas ou superfícies quádricas confocais. Para tal, utilizando os princípios da Óptica Geométrica, foram desenvolvidos algoritmos capazes de sintetizar as superfícies refletoras desejadas. São analisadas duas geometrias distintas: a antena duplo-refletora com cobertura omnidirecional e a antena refletora offset com um único refletor. No primeiro problema, é apresentado um método alternativo para a síntese geométrica de antenas duplo-refletoras com cobertura omnidirecional e diagrama de radiação arbitrário no plano de elevação. O subrefletor é um corpo de revolução gerado por uma única seção cônica e o refletor principal modelado é gerado por uma série de seções cônicas locais sequencialmente concatenadas. Para ilustrar o método, duas configurações axialmente simétrica são sintetizadas para proporcionar diagramas de radiação uniforme ou cossecante ao quadrado no plano de elevação. Os resultados são validados por uma técnica híbrida baseada em Casamento de Modos e o Método de Momentos. No segundo problema, é investigado um procedimento numérico alternativo para a síntese geométrica de antenas refletoras offset com diagrama de radiação arbitrário na região de campo distante. O método usa superfícies quádricas confocais com eixos deslocados para representar localmente a superfície modelada. Nesta abordagem, um operador não linear deve ser resolvido como um problema de contorno. Para ilustrar o método, são apresentadas antenas modeladas para prover diagrama de radiação Gaussiano em contornos de cobertura circular, elíptico e super-elíptico.
This work proposes numerical techniques for synthesis of reflector antennas, using conic sections or confocal quadric surfaces. Under Geometrical Optics principles, algorithms to shape desired reflective surfaces have been developed. Two different geometries have been considered: omnidirectional dual-reflector antenna and single offset reflector antennas. In the first problem, it was presented an alternative method for synthesis of omnidirectional dual-reflector antennas with an arbitrary radiation pattern in elevation plane. The body-of-revolution subreflector is generated by a single conic section, while the shaped main reflector is generated by a series of local conic sections, sequentially consecutively concatenated. In order to illustrate the method, omnidirectional axisdisplaced ellipse (OADE) and Cassegrain (OADC) configurations are synthesized to provide uniform or cosecant squared radiation pattern in the elevation plane. The GO shaping results are validated by a hybrid technique based on Mode Matching and Method of Moments. In the second problem, an alternative numerical procedure was investigated for the geometrical synthesis of offset reflector antennas with an arbitrary radiation pattern in the far-field region, according to geometrical optics. The method uses local axis-displaced confocal quadric surfaces to describe the shaped reflector. In this approach, a nonlinear operator must be solved as a boundary value problem. To illustrate the method, we have chosen several offset configurations with circular, elliptical and super-elliptical contour coverage and Gaussian power density. The results were validated by the physical optics approximation.
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Lui, Ka-wai, and 呂嘉蕙. "Study of conic sections and prime numbers in China: cultural influence on the development, application andtransmission of mathematical ideas." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2003. http://hub.hku.hk/bib/B29499240.

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Seedahmed, Gamal H. "On the suitability of conic sections in a single-photo resection, camera calibration, and photogrammetric triangulation." Columbus, Ohio Ohio State University, 2004. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1073186865.

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Thesis (Ph. D.)--Ohio State University, 2004.
Title from first page of PDF file. Document formatted into pages; contains xix, 138 p.; also includes graphics (some col). Includes abstract and vita. Advisor: Anton F. Schenk, Dept. of Geodetic Science and Surveying. Includes bibliographical references (p. 130-138).
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Farinholt, Kevin. "Modal and Impedance Modeling of a Conical Bore for Control Applications." Thesis, Virginia Tech, 2001. http://hdl.handle.net/10919/35560.

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The research presented in this thesis focuses on the use of feedback control for lowering acoustic levels within launch vehicle payload fairings. Due to the predominance of conical geometries within payload fairings, our work focused on the analytical modeling of conical shrouds using modal and impedance based models. Incorporating an actuating boundary condition within a sealed enclosure, resonant frequencies and mode shapes were developed as functions of geometric and mechanical parameters of the enclosure and the actuator. Using a set of modal approximations, a set of matrix equations have been developed describing the homogeneous form of the wave equation. Extending to impedance techniques, the resonant frequencies of the structure were again calculated, providing analytical validation of each model. Expanding this impedance model to first order form, the acoustic model has been coupled with actuator dynamics yielding a complete model of the system relating pressure to control voltage. Using this coupled state-space model, control design using Linear Quadratic Regulator and Positive Position Feedback techniques has also been presented. Using the properties of LQR analysis, an analytical study into the degree of coupling between actuator and cavity as a function of actuator resonance has been conducted. Constructing an experimetnal test-bed for model validation and control implementation, a small sealed enclosure was built and outfitted with sensors. Placing a control speaker at the small end of the cone the large opening was sealed with a rigid termination. An internal acoustic source was used to excite the system and pressure measurements were captured using an array of microphones located throughout the conic section. Using the parameters of this experimental test-bed, comparisons were made between LQR and PPF control designs. Using an impulse disturbance to excite the system, LQR simulations predicted reductions of 53.2% below those of the PPF design, while the control voltages corresponding to these reductions were 43.8% higher for LQR control. Actual application of these control designs showed that the ability to manually set PPF gains made this design technique much more convenient for actual implementation. Yielding overall attenuation of 38% with control voltages below 200 mV, single-channel low authority control was seen to be an effective solution for low frequency noise reduction. Control was then expanded to a larger geometry representative of Minotaur fairings. Designing strictly from experimental results, overall reductions of 38.5% were observed. Requiring slightly larger control voltages than those of the conical cavity, peak voltages were still found to be less than 306 mV. Extrapolating to higher excitation levels of 140 dB, overall power requirements for 38.5% pressure reductions were estimated to be less than 16 W.
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Ma, Min-Yuan Esclangon Felix Kravtchenko Julien. "Sur le calcul des pièces coniques de révolution travaillant à la flexion." S.l. : Université Grenoble 1, 2008. http://tel.archives-ouvertes.fr/tel-00277384.

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Books on the topic "Conic sections"

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Oldknow, A. J. Conic sections. Bognor Regis: Mathematics Education Centre, West Sussex Institute of Higher Education, 1985.

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Downs, J. W. Practical conic sections. Palo Alto, CA: D. Seymour Publications, 1993.

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Baltus, Christopher. Collineations and Conic Sections. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-46287-1.

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Salmon, George. A treatise on conic sections. 6th ed. Providence, RI: AMS Chelsea Pub., 2005.

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Reyes, Manuel Sobrino. Las cónicas como equidistancias: Una nueva caracterización. Valladolid, Spain: Instituto de Ciencias de la Educación, Universidad de Valladolid, 1991.

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Vladimirovich, Habelashvili Albert. Problem by Apollonius from Perga. Pererva: A.V. Habelashvili, 1994.

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Kendig, Keith. Conics. [Washington, D.C.]: Mathematical Association of America, 2005.

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H, Besant W. Conic Sections. Independently Published, 2019.

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Besant, W. H. Conic Sections. Independently Published, 2019.

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Downs, J. W. Practical Conic Sections. Dale Seymour Publications, 1998.

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Book chapters on the topic "Conic sections"

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Ostermann, Alexander, and Gerhard Wanner. "Conic Sections." In Geometry by Its History, 61–78. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-29163-0_3.

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Stillwell, John. "Conic Sections." In Numbers and Geometry, 247–79. New York, NY: Springer New York, 1998. http://dx.doi.org/10.1007/978-1-4612-0687-3_8.

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Landi, Giovanni, and Alessandro Zampini. "Conic Sections." In Undergraduate Lecture Notes in Physics, 293–327. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-78361-1_16.

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Liu, Andy. "Conic Sections." In Springer Texts in Education, 55–78. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-71743-2_3.

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Goddijn, Aad, Martin Kindt, and Wolfgang Reuter. "Conic sections." In Geometry with Applications and Proofs, 331–41. Rotterdam: SensePublishers, 2014. http://dx.doi.org/10.1007/978-94-6209-860-2_22.

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Pamfilos, Paris. "Conic sections." In Lectures on Euclidean Geometry - Volume 2, 317–98. Cham: Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-48910-5_6.

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Herrmann, Dietmar. "Conic Sections." In Ancient Mathematics, 231–49. Berlin, Heidelberg: Springer Berlin Heidelberg, 2022. http://dx.doi.org/10.1007/978-3-662-66494-0_14.

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Prewett, Philip. "The Conic Sections." In Foundation Mathematics for Science and Engineering Students, 79–89. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-91963-4_8.

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Gorini, Catherine A. "The Conic Sections." In Geometry for the Artist, 99–108. New York: Chapman and Hall/CRC, 2023. http://dx.doi.org/10.1201/9781003110972-10.

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Baltus, Christopher. "Conic Sections in Early Modern Europe. Second Part: Philippe de la Hire on Conics." In Collineations and Conic Sections, 71–86. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-46287-1_6.

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Conference papers on the topic "Conic sections"

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Foreman, J. W. "Conic sections revisited." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1989. http://dx.doi.org/10.1364/oam.1989.mt4.

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In most treatments of the reflecting properties of the conic sections, the properties are stated without proof. In this paper the conic sections are derived from first principles as surfaces which produce specific effects on light rays. For example, the ellipse is taken to be a surface which reflects all rays emanating from one fixed point in a plane through a second fixed point in the plane. Each of the conic sections defined in this way is described by a first-order differential equation of second degree. The differential equations are solved and are shown to produce the expected results. These derivations should prove useful in introductory optics courses to give students a better feel for the reflecting properties of the conic sections.
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Cardona-Nunez, O., A. Cornejo-Rodriguez, R. Diaz-Uribe, J. Pedraza-Contreras, and A. Cordero-Davila. "Conic that best fits an off-axis conic section." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1986. http://dx.doi.org/10.1364/oam.1986.wm2.

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To help in the fabrication of off-axis conic sections, we present a method of approximating this off-axis section by an on-axis conic centered on the portion desired. This method is based on the continuum least-squares method to obtain the vertex’s curvature and conic constant of the fitted conic on-axis, given the curvature at the vertex and the conic constant of the parent conic from where we want the section and the size of that section. Simple analytic expressions for the curvature and conic constant are derived in terms of the parameters of the off-axis section.
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Solares, Cristina, and Rocío Blanco. "VIDEOS AND MATLAB FOR TEACHING CONIC SECTIONS." In 14th International Conference on Education and New Learning Technologies. IATED, 2022. http://dx.doi.org/10.21125/edulearn.2022.1241.

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Карабчевский, Виталий, and Vitaliy Karabchevskiy. "The research of conic sections in AutoCAD environment." In 29th International Conference on Computer Graphics, Image Processing and Computer Vision, Visualization Systems and the Virtual Environment GraphiCon'2019. Bryansk State Technical University, 2019. http://dx.doi.org/10.30987/graphicon-2019-1-188-190.

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The application of solid modelling tools is considered when creating three-dimensional models of a straight circular cone and when studying its sections in AutoCAD. The results are presented that AutoCAD allows obtaining for a section by planes almost parallel to one or two generators. The boundary values of the angles between the plane and the generators, which determine the presence or absence of parallelism, are found. Methods are proposed for obtaining the parameters of the canonical equations of curves representing conical sections for cases when the corresponding curve (hyperbola or parabola) is modelled in AutoCAD using splines. The application of the proposed methods in the educational process is described, which makes it possible to strengthen the relationship of what is stated in the study of sections of descriptive geometry of the material with the development of methods for generating three-dimensional models, solid-state modelling tools and analytical geometry.
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Ulmer, Melville P., Robert I. Altkron, Michael E. Graham, Anita Madan, and Yong S. Chu. "Production and performance of multilayer coated conic sections." In International Symposium on Optical Science and Technology, edited by Paul Gorenstein and Richard B. Hoover. SPIE, 2002. http://dx.doi.org/10.1117/12.454365.

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Caligaris, Marta, María Schivo, María Romiti, and Matías Menchise. "CUSTOM TOOLS FOR ANALYTIC GEOMETRY: THE CONIC SECTIONS." In International Technology, Education and Development Conference. IATED, 2017. http://dx.doi.org/10.21125/inted.2017.0082.

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Azizian, K., P. Cardou, and B. Moore. "On the Boundaries of the Wrench-Closure Workspace of Planar Parallel Cable-Driven Mechanisms." In ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/detc2010-28135.

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The wrench-closure workspace of parallel cable-driven mechanisms is the set of poses for which any wrench can be produced at the end-effector by a set of a non-negative cable tensions. It is already known that the boundary of the constant-orientation wrench-closure workspace of a planar parallel cable-driven mechanism is composed of segments of conic sections. However, the relationship between the geometry of the mechanism and the types of these conic sections is unknown. This paper proposes a graphical method for determining the types of these conic sections. It is also shown that the proposed method can be applied to find the constant-orientation singularities of a 3-RPR planar parallel robot, since these contours correspond to the boundary segment of the analogous three-cable driven planar parallel mechanism.
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El Hamdi, Dhekra, Mai K. Nguyen, Hedi Tabia, and Atef Hamouda. "Image Analysis based on Radon-type Integral Transforms Over Conic Sections." In International Conference on Computer Vision Theory and Applications. SCITEPRESS - Science and Technology Publications, 2018. http://dx.doi.org/10.5220/0006613403560362.

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Moreira, Fernando J. S., and Jose R. Bergmann. "Shaping Axis-Symmetric Dual-Reflector Antennas by consecutively concatenating conic sections." In 2009 SBMO/IEEE MTT-S International Microwave and Optoelectronics Conference (IMOC). IEEE, 2009. http://dx.doi.org/10.1109/imoc.2009.5427566.

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Zioga, M., M. Mikeli, A. Eleftheriou, Ch Pafilis, A. N. Rapsomanikis, and E. Stiliaris. "ComptonRec: Mastering conic sections for a direct 3D compton image reconstruction." In 2015 IEEE Nuclear Science Symposium and Medical Imaging Conference (NSS/MIC). IEEE, 2015. http://dx.doi.org/10.1109/nssmic.2015.7582117.

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Reports on the topic "Conic sections"

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Tooman, Tricia, Waraf Al-Yaseen, Damon Herd, Clio Ding, Maria Corrales, and Jaina Teo Lewen. THE COVID ROLLERCOASTER: Multiple and Multi-dimensional Transitions of Healthcare Graduates. Edited by Divya Jindal-Snape, Chris Murray, and Nicola Innes. UniVerse, May 2022. http://dx.doi.org/10.20933/100001247.

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In this study, we explored the ongoing multiple and multi-dimensional transitions experienced by medicine, nursing and dentistry students due to graduate in summer 2020. Some graduated early to join the NHS workforce and others had their graduation deferred for a year due to lack of clinical experience. We explored the expectations and realities of their transition experiences; their perceptions of the impact of their transitions on them, their wellbeing, and on their significant others. This longitudinal study helped understand each individual’s adaptations to multiple concurrent changes over time. The cross-sectional data revealed trends and patterns for each group of graduates. This comic anthology presents the interpretations of interview data from doctor, nurse, and dentist graduates. The five comics present both individual and composite narratives of different participants. The visualisation of the data through comics was valuable to portray the wider context of COVID-19, and participants’ related transition experiences and emotions.
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