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  2. Conic section - Wikipedia

    en.wikipedia.org/wiki/Conic_section

    A conic is the curve obtained as the intersection of a plane, called the cutting plane, with the surface of a double cone (a cone with two nappes).It is usually assumed that the cone is a right circular cone for the purpose of easy description, but this is not required; any double cone with some circular cross-section will suffice.

  3. List of circle topics - Wikipedia

    en.wikipedia.org/wiki/List_of_circle_topics

    Mrs. Miniver's problemProblem on areas of intersecting circles; Pivot theorem – Concerns 3 circles through triples of points on the vertices and sides of a triangle; Pizza theorem – Equality of areas of a sliced disk; Squaring the circleProblem of constructing equal-area shapes

  4. Concentric objects - Wikipedia

    en.wikipedia.org/wiki/Concentric_objects

    The region of the plane between two concentric circles is an annulus, and analogously the region of space between two concentric spheres is a spherical shell. [6] For a given point c in the plane, the set of all circles having c as their center forms a pencil of circles. Each two circles in the pencil are concentric, and have different radii.

  5. Confocal conic sections - Wikipedia

    en.wikipedia.org/wiki/Confocal_conic_sections

    A pencil of confocal ellipses and hyperbolas is specified by choice of linear eccentricity c (the x-coordinate of one focus) and can be parametrized by the semi-major axis a (the x-coordinate of the intersection of a specific conic in the pencil and the x-axis). When 0 < a < c the conic is a hyperbola; when c < a the conic is an ellipse.

  6. Circular symmetry - Wikipedia

    en.wikipedia.org/wiki/Circular_symmetry

    In geometry, circular symmetry is a type of continuous symmetry for a planar object that can be rotated by any arbitrary angle and map onto itself.. Rotational circular symmetry is isomorphic with the circle group in the complex plane, or the special orthogonal group SO(2), and unitary group U(1).

  7. Cone - Wikipedia

    en.wikipedia.org/wiki/Cone

    The axis of a cone is the straight line passing through the apex about which the cone has a circular symmetry. In common usage in elementary geometry, cones are assumed to be right circular, i.e., with a circle base perpendicular to the axis. [1] If the cone is right circular the intersection of a plane with the lateral surface is a conic section.

  8. Pole and polar - Wikipedia

    en.wikipedia.org/wiki/Pole_and_polar

    The concepts of pole, polar and reciprocation can be generalized from circles to other conic sections which are the ellipse, hyperbola and parabola. This generalization is possible because conic sections result from a reciprocation of a circle in another circle, and the properties involved, such as incidence and the cross-ratio , are preserved ...

  9. Quadric - Wikipedia

    en.wikipedia.org/wiki/Quadric

    In mathematics, a quadric or quadric surface (quadric hypersurface in higher dimensions), is a generalization of conic sections (ellipses, parabolas, and hyperbolas).It is a hypersurface (of dimension D) in a (D + 1)-dimensional space, and it is defined as the zero set of an irreducible polynomial of degree two in D + 1 variables; for example, D = 1 in the case of conic sections.

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