SPIRALS

In mathematics, a spiral is a curve which emanates from a point, moving farther away as it revolves around the point. It is a subtype of whorled patterns.

This list of spirals includes named spirals that have been described mathematically.

Image	Name	First described	Equation	Comment
	circle		${\displaystyle 𝑟=𝑘}$	The trivial spiral
	Archimedean spiral (also arithmetic spiral)	c. 320 BC	${\displaystyle 𝑟=𝑎+𝑏\cdot 𝜃}$
	Fermat's spiral (also parabolic spiral)	1636[1]	${\displaystyle {𝑟}^2={𝑎}^2\cdot 𝜃}$
	Euler spiral (also Cornu spiral or polynomial spiral)	1696[2]	${\displaystyle 𝑥(𝑡)=\mathrm{C}(𝑡),}$${\displaystyle 𝑦(𝑡)=\mathrm{S}(𝑡)}$	using Fresnel integrals[3]
	hyperbolic spiral (also reciprocal spiral)	1704	${\displaystyle 𝑟=\frac{𝑎}{𝜃}}$
	lituus	1722	${\displaystyle {𝑟}^2\cdot 𝜃=𝑘}$
	logarithmic spiral (also known as equiangular spiral)	1638[4]	${\displaystyle 𝑟=𝑎\cdot {𝑒}^{𝑏\cdot 𝜃}}$	Approximations of this are found in nature