Spiral

A spiral is a curve that winds around a point while its radial distance varies. Spirals can wind outward or inward; the name is also applied more broadly to curves such as the Cornu spiral, which winds about two limiting points. In Archimedes' spiral, the radial distance increases linearly with polar angle.

The following table compares named spirals using finite portions, independently scaled, with the chosen parameters and intervals in the last column. Here is the parameter used in the corresponding entry. The atom-spiral and epispiral are cropped near their asymptotes; in the latter, the poles of the radial formula are omitted.

representative	spiral	radial formula	representative parameters and interval
	Archimedean spiral		, ;
	Archimedes' spiral		;
	atom-spiral		;
	circle involute		;
	Cornu spiral
	Cotes' spiral		, , ( case);
	epispiral		, ;
	Fermat's spiral		;
	Galilean spiral		, ;
	hyperbolic spiral		;
	lituus		;
	logarithmic spiral		, ;
	Nielsen's spiral		;
	polygonal spiral		; 24 segments
	Theodorus spiral		24 unit outer segments
	tractrix spiral		;