

Here is the involute of a circle, along with its parametric equation.



Here is an Epi Spiral, shown with its polar equation



Here are Poinsot's two spirals. The one in red is given by the equation r*cosh(n*T), while the one in blue is r*sinh(n*T)



This curve has an asymptote at the origin and was originally studied by Bernoulli in 1726.



The cycloid is defined as the locus of a point on the circumference of a circle rolling along a line.



The caternary, also known as the chainette and the alysoid, describes the form assumed by a perfect flexible chain of uniform density hanging from two...



Archimedes' spiral is the Archimedean spiral with the polar equation shown below.



An Archimedean spiral is a spiral with a constant "m" that determines how tightly the spiral is wrapped.



Fermat's spiral is the Archimedean spiral with m=2. Both the lefthand and righthand spirals are shown below.



The Hyperbolic spiral is the Archimedean spiral with m=(1).



The Lituus is the Archimedean spiral with m=(2). Both the lefthand and righthand spirals are shown below.



The Logarithmic spiral is the locus of the equations shown below.



The Sinusoidal spiral is the locus of the equations shown below.



The Tractrix is the evolute of the catnary.



A Curtate cycloid is a cycloid where the locus is drawn from a point closer to the center of the circle than the circle's circumference.



A Prolate cycloid is a cycloid where the locus is drawn from a point farther from the center of the circle than the circle's circumference.



