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  2. Asymptote - Wikipedia

    en.wikipedia.org/wiki/Asymptote

    Asymptote. The graph of a function with a horizontal ( y = 0), vertical ( x = 0), and oblique asymptote (purple line, given by y = 2 x ). A curve intersecting an asymptote infinitely many times. In analytic geometry, an asymptote ( / ˈæsɪmptoʊt /) of a curve is a line such that the distance between the curve and the line approaches zero as ...

  3. Semi-log plot - Wikipedia

    en.wikipedia.org/wiki/Semi-log_plot

    On a semi-log plot the spacing of the scale on the y -axis (or x -axis) is proportional to the logarithm of the number, not the number itself. It is equivalent to converting the y values (or x values) to their log, and plotting the data on linear scales. A log–log plot uses the logarithmic scale for both axes, and hence is not a semi-log plot.

  4. Folium of Descartes - Wikipedia

    en.wikipedia.org/wiki/Folium_of_Descartes

    The folium of Descartes is related to the trisectrix of Maclaurin by affine transformation. To see this, start with the equation and change variables to find the equation in a coordinate system rotated 45 degrees. This amounts to setting. In the plane the equation is. If we stretch the curve in the direction by a factor of this becomes which is ...

  5. Sigmoid function - Wikipedia

    en.wikipedia.org/wiki/Sigmoid_function

    A sigmoid function is any mathematical function whose graph has a characteristic S-shaped or sigmoid curve . A common example of a sigmoid function is the logistic function shown in the first figure and defined by the formula: [ 1] Other standard sigmoid functions are given in the Examples section. In some fields, most notably in the context of ...

  6. Line–line intersection - Wikipedia

    en.wikipedia.org/wiki/Lineline_intersection

    In Euclidean geometry, the intersection of a line and a line can be the empty set, a point, or another line. Distinguishing these cases and finding the intersection have uses, for example, in computer graphics, motion planning, and collision detection . In three-dimensional Euclidean geometry, if two lines are not in the same plane, they have ...

  7. Generalised logistic function - Wikipedia

    en.wikipedia.org/wiki/Generalised_logistic_function

    The generalized logistic function or curve is an extension of the logistic or sigmoid functions. Originally developed for growth modelling, it allows for more flexible S-shaped curves. The function is sometimes named Richards's curve after F. J. Richards, who proposed the general form for the family of models in 1959.

  8. Logistic function - Wikipedia

    en.wikipedia.org/wiki/Logistic_function

    Logistic function. A logistic function or logistic curve is a common S-shaped curve ( sigmoid curve) with the equation. where. is the carrying capacity, the supremum of the values of the function; is the logistic growth rate, the steepness of the curve; and. is the value of the function's midpoint.

  9. Hyperbola - Wikipedia

    en.wikipedia.org/wiki/Hyperbola

    Hyperbola. A hyperbola is an open curve with two branches, the intersection of a plane with both halves of a double cone. The plane does not have to be parallel to the axis of the cone; the hyperbola will be symmetrical in any case. Hyperbola (red): features. In mathematics, a hyperbola is a type of smooth curve lying in a plane, defined by its ...