Heliks

Heliks is the plural form of helix in several languages and may appear in English transliteration as well. In geometry, heliks describe three-dimensional spirals created by a point moving around an axis while progressing along it. The most common type is the circular helix, parameterized by x = r cos t, y = r sin t, z = c t. Here r is the radius and c controls the pitch, the height gained per full revolution, equal to 2π c. The sense of the spiral can be right-handed or left-handed depending on the orientation. If the radius is constant, the heliks lie on the surface of a cylinder. In differential geometry, a circular helix has constant curvature κ = r/(r^2 + c^2) and constant torsion τ = c/(r^2 + c^2).

In biology and biochemistry, heliks motifs include the alpha-helix, a right-handed coil stabilized by hydrogen bonds between backbone amide groups. An alpha-helix typically contains about 3.6 amino acids per turn. A related 3-10 helix has roughly 3 residues per turn. The DNA molecule features a double helix, two polynucleotide strands wound around an axis.

In engineering and design, helices appear in springs, screws, and helical gears, where the helix angle governs motion and load transmission. The term also appears in architecture and nanotechnology, where helical structures are used to transmit forces or encode information.

Etymology traces helix to Greek hēlix, meaning “spiral” or “coil.” In English, plurals helices or helixes are common; heliks is used in some languages as a direct transliteration of the same concept.