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.
A circular helix (i.e. one with constant radius) has constant band curvature and constant torsion.
A conic helix, also known as a conic spiral, may be defined as a spiral on a conic surface, with the distance to the apex an exponential function of the angle indicating direction from the axis.
A curve is called a general helix or cylindrical helix if its tangent makes a constant angle with a fixed line in space. A curve is a general helix if and only if the ratio of curvature to torsion is constant.
A curve is called a slant helix if its principal normal makes a constant angle with a fixed line in space. It can be constructed by applying a transformation to the moving frame of a general helix.
Helices can be either right-handed or left-handed. With the line of sight along the helix's axis, if a clockwise screwing motion moves the helix away from the observer, then it is called a right-handed helix; if towards the observer, then it is a left-handed helix. Handedness (or chirality) is a property of the helix, not of the perspective: a right-handed helix cannot be turned to look like a left-handed one unless it is viewed in a mirror, and vice versa.
Two types of helix shown in comparison. This shows the two chiralities of helices. One is left-handed and the other is right-handed. Each row compares the two helices from a different perspective. The chirality is a property of the object, not of the perspective (view-angle)
A circular helix of radius a and slope a/b (or pitch 2πb) is described by the following parametrisation:
Another way of mathematically constructing a helix is to plot the complex-valued function exi as a function of the real number x (see Euler's formula).
The value of x and the real and imaginary parts of the function value give this plot three real dimensions.
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.
In aviation, geometric pitch is the distance an element of an airplane propeller would advance in one revolution if it were moving along a helix having an angle equal to that between the chord of the element and a plane perpendicular to the propeller axis; see also: pitch angle (aviation).