Spiral
In
mathematics, a
spiral is a
curve which emanates from a central point, getting progressively farther away as it revolves around the point.
A
two-dimensional spiral may be described using
polar coordinates by saying that the
radius r is a
continuous monotonic function of 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:
r =
a +
bθ
* The
Cornu spiral or
clothoid*
Fermat's spiral:
r = θ
1/2* The
hyperbolic spiral:
r =
a/θ
* The
lituus:
r = 1/θ
1/2* The
logarithmic spiral:
r =
abθ; approximations of this are found in nature
* The
Fibonacci spiral and
golden spiral: special cases of the logarithmic spiral.
As in the two-dimensional case,
r is a
continuous monotonic function of θ.
For simple 3-d spirals, the 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.
For compound 3-d spirals, such as the
spherical spiral described below,
h increases with θ on one side of a point, and decreases with θ on the other side.
The
helix and
vortex can be viewed as a kind of
three-dimensional spiral.
For a helix with thickness, see
spring (math).
Spherical spiral
A
spherical spiral (
rhumb line) is the curve on a sphere traced by a ship traveling from one pole to the other while keeping a fixed
angle (but not a
right angle) 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.
Spiraling is a wave function of spherical or 4-D spiral torusphere, a gyroscope orb with axis & magnetic waves flowing from south pole to top or north pole, holding it balanced when spinning in larger magnetic field, like in airplanes & rockets guidence systems to help stabalize their flight path. However gyroscope magnetic field is invisible, as is earth magnetosphere, we see by its attraction on flowing air, clouds, water, falling, balancing flowing & flying things usually in spiraling patterns from micro to macro; DNA to cells to currents to clouds to tornadoes to hurricanes to planets, suns & galaxies. So spirals are universal geometry of space & consciousness, we're attracted to being in every living cell & moving thru space & rotating around centers of attrraction & radiating vibrations in omni-directional waves of harmonic frequencies & orbits. m. sunanda.
Films
*
Uzumaki*
The psychology behind the Spiral*
Spirals in photographshttp://www.efn.org/~ecozma/sunergy/chiether/ABCs%20of%20spirals.html
