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Relevant bibliographies by topics / Conic section

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Academic literature on the topic 'Conic section'

Author: Grafiati

Published: 4 June 2021

Last updated: 18 February 2022

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Journal articles on the topic "Conic section"

1

Lipp, Alan. "Cubic Polynomials." Mathematics Teacher 93, no. 9 (December 2000): 788–92. http://dx.doi.org/10.5951/mt.93.9.0788.

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Rizal, Yusmet. "DIAGONALISASI BENTUK KUADRATIK IRISAN KERUCUT." EKSAKTA: Berkala Ilmiah Bidang MIPA 19, no. 1 (April 25, 2018): 83–90. http://dx.doi.org/10.24036/eksakta/vol19-iss1/132.

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In general, the conic section equation consists of three parts, namely quadratic, cross-product, and linear terms. A conic sections will be easily determined by its shape if it does not contain cross-product term, otherwise it is difficult to determine. Analytically a cone slice is a quadratic form of equation. A concept in linear algebraic discussion can be applied to facilitate the discovery of a shape of a conic section. The process of diagonalization can transform a quadratic form into another form which does not contain crosslinking tribes, ie by diagonalizing the quadrate portion. Hence this paper presents the application of an algebraic concept to find a form of conic sections.

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Cardona-Nunez, Octavio, Alejandro Cornejo-Rodriguez, Rufino Diaz-Uribe, Alberto Cordero-Davila, and Jesus Pedraza-Contreras. "Conic that best fits an off-axis conic section." Applied Optics 25, no. 19 (October 1, 1986): 3585. http://dx.doi.org/10.1364/ao.25.003585.

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Marinov, Marin, and Petya Asenova. "Teaching the Notion Conic Section with Computer." Mathematics and Informatics LXIV, no. 4 (August 30, 2021): 395–409. http://dx.doi.org/10.53656/math2021-4-5-pred.

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The article discusses the problem of introducing and constructing mathematical concepts using a computer. The Wolfram Mathematica 12 symbolic calculation system is used at each stage of the complex spiral process to form the notion of conic section and the related concepts of focus, directrix and eccentricity. The nature of these notions implies the use of appropriate animations, 3D graphics and symbolic calculations. Our vision of the process of formation of mathematical concepts is presented. The notions ellipse, parabola and hyperbola are defined as the intersection of a conical surface with a plane not containing the vertex of the conical surface. The conical section is represented as a geometric location of points on the plane for which the ratio of the distance to the focus to the distance to the directrix is a constant value. The lines of hyperbola and ellipse are determined by their foci. The equivalence of different definitions for conical sections is commented.

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Ayoub, Ayoub B. "The Eccentricity of a Conic Section." College Mathematics Journal 34, no. 2 (March 2003): 116. http://dx.doi.org/10.2307/3595784.

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Shklyar, Sergiy, Alexander Kukush, Ivan Markovsky, and Sabine Van Huffel. "On the conic section fitting problem." Journal of Multivariate Analysis 98, no. 3 (March 2007): 588–624. http://dx.doi.org/10.1016/j.jmva.2005.12.003.

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Ayoub, Ayoub B. "The Eccentricity of a Conic Section." College Mathematics Journal 34, no. 2 (March 2003): 116–21. http://dx.doi.org/10.1080/07468342.2003.11921994.

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Wilkins, Daniel. "The Tangent Lines of a Conic Section." College Mathematics Journal 34, no. 4 (September 2003): 296. http://dx.doi.org/10.2307/3595767.

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Hosseinyalmdary, S., and A. Yilmaz. "TRAFFIC LIGHT DETECTION USING CONIC SECTION GEOMETRY." ISPRS Annals of Photogrammetry, Remote Sensing and Spatial Information Sciences III-1 (June 2, 2016): 191–200. http://dx.doi.org/10.5194/isprsannals-iii-1-191-2016.

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Traffic lights detection and their state recognition is a crucial task that autonomous vehicles must reliably fulfill. Despite scientific endeavors, it still is an open problem due to the variations of traffic lights and their perception in image form. Unlike previous studies, this paper investigates the use of inaccurate and publicly available GIS databases such as OpenStreetMap. In addition, we are the first to exploit conic section geometry to improve the shape cue of the traffic lights in images. Conic section also enables us to estimate the pose of the traffic lights with respect to the camera. Our approach can detect multiple traffic lights in the scene, it also is able to detect the traffic lights in the absence of prior knowledge, and detect the traffics lights as far as 70 meters. The proposed approach has been evaluated for different scenarios and the results show that the use of stereo cameras significantly improves the accuracy of the traffic lights detection and pose estimation.

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Hosseinyalmdary, S., and A. Yilmaz. "TRAFFIC LIGHT DETECTION USING CONIC SECTION GEOMETRY." ISPRS Annals of Photogrammetry, Remote Sensing and Spatial Information Sciences III-1 (June 2, 2016): 191–200. http://dx.doi.org/10.5194/isprs-annals-iii-1-191-2016.

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Traffic lights detection and their state recognition is a crucial task that autonomous vehicles must reliably fulfill. Despite scientific endeavors, it still is an open problem due to the variations of traffic lights and their perception in image form. Unlike previous studies, this paper investigates the use of inaccurate and publicly available GIS databases such as OpenStreetMap. In addition, we are the first to exploit conic section geometry to improve the shape cue of the traffic lights in images. Conic section also enables us to estimate the pose of the traffic lights with respect to the camera. Our approach can detect multiple traffic lights in the scene, it also is able to detect the traffic lights in the absence of prior knowledge, and detect the traffics lights as far as 70 meters. The proposed approach has been evaluated for different scenarios and the results show that the use of stereo cameras significantly improves the accuracy of the traffic lights detection and pose estimation.

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Dissertations / Theses on the topic "Conic section"

1

Kodipaka, Santhosh. "A novel conic section classifier with tractable geometric learning algorithms." [Gainesville, Fla.] : University of Florida, 2009. http://purl.fcla.edu/fcla/etd/UFE0024624.

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Aung, Min Soe Hane. "Multi layer perception and conic section function neural networks applied to breast cancer risk factors including asymmetry." Thesis, University of Liverpool, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.400194.

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Nogueira, Leonardo Bernardes. "Transformações lineares no plano e aplicações." Universidade Federal de Goiás, 2013. http://repositorio.bc.ufg.br/tede/handle/tede/3123.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
This paper begins with a brief history about the development of vector spaces and linear transformations, then presents fundamental concepts for the study of Linear Algebra, with greater focus on linear operators in the R2 space. Through examples it explores a wide range of operators in R2 in order to show other applications of matrices in high school and prepares the ground for the presentation a version of Spectral Theorem for selfadjoint operators in R2, which says that for every operator self-adjoint T : E!E in finite dimensional vector space with inner product, exists an orthonormal basis fu1; : : : ;ung E formed by eigenvectors of T, and culminates with their applications on the study of conic sections, quadratic forms and equations of second degree in x and y; on the study of operators associated to quadratic forms, a version of Spectral Theorem could be called as The Main Axis Theorem albeit this nomenclature is not used in this paper. Thereby summarizing a study made by Lagrange in "Recherche d’arithmétique ", between 1773 and 1775, which he studied the property of numbers that are the sum of two squares. Thus he was led to study the effects of linear transformation with integer coefficients in a quadratic form in two variables.
Este trabalho inicia-se com um breve embasamento histórico sobre o desenvolvimento de espaços vetoriais e transformações lineares. Em seguida, apresenta conceitos fundamentais básicos, que formam uma linguagem mínima necessária para falar sobre Álgebra Linear, com enfoque maior nos operadores lineares do plano R2. Através de exemplos, explora-se um vasto conjunto de transformações no plano a fim de mostrar outras aplicações de matrizes no ensino médio e prepara o terreno para a apresentação do Teorema Espectral para operadores auto-adjuntos de R2. Este Teorema diz que para todo operador auto-adjunto T : E!E, num espaço vetorial de dimensão finita, munido de produto interno, existe uma base ortonormal fu1; : : : ;ung E formada por autovetores de T. O trabalho culmina com aplicações sobre o estudo das secções cônicas, formas quadráticas e equações do segundo grau em x e y, no qual o Teorema Espectral se traduz como Teorema dos Eixos Principais, embora essa nomenclatura não seja usada nesse trabalho (para um estudo mais aprofundado neste tema ver [3], [4], [5], [7]). Retomando assim um estudo feito por Joseph Louis Lagrange em "Recherche d’Arithmétique", entre 1773 e 1775, no qual estudou a propriedade de números que são a soma de dois quadrados. Assim, foi levado a estudar os efeitos das transformações lineares com coeficientes inteiros numa forma quadrática de duas variáveis.

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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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Hosseinyalamdary, Saivash Hosseinyalamdary. "Traffic Scene Perception using Multiple Sensors for Vehicular Safety Purposes." The Ohio State University, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=osu1462803166.

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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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Loučka, Pavel. "Měření ovality extrudovaného vlákna pomocí tří kamer." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2019. http://www.nusl.cz/ntk/nusl-401570.

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One of the important parameters observed during extruded fibre fabrication is its diameter. The diameter can be measured with a single scanning camera assuming that the fibre section has a circular shape. As proved in practice, another important parameter is ovality, that is the rate of fibre flattening. This paper assumes that the fibre section shape is elliptical. In such a case, at least three different views on examined fibre are needed. Mathematical part of this paper is concerned with analytical description of fibre ovality measurement using two different approaches based on the knowledge of linear algebra, projective geometry and conic sections theory. Main goal of this paper is thus to use both mathematical theory and image analysis methods for ovality and diameter determination. Precise calcluation of such quantities is, however, conditioned on precise camera system calibration, which is described in the paper as well. Additionally, the work contains a brief mention of technical realization of ovality measurement and its possible difficulties.

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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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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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Books on the topic "Conic section"

1

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

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2

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

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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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8

Dana, Densmore, ed. Conics. Santa Fe, N.M: Green Lion Press, 1998.

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Wilhelm, Leibniz Gottfried. Quadrature arithmétique du cercle, de l'ellipse et de l'hyperbole et la trigonométrie sans tables trigonométriques qui en est le corollaire. Paris: Vrin, 2004.

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10

Apollonius. Apollonius de Perge, Coniques. Berlin: Walter de Gruyter, 2010.

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Book chapters on the topic "Conic section"

1

Yaqi, Xu, Zhang Chengfang, and Mi Xinwu. "Geometric Analysis and Engineering Application of Conic Section." In Advances in Intelligent Systems and Computing, 2274–81. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-95588-9_219.

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Şenol, Canan, and Tülay Yıldırım. "Signature Verification Using Conic Section Function Neural Network." In Computer and Information Sciences - ISCIS 2005, 524–32. Berlin, Heidelberg: Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/11569596_55.

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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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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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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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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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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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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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Banchoff, Thomas, and John Wermer. "Classification of Conic Sections." In Undergraduate Texts in Mathematics, 85–97. New York, NY: Springer US, 1992. http://dx.doi.org/10.1007/978-1-4612-4390-8_9.

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Arnold, Vladimir I. "Geometry of Conic Sections." In UNITEXT, 3–18. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-36243-9_2.

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Conference papers on the topic "Conic section"

1

Shashua, A., S. Avidan, and M. Werman. "Trajectory triangulation over conic section." In Proceedings of the Seventh IEEE International Conference on Computer Vision. IEEE, 1999. http://dx.doi.org/10.1109/iccv.1999.791238.

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Wang Shuxia, Wang Guanfeng, and Cao Mantun. "On-line freehand sketching recognition using conic section." In 2009 4th IEEE Conference on Industrial Electronics and Applications (ICIEA). IEEE, 2009. http://dx.doi.org/10.1109/iciea.2009.5138917.

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Kodipaka, Santhosh, Arunava Banerjee, and Baba C. Vemuri. "Large margin pursuit for a Conic Section classifier." In 2008 IEEE Conference on Computer Vision and Pattern Recognition (CVPR). IEEE, 2008. http://dx.doi.org/10.1109/cvpr.2008.4587406.

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Ozyilmaz, L., and T. Yildirim. "Sensitivity analysis for conic section function neural networks." In Proceedings of the IEEE-INNS-ENNS International Joint Conference on Neural Networks. IJCNN 2000. Neural Computing: New Challenges and Perspectives for the New Millennium. IEEE, 2000. http://dx.doi.org/10.1109/ijcnn.2000.860780.

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Banissi, E., and M. K. Golipour. "A New General Incremental Algorithm for Conic Section." In 2014 11th International Conference on Computer Graphics, Imaging and Visualization (CGIV). IEEE, 2014. http://dx.doi.org/10.1109/cgiv.2014.24.

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Cardona-Nuilez, O., A. Cornejo-Rodriguez, R. Diaz-Uribe, A. Cordero-Davila, and J. Pedraza-Contreras. "A Comparison Between Toroidal And Conic Surfaces That Best Fit An Off-Axis Conic Section." In 14th Congress of the International Commission for Optics, edited by Henri H. Arsenault. SPIE, 1987. http://dx.doi.org/10.1117/12.967183.

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Lin, Liming, Xingfu Zhong, and Yingxiang Wu. "The Drag, Lift and Strouhal Number of a Circular-Section Cylinder With a Conic Disturbance at Subcritical Reynolds Numbers." In ASME 2014 33rd International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/omae2014-23017.

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Through numerical simulations, the flow past a circular-section cylinder with a conic disturbance is investigated at sub-critical Reynolds numbers of 102, 103 and 104. At higher Reynolds numbers, LES is employed in simulating the turbulence transition in the near wake. Computations with a series of parameters, the wavelength and wave steepness, are carried out. Generally, the drag of conic cylinder is gradually increased with the increasing wave steepness and in most cases greater than that of the cylinder without disturbance. However, the total lift in most cases is obviously reduced. The phenomenon of local minimum is found out in variation of drag and lift. The introduction of conic disturbance also leads to the decrease of frequency of vortex shedding as the wave steepness increases.

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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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Murray, N., G. Lyons, C. E. Tinney, B. Donald, W. Baars, B. Thurow, H. Haynes, and P. Panickar. "A Laboratory Framework for Synchronous Near/Far-Field Acoustics and MHz PIV in High-Temperature, Shock-Containing, Jets." In ASME 2012 Noise Control and Acoustics Division Conference at InterNoise 2012. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/ncad2012-1270.

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This paper describes the experimental study of the noise generating characteristics of high-temperature, shock-containing jets emanating from conic-section, converging-diverging (C-D) nozzles. Conic C-D nozzles consist of two conic sections, one contracting and the other expanding, joined to form a supersonic nozzle with a very sharp radius of curvature at the nozzle throat. An experiment is conducted in which temporally resolved flow-field measurements are acquired simultaneously with near-field and far-field acoustics to allow investigation of the turbulence associated with noise generation. The MHz rate PIV system and its synchronization with acoustic measurements is described along with methods for data analysis. General acoustic results are presented to characterize the spectral content present, and preliminary results on the measured turbulence structures are discussed.

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Vural, Revna Acar, Nihan Kahraman, Burcu Erkmen, and Tulay Yildirim. "Object recognition on general purposed Conic Section Function Neural Network integrated circuit." In 2008 IEEE 16th Signal Processing, Communication and Applications Conference (SIU). IEEE, 2008. http://dx.doi.org/10.1109/siu.2008.4632598.

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