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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. If the floor projection is a logarithmic spiral , it is called conchospiral (from conch ).
The efficiency can be plotted versus the helix angle for a constant friction, as shown in the adjacent diagram. The maximum efficiency is a helix angle between 40 and 45 degrees, however a reasonable efficiency is achieved above 15°. Due to difficulties in forming the thread, helix angle greater than 30° are rarely used.
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 ...
fold.it download page Archived 2011-04-04 at the Wayback Machine: FoldX: I Yes Yes No No No No No No Energy calculations, protein design Proprietary, commercial or gratis CRG: GROMACS: No No Yes Yes No [2] Yes I Yes [3] Yes High performance MD Free open source GNU GPL: gromacs.org: GROMOS: No No Yes Yes Yes Yes Yes Yes Yes Intended for biomolecules
A spiral staircase in the Cathedral of St. John the Divine.Several helical curves in the staircase project to hyperbolic spirals in its photograph.. A hyperbolic spiral is a type of spiral with a pitch angle that increases with distance from its center, unlike the constant angles of logarithmic spirals or decreasing angles of Archimedean spirals.
A mechanical method for constructing the arithmetic spiral uses a modified string compass, where the string wraps and winds (or unwraps/unwinds) about a fixed central pin (that does not pivot), thereby incrementing (or decrementing) the length of the radius (string) as the angle changes (the string winds around the fixed pin which does not pivot).
Complex exponential function: The exponential function exactly maps all lines not parallel with the real or imaginary axis in the complex plane, to all logarithmic spirals in the complex plane with centre at : () = (+) + ⏟ = + = ( + ) ⏟ The pitch angle of the logarithmic spiral is the angle between the line and the imaginary axis.
Fermat's spiral: a>0, one branch = + Fermat's spiral, both branches. A Fermat's spiral or parabolic spiral is a plane curve with the property that the area between any two consecutive full turns around the spiral is invariant.