Mathematical Description
In mathematics, a helix is a curve in 3-dimensional space. The following parametrisation in Cartesian coordinates defines a helix:
As the parameter t increases, the point (x(t),y(t),z(t)) traces a right-handed helix of pitch 2π and radius 1 about the z-axis, in a right-handed coordinate system.
In cylindrical coordinates (r, θ, h), the same helix is parametrised by:
A circular helix of radius a and pitch 2πb is described by the following parametrisation:
Another way of mathematically constructing a helix is to plot a complex valued exponential function (exi) taking imaginary arguments (see Euler's formula).
Except for rotations, translations, and changes of scale, all right-handed helices are equivalent to the helix defined above. The equivalent left-handed helix can be constructed in a number of ways, the simplest being to negate any one of the x, y or z components.
Read more about this topic: Helix
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