Spiral
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For other uses of this word, see
spiral (disambiguation).
Cutaway of a
nautilus shell showing the chambers arranged in an approximately
logarithmic spiral.
In
mathematics, a
spiral is a
curve which emanates from a central point, getting progressively farther away as it revolves around the point.
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[edit] Spiral or helix
An Archimedean spiral, a helix, and a conic spiral.
A "spiral" and a "
helix" are two terms that are easily confused, but represent different objects.
A spiral is typically a
planar curve (that is, flat), like the groove on a
record or the arms of a
spiral galaxy. A helix, on the other hand, is a three-dimensional coil that runs along the surface of a cylinder, like a
screw. There are many instances where in
colloquial usage spiral is used as a synonym for helix, notably
spiral staircase and
spiral binding of books.
In the side picture, the black curve at the bottom is an
Archimedean spiral, while the green curve is a helix. A cross between a spiral and a helix, such as the curve shown in red, is known as a conic helix. An example of a conic helix is the spring used to hold and make contact with the negative terminals of AA or AAA batteries in remote controls.
[edit] Two-dimensional spirals
A
two-dimensional spiral may be described most easily using
polar coordinates, where the
radius r is a
continuous monotonic 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:
Archimedean spiral
Cornu spiral