[edit] Three-dimensional spirals
For simple 3-d spirals, a third variable,
h (height), is also a continuous,
monotonic function of θ. For example, a conic
helix may be defined as a spiral on a conic surface, with the distance to the apex an exponential function of θ.
The
helix and
vortex can be viewed as a kind of
three-dimensional spiral.
For a helix with thickness, see
spring (math).
Another kind of spiral is a conic spiral along a circle. This spiral is formed along the surface of a
cone whose axis is bent and restricted to a circle:
This image is reminiscent of a
Ouroboros symbol and could be mistaken for a torus with a continuously-increasing diameter:
[edit] Spherical spiral
Rhumb line
Archimedean Spherical Spiral
A
spherical spiral (
rhumb line or loxodrome, left picture) is the curve on a sphere traced by a ship traveling from one pole to the other while keeping a fixed
angle (unequal to 0° and to 90°) with respect to the meridians of
longitude, i.e. keeping the same
bearing. The curve has an
infinite number of
revolutions, with the distance between them decreasing as the curve approaches either of the poles.
The gap between the curves of an
Archimedean spiral (right picture) remains constant as the radius changes and is hence not a
rhumb line.
[edit] As a symbol
The Newgrange entrance slab
The spiral plays a specific role in
symbolism, and appears in
megalithic art, notably in the
Newgrange tomb or in many Galician petroglyphs such as the one in Mogor. See also
triple spiral.
While scholars are still debating the subject, there is a growing acceptance that the simple spiral, when found in Chinese art, is an early symbol for the sun. Roof tiles dating back to the
Tang Dynasty with this symbol have been found west of the ancient city of
Chang'an (modern-day Xian).
The spiral is the most ancient symbol found on every civilized continent. Due to its appearance at burial sites across the globe, the spiral most likely represented the "life-death-rebirth" cycle. Similarly, the spiral symbolized the sun, as ancient people thought the sun was born each morning, died each night, and was reborn the next morning.
Spirals are also a symbol of
hypnosis, stemming from the
cliché of people and cartoon characters being hypnotized by staring into a spinning spiral (One example being
Kaa in Disney's
The Jungle Book). They are also used as a symbol of
dizziness, where the eyes of a cartoon character, especially in
anime and
manga, will turn into spirals to show they are dizzy or dazed. The spiral is also a prominent symbol in the anime
Gurren Lagann, where it symbolizes the
double helix structure of
DNA, representing biological
evolution, and the spiral structure of a
galaxy, representing
universal evolution.