The Archimedean spiral: r = a + b θ The Euler spiral, Cornu spiral or clothoid Fermat's spiral: r = θ 1/2 The hyperbolic spiral: r = a /θ The lituus: r = θ -1/2 The logarithmic spiral: r = abθ; approximations of this are found in nature

In modern notation the equation of the spiral is r = aeθ cot b, in which r is the radius of each turn of the spiral, a and b are constants that depend on the particular spiral, θ is the angle of rotation as the curve spirals, and e is the base of the natural logarithm.