helical

Helical is a term used to describe anything shaped like a helix, a three-dimensional curve obtained by rotating a line about a fixed axis while advancing along the axis. In everyday use it often refers to components, structures, or molecules that exhibit this spiraling form.

In geometry, the circular helix is the most common example, characterized by a constant radius r and a constant pitch p, the vertical advance per revolution. A standard parameterization is x = r cos t, y = r sin t, z = (p/2π) t. A helix can be right-handed or left-handed depending on rotation direction as it ascends the axis. The axis is the line around which the curve winds.

Natural and technological examples include the DNA double helix, a fundamental biological structure, and α-helix regions in proteins. Helical shapes appear in springs, screws and threaded fasteners, helical gears, coils, and antennas. In crystallography and materials science, helices describe motifs with helical symmetry and are studied for their mechanical and optical properties. Helical geometry also informs analyses of screw-like motion in mechanics and biomechanics.

Notes: not all spiral shapes are helices; a spiral lies in a plane, while a helix is a three-dimensional curve. The term is widely used across science and engineering to indicate a twist around an axis.