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:
1) Spira (Lat.) = twisting (of a snake)
2) 3D spirals are often composed of a circular and a linear movement (in different
- 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.