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Spiral vs. helix 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 ridges of 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. 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. Two-dimensional spirals A two-dimensional spiral may be described easiest 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: 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: Spherical spiral
As a symbol The spiral plays a certain role in symbolism, and appears in megalithic art, notably in the Newgrange tomb. See also triple spiral, Popular culture | ||||||||||||
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