Search results
Results from the WOW.Com Content Network
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 ...
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 ).
A negatively supercoiled DNA molecule will produce either a one-start left-handed helix, the toroid, or a two-start right-handed helix with terminal loops, the plectoneme. Plectonemes are typically more common in nature, and this is the shape most bacterial plasmids will take. For larger molecules it is common for hybrid structures to form ...
Animation of the torsion and the corresponding rotation of the binormal vector. Let r be a space curve parametrized by arc length s and with the unit tangent vector T.If the curvature κ of r at a certain point is not zero then the principal normal vector and the binormal vector at that point are the unit vectors
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.
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 suitable bounded function is the arctan function: Example 1 Setting r = a arctan ( k φ ) {\displaystyle \;r=a\arctan(k\varphi )\;} and the choice k = 0.1 , a = 4 , φ ≥ 0 {\displaystyle \;k=0.1,a=4,\;\varphi \geq 0\;} gives a spiral, that starts at the origin (like an Archimedean spiral) and approaches the circle with radius r = a π ...
In statistical mechanics, the Zimm–Bragg model is a helix-coil transition model that describes helix-coil transitions of macromolecules, usually polymer chains. Most models provide a reasonable approximation of the fractional helicity of a given polypeptide; the Zimm–Bragg model differs by incorporating the ease of propagation (self-replication) with respect to nucleation.