Spiral - Two-dimensional Spirals

Two-dimensional Spirals

A two-dimensional spiral may be described most easily using polar coordinates, where the radius r is a monotonic continuous function of angle θ. The circle would be regarded as a degenerate case (the function not being strictly monotonic, but rather constant).

Some of the more important sorts of two-dimensional spirals include:

• The Archimedean spiral: (see also:Involute)
• The Euler spiral, Cornu spiral or clothoid
• Fermat's spiral:
• The hyperbolic spiral:
• The lituus:
• The logarithmic spiral: ; approximations of this are found in nature
• The Fibonacci spiral and golden spiral: special cases of the logarithmic spiral
• The Spiral of Theodorus: an approximation of the Archimedean spiral composed of contiguous right triangles

• Archimedean spiral

• Cornu spiral

• Fermat's spiral

• hyperbolic spiral

• lituus

• logarithmic spiral

• spiral of Theodorus