Helix

A helix is a shape like a spring or a spiral staircase.

In mathematics, a helix is a 3-dimensional curve. The following three equations in rectangular coordinates define a helix:

x = cos t

y = sin t

z = t

Here t is a real parameter. If we think of t as an increasing number, then as t increases, the point (x,y,z) traces a helix about the z-axis.

In cylindrical coordinates, the same helix is described by:

r = 1

θ = h

Helices have chirality. By convention, the helix defined above is said to be right-handed because if the right-hand thumb is taken to be the positive z-axis, then as z increases, the fingers of the right hand point in the same direction in which the helix is traced.

Except for rotations, translationss, and changes of scale, all right-handed helices are equivalent to the helix defined above.

The pitch of a helix is the length of the helix axis for one complete helix turn. The pitch of the helix defined above is 2π.

The general cylindrical form for a right-handed helix along the h-axis passing through (R, 0, 0) is:

r = R

θ = t

h = k t

where R and k are constants.

Helix

See also