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Conical spiral with an archimedean spiral as floor projection Floor projection: Fermat's spiral Floor projection: logarithmic spiral Floor projection: hyperbolic spiral. In mathematics, a conical spiral, also known as a conical helix, [1] is a space curve on a right circular cone, whose floor projection is a plane spiral.
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Two well-known spiral space curves are conical spirals and spherical spirals, defined below. Another instance of space spirals is the toroidal spiral. [8] A spiral wound around a helix, [9] also known as double-twisted helix, [10] represents objects such as coiled coil filaments.
The pitch of a helix is the height of one complete helix turn, measured parallel to the axis of the helix. A double helix consists of two (typically congruent) helices with the same axis, differing by a translation along the axis. [3] A circular helix (i.e. one with constant radius) has constant band curvature and constant torsion. The slope of ...
Examples include the plane, the lateral surface of a cylinder or cone, a conical surface with elliptical directrix, the right conoid, the helicoid, and the tangent developable of a smooth curve in space. A ruled surface can be described as the set of points swept by a moving straight line.
In mathematics, a conchospiral a specific type of space spiral on the surface of a cone (a conical spiral), whose floor projection is a logarithmic spiral. Conchospirals are used in biology for modelling snail shells, and flight paths of insects [1] [2] and in electrical engineering for the construction of antennas. [3] [4]
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A spiral antenna is a type of radio frequency antenna shaped as a spiral, [1]: 14‑2 first described in 1956. [2] Archimedean spiral antennas are the most popular, while logarithmic spiral antennas are independent of frequency: [3] the driving point impedance, radiation pattern and polarization of such antennas remain unchanged over a large bandwidth. [4]