Information AboutSpiral |
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In Mathematics , a spiral is a Curve which turns around some central point or axis, getting progressively closer to or farther from it, depending on which way one follows the curve. )]] TWO-DIMENSIONAL SPIRALS 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:
THREE-DIMENSIONAL SPIRALS 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 Revolution s, with the distance between them decreasing as the curve approaches either of the poles. |
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