Curves

In algebra, a cubic function is a function of the form where a is nonzero.

A logistic function or logistic curve is a common "S" shape (sigmoid curve), with equation: where * e = the natural logarithm base (also known as Euler's number), * x0 = the x-value of the sigmoid's midpoint, * L = the curve's maximum value, and * k = the steepness of the curve.

A parallel of a curve is the envelope of a family of congruent circles centered on the curve.

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 they tend to infinity.

An astroid is a particular mathematical curve: a hypocycloid with four cusps.

In mathematics, an ellipse is a curve in a plane surrounding two focal points such that the sum of the distances to the two focal points is constant for every point on the curve.

In mathematics, a hyperbola (plural hyperbolas or hyperbolae) is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set.

(Not to be confused with spirographs, which are generally enclosed by a circular boundary, whereas Lissajous curves are enclosed by rectangular boundaries.) In mathematics, a Lissajous curve /ˈlɪsəʒuː/, also known as Lissajous figure or Bowditch curve /ˈbaʊdɪtʃ/, is the graph of a system of parametric equations which describe complex harmonic motion.

In economics, the Lorenz curve is a graphical representation of the distribution of income or of wealth.

In Euclidean geometry, an arc (symbol: ⌒) is a closed segment of a differentiable curve.

Determining the length of an irregular arc segment is also called rectification of a curve.

A contour line (also isoline, isopleth, or isarithm) of a function of two variables is a curve along which the function has a constant value.

Differential geometry of curves is the branch of geometry that deals with smooth curves in the plane and in the Euclidean space by methods of differential and integral calculus.

The Sierpinski triangle (also with the original orthography Sierpiński), also called the Sierpinski gasket or the Sierpinski Sieve, is a fractal and attractive fixed set with the overall shape of an equilateral triangle, subdivided recursively into smaller equilateral triangles.

An airfoil (in American English) or aerofoil (in British English) is the shape of a wing, blade (of a propeller, rotor, or turbine), or sail (as seen in cross-section).

A sine wave or sinusoid is a mathematical curve that describes a smooth repetitive oscillation.

In geometry, curve sketching (or curve tracing) includes techniques that can be used to produce a rough idea of overall shape of a plane curve given its equation without computing the large numbers of points required for a detailed plot.

In navigation, a rhumb line, rhumb, or loxodrome is an arc crossing all meridians of longitude at the same angle, i.

In the geometry of planar curves, a vertex is a point of where the first derivative of curvature is zero.

In mathematics, an Osgood curve is a non-self-intersecting curve (either a Jordan curve or a Jordan arc) of positive area.