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Journal articles on the topic 'Conic section'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

.., 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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2

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 sectio

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3

Said, Arwan Mhd. "Menentukan Bentuk Kuadrat Bagian Kerucut Dan Permukaan Kuadratik dengan Menggunakan Matriks." Foramadiahi: Jurnal Kajian Pendidikan dan Keislaman 8, no. 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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4

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

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5

Rizal, Yusmet. "DIAGONALISASI BENTUK KUADRATIK IRISAN KERUCUT." EKSAKTA: Berkala Ilmiah Bidang MIPA 19, no. 1 (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

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6

Ou, Kaiming. "Research and analysis of problem-solving strategies of conic section in high school mathematics." Theoretical and Natural Science 25, no. 1 (2023): 57–65. http://dx.doi.org/10.54254/2753-8818/25/20240901.

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The conic section is a crucial part of high school mathematics and usually plays the role of tough problem in examinations. Hence, this dissertation will use the literature analysis method to introduce the mathematical background of the conic section to enable students to know about the conic section more clearly and explain the basic concept of the conic section such as the first and second definitions of conic section, then introduce some second level conclusions such as focus length formula and average property of parabola. After that, this dissertation will provide some conic section probl

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7

Suresh, Kumar Sahani, and Sindhu Prasad Kripa. "Relative Strength of Conic Section." MATHEMATICS EDUCATION LVII, no. 1, March 2023 (2023): 1–22. https://doi.org/10.5281/zenodo.7880464.

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          <em>Conic sections one a group of curves which one generated by slicing a cone with a plane. If the plane is titled parallel to the slope of the cone, the cut produces a parabola. When a parabola is expressed in Cartesian co-ordinates, the second order polynomial. This curve is commonly found in nature, engineering applications and architecture. The study of projectile motion is a real lite application of the parabolic conic section. The projectile moves under the influence of gravity, which for simplicity is assumed to be constant. Thus, it is possible

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8

Poudel, Gajendra. "Use of ICT in Teaching Conic Section." Journal of Aadikavi 12, no. 1 (2023): 16–26. http://dx.doi.org/10.3126/joaa.v12i1.65810.

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This study entitled “Use of ICT in conic section: An experimental study” is an experimental research. ICT can be applied in conic sections which include parabola, ellipse, hyperbola, circle etc. For graphics and visualisation, geometric modelling, optics and imaging, satellite orbits, signal processing, engineering design, architectural design; ICT is used. The objectives of the study was “to compare the achievement of students taught by using ICT software and conventional teaching method while teaching conic section of grade XII.” The research was based on Vigotski’s constructivist view of le

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9

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 (1986): 3585. http://dx.doi.org/10.1364/ao.25.003585.

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10

Franco Filho, Antonio de Padua, and Anuar Paternina Montalvo. "Sections of the light cone in Minkowski 4-space." Revista Colombiana de Matemáticas 57, no. 1 (2024): 1–18. http://dx.doi.org/10.15446/recolma.v57n1.112371.

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The intersection of an affine hyperplane in L4 with the light cone C is called a conic section. In this paper, it is proved that the conic sections in L4 are either Riemannian spheres, hyperbolic spaces or horospheres, depending on the causal character of the hyperplane. Analogous results for affine sections of de Sitter and hyperbolic spaces in L4 are also presented at the end.

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11

Cholily, Yus Mochamad, Anis Farida Jamil, and Mayang Dintarini. "Metacognitive Regulation Strategies Among Indonesian Undergraduate Students During Conic Sections Conceptualization." AL-ISHLAH: Jurnal Pendidikan 16, no. 2 (2024): 948–59. http://dx.doi.org/10.35445/alishlah.v16i2.5252.

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Metacognitive regulation ability can assist students in abstracting the concept of a conic section. However, research exploring students’ metacognitive regulation in abstracting a mathematical concept is still rare. Thus, this study aims to analyze students' metacognitive regulation consisting of monitoring and controlling in abstracting the conic sections concept. Three students were selected as research subjects from 26 undergraduate of mathematics education Indonesian students who were engaged in abstraction assignments. Three students were selected based on their abstraction of the conic s

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12

Marinov, Marin, and Petya Asenova. "Teaching the Notion Conic Section with Computer." Mathematics and Informatics LXIV, no. 4 (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 wit

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13

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

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14

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

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15

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

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16

Хейфец and Aleksandr Kheyfets. "Conics As Sections of Quadrics by Plane (Generalized Dandelin Theorem)." Geometry & Graphics 5, no. 2 (2017): 45–58. http://dx.doi.org/10.12737/article_5953f32172a8d8.94863595.

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Has been presented a geometrical proof of a theorem stating that when a plane section crosses second-order revolution surfaces (rotation quadrics, RQ), such types of conics as ellipse, hyperbola or parabola are formed. The theorem amplifies historically famous Dandelin theorem, which provides geometric proof only for the circular cone, and extends the proof to all RQ: ellipsoid, hyperboloid, paraboloid and cylinder. That is why the theorem described below has been called as Generalized Dandelin theorem (GDT). The GDT proof has been constructed on a little-known generalized definition (GDD) of

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17

Das, Prem Kumar, Suresh Kumar Sahani, and Shyam Kishore Mahto. "Significance of Conic Section in Daily Life and Real Life Questions Related to it in Different Sectors." Jurnal Pendidikan Matematika 1, no. 4 (2024): 14. http://dx.doi.org/10.47134/ppm.v1i4.902.

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Students tend to think of mathematics as, “that difficult, boring subject” that only exists within the walls of a classroom. Many students do not realize that mathematics is all around us occurring in our daily lives. Mathematics can be found easily in everyday activities such as cooking, driving, and even walking. Here, we are going to overview the conic section: ellipse, circle, parabola, hyperbola from different angle of life. In this report we will be analyzing a very crucial applications of conic section in the medical field, engineering field, some real life based questions will be slove

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18

Yiting, Ning, Jianlan Tang, Rafiantika M. Prihandini, and Usman Aripin. "Modeling Conic Section Using Hawgent Dynamic Mathematics Software." ARITHMETIC: Academic Journal of Math 4, no. 1 (2022): 61. http://dx.doi.org/10.29240/ja.v4i1.4320.

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Teachers should pay attention to the deep integration of information technology and mathematics courses, so as to achieve the effect that traditional teaching methods are difficult to achieve. Conic section in high school is an important carrier for cultivating students' mathematical literacy, but it is highly abstract and comprehensive, making it a "difficult point" in high school mathematics teaching. Hawgent dynamic mathematics software has powerful dynamic and visual functions, which can effectively assist the teaching of ellipse in high school. The questions to be studied in this paper ar

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19

Thele, Kent. "Conic Connections with Polar Functions." Mathematics Teacher 110, no. 4 (2016): 320. http://dx.doi.org/10.5951/mathteacher.110.4.0320.

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20

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 c

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21

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 c

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22

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

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23

Wilkins, Daniel. "The Tangent Lines of a Conic Section." College Mathematics Journal 34, no. 4 (2003): 296–303. http://dx.doi.org/10.1080/07468342.2003.11922021.

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24

Dintarini, Mayang, Yusuf Fuad, and Mega Teguh Budiarto. "Examining undergraduate students' abstraction of conic sections in a dynamic geometry environment." Journal on Mathematics Education 15, no. 3 (2024): 717–34. http://dx.doi.org/10.22342/jme.v15i3.pp717-734.

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In solid geometry, the concept of conic sections plays an important role in teaching graphs such as parabolas, ellipses, and hyperbolas to undergraduate students in Mathematics Education. It is understood that the abstraction process in mastering conic sections is strongly needed. This study examines the abstraction process of conic sections among third-year undergraduate Mathematics Education students (4 males and 21 females) at Universitas Muhammadiyah Malang (UMM), Indonesia. The data was collected by analyzing students' responses in a 60-minute diagnostic test using the Abstraction in Cont

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25

Srestasathiern, P., and N. Soontranon. "A novel camera calibration method for fish-eye lenses using line features." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XL-3 (August 11, 2014): 327–32. http://dx.doi.org/10.5194/isprsarchives-xl-3-327-2014.

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In this paper, a novel method for the fish-eye lens calibration is presented. The method required only a 2D calibration plane containing straight lines i.e., checker board pattern without a priori knowing the poses of camera with respect to the calibration plane. The image of a line obtained from fish-eye lenses is a conic section. The proposed calibration method uses raw edges, which are pixels of the image line segments, in stead of using curves obtained from fitting conic to image edges. Using raw edges is more flexible and reliable than using conic section because the result from conic fit

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26

Cardona-Nuñez, Octavio, Alejandro Cornejo-Rodriguez, Rufino Diaz-Uribe, Alberto Cordero-Dávila, and Jesús Pedraza-Contreras. "Comparison between toroidal and conic surfaces that best fit an off-axis conic section." Applied Optics 26, no. 22 (1987): 4832. http://dx.doi.org/10.1364/ao.26.004832.

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27

HERR, DAVID LINCOLN. "CONIC-SECTION ORBITS DERIVED FROM THE GRAVITATIONAL POTENTIAL." Journal of the American Society for Naval Engineers 70, no. 4 (2009): 595–98. http://dx.doi.org/10.1111/j.1559-3584.1958.tb01775.x.

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28

Mahony, John D. "Locating parameters of interest in a conic section." Mathematical Gazette 103, no. 557 (2019): 196–203. http://dx.doi.org/10.1017/mag.2019.50.

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In an interesting Note [1] a method for constructing the directrices of a conic section using simple tools, viz. a pencil, a pair of compasses and a straight edge, was presented and it was wondered if the method might have been known before. From earlier days at school this author was aware that for a specific conic section (parabola, ellipse or hyperbola) displayed without reference on a piece of paper it was possible to determine not just the directrices but also the focal points and the usual axis set, again using just the simple tools. Others might also be aware of these facts, but if they

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29

Yildirim, Tulay, and Lale Ozyilmaz. "Dimensionality reduction in conic section function neural network." Sadhana 27, no. 6 (2002): 675–83. http://dx.doi.org/10.1007/bf02703358.

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30

Bétend-Bon, Jean-Pierre, Lech Wosinski, Magnus Breidne, and Lennart Robertsson. "Fiber optic interferometer for testing conic section surfaces." Applied Optics 30, no. 13 (1991): 1715. http://dx.doi.org/10.1364/ao.30.001715.

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31

Anwar, Y. R., H. Tasman, and N. Hariadi. "Determining implicit equation of conic section from quadratic rational Bézier curve using Gröbner basis." Journal of Physics: Conference Series 2106, no. 1 (2021): 012017. http://dx.doi.org/10.1088/1742-6596/2106/1/012017.

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Abstract The Gröbner Basis is a subset of finite generating polynomials in the ideal of the polynomial ring k[x 1,…,xn ]. The Gröbner basis has a wide range of applications in various areas of mathematics, including determining implicit polynomial equations. The quadratic rational Bézier curve is a rational parametric curve that is generated by three control points P 0(x 0,y 0), P 1(xi ,yi ), P 2(x 2,y 2) in ℝ2 and weights ω 0, ω 1, ω 2, where the weights ω i are corresponding to control points Pi (xi, yi ), for i = 0,1, 2. According to Cox et al (2007), the quadratic rational Bézier curve can

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32

Kung, Sidney H. "Finding the Tangent to a Conic Section without Calculus." College Mathematics Journal 34, no. 5 (2003): 394. http://dx.doi.org/10.2307/3595824.

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33

Mathews, John H. "The Five Point Conic Section: Exploration with Computer Software." School Science and Mathematics 95, no. 4 (1995): 206–8. http://dx.doi.org/10.1111/j.1949-8594.1995.tb15764.x.

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34

Jaiswal, Sushma, Sarita Singh Bhad, and Rakesh Singh Jado. "Creation 3D Animatable Face Methodology Using Conic Section-Algorithm." Information Technology Journal 7, no. 2 (2008): 292–98. http://dx.doi.org/10.3923/itj.2008.292.298.

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35

GATES, J. "A New Conic Section Extraction Approach and Its Applications." IEICE Transactions on Information and Systems E88-D, no. 2 (2005): 239–51. http://dx.doi.org/10.1093/ietisy/e88-d.2.239.

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36

O¨zylmaz, Lale, and Tu¨lay Yldrm. "Reduction of complexity in conic section function neural network." Kybernetes 32, no. 4 (2003): 540–47. http://dx.doi.org/10.1108/03684920310463920.

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37

Helsø, Martin. "Rational quartic symmetroids." Advances in Geometry 20, no. 1 (2020): 71–89. http://dx.doi.org/10.1515/advgeom-2018-0037.

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38

Shpitalni, M., and H. Lipson. "Classification of Sketch Strokes and Corner Detection Using Conic Sections and Adaptive Clustering." Journal of Mechanical Design 119, no. 1 (1997): 131–35. http://dx.doi.org/10.1115/1.2828775.

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This paper presents a method for classifying pen strokes in an on-line sketching system. The method, based on linear least squares fitting to a conic section equation, proposes using the conic equation’s natural classification property to help classify sketch strokes and identify lines, elliptic arcs, and corners composed of two lines with an optional fillet. The hyperbola form of the conic equation is used for corner detection. The proposed method has proven to be fast, suitable for real-time classification, and capable of tolerating noisy input, including cusps and spikes. The classification

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39

배동훈. "Study on Conic Section Implementation for Product Design Technical Drawing." Journal of Digital Design 11, no. 2 (2011): 83–91. http://dx.doi.org/10.17280/jdd.2011.11.2.009.

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40

Cardona-Nuñez, O., A. Cornejo-Rodriguez, A. Cordero-Davila, and J. Pedraza-Contreras. "Inclined toroidal surface that fits an off-axis conic section." Applied Optics 35, no. 19 (1996): 3559. http://dx.doi.org/10.1364/ao.35.003559.

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41

Zhu, Qiuming, and Lu Peng. "A new approach to conic section approximation of object boundaries." Image and Vision Computing 17, no. 9 (1999): 645–58. http://dx.doi.org/10.1016/s0262-8856(98)00148-6.

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42

王, 幼宁. "Metrical Geometry Classification of Conic Section in Hyperbolic Space Form." Pure Mathematics 02, no. 02 (2012): 97–102. http://dx.doi.org/10.12677/pm.2012.22016.

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43

Erkmen, B., N. Kahraman, R. A. Vural, and T. Yildirim. "Conic Section Function Neural Network Circuitry for Offline Signature Recognition." IEEE Transactions on Neural Networks 21, no. 4 (2010): 667–72. http://dx.doi.org/10.1109/tnn.2010.2040751.

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44

Khan, Asif, Mohammad Iliyas, Khalid Khan, and Mohammad Mursaleen. "Approximation of conic sections by weighted Lupaş post-quantum Bézier curves." Demonstratio Mathematica 55, no. 1 (2022): 328–42. http://dx.doi.org/10.1515/dema-2022-0016.

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Abstract This paper deals with weighted Lupaş post-quantum Bernstein blending functions and Bézier curves constructed with the help of bases via ( p , q ) \left(p,q) -integers. These blending functions form normalized totally positive bases. Due to the rational nature of weighted Lupaş post-quantum Bézier curves and positive weights, they help in investigating from geometric point of view. Their degree elevation properties and de Casteljau algorithm have been studied. It has been shown that quadratic weighted Lupaş post-quantum Bézier curves can represent conic sections in two-dimensional plan

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45

Ionescu, Paltin, and Francesco Russo. "Varieties with quadratic entry locus, II." Compositio Mathematica 144, no. 4 (2008): 949–62. http://dx.doi.org/10.1112/s0010437x08003539.

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AbstractWe continue the study, begun in [F. Russo, Varieties with quadratic entry locus. I, Preprint (2006), math. AG/0701889] , of secant defective manifolds having ‘simple entry loci’. We prove that such manifolds are rational and describe them in terms of tangential projections. Using also the work of [P. Ionescu and F. Russo, Conic-connected manifolds, Preprint (2006), math. AG/0701885], their classification is reduced to the case of Fano manifolds of high index, whose Picard group is generated by the hyperplane section class. Conjecturally, the former should be linear sections of rational

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46

Kuhnke, Stefan, Felix Gensch, René Nitschke, Vidal Sanabria, and Soeren Mueller. "Influence of Die Surface Topography and Lubrication on the Product Quality during Indirect Extrusion of Copper-Clad Aluminum Rods." Metals 10, no. 7 (2020): 888. http://dx.doi.org/10.3390/met10070888.

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Copper-clad aluminum rods are usually fabricated using hydrostatic extrusion, since during direct and indirect extrusion fracture of the copper sleeve is difficult to avoid. In this study, different die surface topographies and lubrication conditions were applied to improve the material flow during indirect extrusion of copper-clad aluminum rods. Thus, conic dies with different roughness (polished and sandblasted) and surfaces shapes (fine and coarse grooves) were tested. Additionally, the effects of a wax-graphite-based lubricant as well as a graphite-like carbon (GLC) coating of the die coni

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47

Markin, O. Yu, M. M. Makhmutov, and Yu A. Kudryashov. "Substantiation of design of elastic drive shaft of a vibratory crusher." Traktory i sel hozmashiny 81, no. 6 (2014): 9–11. http://dx.doi.org/10.17816/0321-4443-65552.

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Different designs of elastic drive shafts of conic vibratory crushers distinguishing by method of affixment and section are considered. Substantiation of the shaft design is carried out by flexibility, which defines the length. The best results are obtained for spring drive shafts.

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48

Pierce, David. "Conics in Place." Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia 13 (December 31, 2021): 127–50. http://dx.doi.org/10.24917/20809751.13.2.

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A method is presented for creating a problem, solving it, and confirming that the solution is correct. The problem is to analyze a second-degree polynomial equation in two variables, in order to identify and draw the defined conic section, with its axes, without changing coordinates. One creates the problemby choosing conjugate diameters that are not axes.

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49

Ahn, Young-Joon. "AN ERROR BOUND ANALYSIS FOR CUBIC SPLINE APPROXIMATION OF CONIC SECTION." Communications of the Korean Mathematical Society 17, no. 4 (2002): 741–54. http://dx.doi.org/10.4134/ckms.2002.17.4.741.

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50

Sato, Eiichi. "Hyperplane section principle of Lefschetz on conic-bundle and blowing-down." Kodai Mathematical Journal 31, no. 3 (2008): 307–22. http://dx.doi.org/10.2996/kmj/1225980438.

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