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A curve obtained by fitting polynomials to each ordinate of an ordered sequence of points. The above plots show polynomial curves where the order of the fitting polynomial ...

The pedal curve of a sinusoidal spiral r=a[cos(nt)]^(1/n) with pedal point at the center is another sinusoidal spiral with polar equation r=a[cos(nt)]^(1+1/n). A few examples ...

The ophiuride is a cubic curve (left figure) given by the implicit equation x(x^2+y^2)+(ax-by)y=0, (1) where a>0,b>=0, or by the polar equation ...

A fractal is an object or quantity that displays self-similarity, in a somewhat technical sense, on all scales. The object need not exhibit exactly the same structure at all ...

Inversion is the process of transforming points P to a corresponding set of points P^' known as their inverse points. Two points P and P^' are said to be inverses with ...

A regular polygon is an n-sided polygon in which the sides are all the same length and are symmetrically placed about a common center (i.e., the polygon is both equiangular ...

A plane curve is a curve that lies in a single plane. A plane curve may be closed or open. Curves which are interesting for some reason and whose properties have therefore ...

The point with respect to which a radial curve is computed.

The point of illumination for a caustic.

A semicubical parabola is a curve of the form y=+/-ax^(3/2) (1) (i.e., it is half a cubic, and hence has power 3/2). It has parametric equations x = t^2 (2) y = at^3, (3) and ...