spiral

A spiral is a curve that winds itself round a certain point ¹⁾. While not being a circle, the radius will vary along the angle. For this reason a spiral has often a polar equation as representation.
Not all spiral-named curves have this winding quality, see e.g. the epi spiral.

I am not primarily concerned with 3D spirals ²⁾.
Maclaurin writes about spirals in his work Harmonia Mensurarum (1722).

In 2D we see the spiral in nature in the snail-shell, the cochlea (in your ear), the composites' flower-head, the shell, spiral star constellations. The spiral is also used in architecture, it's a very old ornament. According to Proclus the Greek Perseus was the first to describe the spiral curve.

In the universe some of the star systems have a spiral form. And the spiral theory is a model of our solar system, which has been constructed by the medieval Alpetragius. This theory is a variant on the system of Aristotle. The naming to a spiral is not that precise, because concentric spheres instead of spirals are used in the theory.

The following spirals can be distinguished:

• Archimedean spiral
• Archimedes' spiral
• hyperbolic spiral
• lituus
• spiral of Fermat
• atom-spiral
• Atzema spiral
• cochleoid
• Cotes' spiral
• cubic spiral
• epi spiral
• Euler's spiral
• involute of a circle
• line spiral
• logarithmic spiral
• Poinsot's spiral
• polynomial spiral
• spiral of Theodore of Cyrene
• sinusoidal spiral
• super spiral

notes

1) Spira (Lat.) = twisting (of a snake)

2) 3D spirals are often composed of a circular and a linear movement (in different directions). E.g.:

• the spiral staircase
• the movement of a particle in a magnetic field
• the contraceptive spiral
• the spiral grain in some kinds of trees (clockwise)

A three-dimensional spiral movement with water or air material is called a vortex.