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Everything about Conic section
Curve from a cone intersecting a plane
A conic section, conic or a quadratic curve is a curve obtained from a cone's surface intersecting a plane. The three types of conic section are the hyperbola, the parabola, and the ellipse; the circle is a special case of the ellipse, though it was sometimes considered a fourth type. The ancient Greek mathematicians studied conic sections, culminating around 200 BC with Apollonius of Perga's systematic work on their properties. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Conic sectionA 5-minute orientation
- Skim a recent paper: Splay-bend elastic inequalities shape tactoids, toroids, umbilics, and conic section walls in paraelectric, twist-bend, and ferroelectric nematicsInfluential work since 2022
- Pick up a classic book: ConicsThe most-reprinted book on the subject
- Read the landmark paper: Design of symmetric conic-section flexure hinges based on closed-form compliance equationsCited 199 times
- Go sideways: Eccentricity (mathematics)A closely related topic
- Go sideways: Matrix representation of conic sectionsA closely related topic
📖 Definitions
Noun Any of the four distinct shapes that are the intersections of a cone with a plane, namely the circle, ellipse, parabola, and hyperbola.
🏆 Landmark papers (most cited)
Design of symmetric conic-section flexure hinges based on closed-form compliance equations
UNIFIED FRAMEWORK FOR MLPs AND RBFNs: INTRODUCING CONIC SECTION FUNCTION NETWORKS
Laser beam scanning by rotary mirrors II Conic-section scan patterns
Some important geometrical features of conic-section-generated offset refelector antennas
Conic Section Function Neural Network Circuitry for Offline Signature Recognition
The Eccentricity of a Conic Section
Beam squint determination in conic-section reflector antennas with circularly polarized feeds
Conic that best fits an off-axis conic section
🆕 Influential since 2022
Splay-bend elastic inequalities shape tactoids, toroids, umbilics, and conic section walls in paraelectric, twist-bend, and ferroelectric nematics
Time-domain distance protection of transmission lines based on the conic section general equation
CSD-R k NN: reverse k nearest neighbors queries with conic section discriminances
Geometric properties of integrable Kepler and Hooke billiards with conic section boundaries
Hyperquaternionic Representations of Conic Sections
📚 Books worth reading
ConicsApollonius of Perga, William H. Donahue · 1655
A treatise on conic sectionsGeorge Salmon · 1850
Elements of geometry, conic sections, and plane trigonometryElias Loomis · 1847
A Treatise on Geometrical ConicsArthur Cockshott · 1889
A treatise on conic sectionsGeorge Salmon · 1869
An elementary treatise on the geometry of conicsAsutosh Mookerjee · 1893
A treatise on plane co-ordinate geometry as applied to the straight line and the conic sectionsIsaac Todhunter · 1858
A treatise on the geometry of the circle and some extensions to conic sections by the method of reciprocation with numerous examplesWilliam J. M'Clelland · 1891
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Eccentricity (mathematics) In mathematics, the eccentricity of a conic section is a non-negative real number that uniquely characterizes its shape. One can think of the eccentricity…
- Matrix representation of conic sections In mathematics, the matrix representation of conic sections permits the tools of linear algebra to be used in the study of conic sections. It provides…
- Focus (geometry) In geometry, focuses or foci (/ˈfoʊsaɪ/ or /ˈfoʊkaɪ/; sing.: focus) are special points with reference to which any of a variety of curves is constructed…
- Degenerate conic In geometry, a degenerate conic is a conic (a second-degree plane curve, defined by a polynomial equation of degree two) that fails to be an irreducible…
- Hyperbola In mathematics, a hyperbola (/haɪˈpɜːrbələ/ hy-PUR-bə-lə) is a type of smooth curve lying in a plane, defined by its geometric properties or by equations…
- Parabola In mathematics, a parabola (/pəˈræbələ/ pə-RA-bə-lə) is a plane curve which is mirror-symmetrical and is approximately U-shaped. It fits several superficially…
- Confocal conic sections In geometry, two conic sections are called confocal if they have the same foci. Because ellipses and hyperbolas have two foci, there are confocal ellipses…
- Director circle In geometry, the director circle of an ellipse or hyperbola (also called the orthoptic circle or Fermat–Apollonius circle) is a circle consisting of all…