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  2. Asymptote - Wikipedia

    en.wikipedia.org/wiki/Asymptote

    In analytic geometry, an asymptote (/ ˈ æ s ɪ m p t oʊ t /) of a curve is a line such that the distance between the curve and the line approaches zero as one or both of the x or y coordinates tends to infinity. In projective geometry and related contexts, an asymptote of a curve is a line which is tangent to the curve at a point at infinity ...

  3. Asymptotic curve - Wikipedia

    en.wikipedia.org/wiki/Asymptotic_curve

    The asymptotic directions are the same as the asymptotes of the hyperbola of the Dupin indicatrix through a hyperbolic point, or the unique asymptote through a parabolic point. [1] An asymptotic direction is a direction along which the normal curvature is zero: take the plane spanned by the direction and the surface's normal at that point. The ...

  4. Curve - Wikipedia

    en.wikipedia.org/wiki/Curve

    The points of a curve C with coordinates in a field G are said to be rational over G and can be denoted C(G). When G is the field of the rational numbers, one simply talks of rational points. For example, Fermat's Last Theorem may be restated as: For n > 2, every rational point of the Fermat curve of degree n has a zero coordinate.

  5. List of curves - Wikipedia

    en.wikipedia.org/wiki/List_of_curves

    This page was last edited on 2 December 2024, at 16:34 (UTC).; Text is available under the Creative Commons Attribution-ShareAlike 4.0 License; additional terms may apply.

  6. Parabola - Wikipedia

    en.wikipedia.org/wiki/Parabola

    This can be done with calculus, or by using a line that is parallel to the axis of symmetry of the parabola and passes through the midpoint of the chord. The required point is where this line intersects the parabola. [e] Then, using the formula given in Distance from a point to a line, calculate the perpendicular distance from this point to the ...

  7. Cartesian coordinate system - Wikipedia

    en.wikipedia.org/wiki/Cartesian_coordinate_system

    For example, a circle of radius 2, centered at the origin of the plane, may be described as the set of all points whose coordinates x and y satisfy the equation x 2 + y 2 = 4; the area, the perimeter and the tangent line at any point can be computed from this equation by using integrals and derivatives, in a way that can be applied to any curve.

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    mail.aol.com

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  9. Convex curve - Wikipedia

    en.wikipedia.org/wiki/Convex_curve

    Four intersections of a line and a convex curve (here, a pentagon), top–bottom: the empty set, one point, two points, and an interval. For a convex curve, every line in the plane intersects the curve in one of four ways: its intersection can be the empty set, a single point, a pair of points, or an interval.