page_title: Spiral
section_title: Helices
hierarchical_section_title: Spiral / Helices
caption_attribution_description: English: A helix and an Archimedean spiral, combined to form a conic helix.
context_page_description: In mathematics, a spiral is a curve which emanates from a point, moving farther away as it revolves around the point.
context_section_description: Two major definitions of "spiral" in the American Heritage Dictionary are:
  a curve on a plane that winds around a fixed center point at a continuously increasing or decreasing distance from the point.
  a three-dimensional curve that turns around an axis at a constant or continuously varying distance while moving parallel to the axis; a helix.
  The first definition describes a planar curve, that extends in both of the perpendicular directions within its plane; the groove on one side of a record closely approximates a plane spiral (and it is by the finite width and depth of the groove, but not by the wider spacing between than within tracks, that it falls short of being a perfect example); note that successive loops differ in diameter. In another example, the "center lines" of the arms of a spiral galaxy trace logarithmic spirals.
  The second definition includes two kinds of 3-dimensional relatives of spirals:
  a conical or volute spring (including the spring used to hold and make contact with the negative terminals of AA or AAA batteries in a battery box), and the vortex that is created when water is draining in a sink is often described as a spiral, or as a conical helix.
  quite explicitly, definition 2 also includes a cylindrical coil spring and a strand of DNA, both of which are quite helical, so that "helix" is a more useful description than "spiral" for each of them; in general, "spiral" is seldom applied if successive "loops" of a curve have the same diameter.
  In the side picture, the black curve at the bottom is an Archimedean spiral, while the green curve is a helix. The curve shown in red is a conic helix.
caption: An Archimedean spiral (black), a helix (green), and a conic spiral (red)
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