# Helix

**helicalheliceshelicallyspiralhelical structurecoilshelical screwshelical shapehelical spiralhelical-shaped**

A helix, plural helixes or helices, is a type of smooth space curve, i.e. a curve in three-dimensional space.wikipedia

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### Coil spring

**coil springscoilHelical spring**

Examples of helices are coil springs and the handrails of spiral staircases.

They are made of an elastic material formed into the shape of a helix which returns to its natural length when unloaded.

### Alpha helix

**alpha helicesα-helicesalpha-helices**

Helices are important in biology, as the DNA molecule is formed as two intertwined helices, and many proteins have helical substructures, known as alpha helices.

The alpha helix (α-helix) is a common motif in the secondary structure of proteins and is a right hand-helix conformation in which every backbone N−H group hydrogen bonds to the backbone C=O group of the amino acid located three or four residues earlier along the protein sequence.

### Screw thread

**threadedthreadthreads**

Most hardware screw threads are right-handed helices.

A screw thread, often shortened to thread, is a helical structure used to convert between rotational and linear movement or force.

### Stairs

**staircasespiral staircasestairway**

Examples of helices are coil springs and the handrails of spiral staircases.

The mathematical term for motion where the locus remains at a fixed distance from a fixed line whilst moving in a circular motion about it is "helical".

### Helicoid

**helicoidalaxishelical**

A "filled-in" helix – for example, a "spiral" (helical) ramp – is called a helicoid.

Its name derives from its similarity to the helix: for every point on the helicoid, there is a helix contained in the helicoid which passes through that point.

### Nucleic acid double helix

**double helixminor grooveB-DNA**

Helices are important in biology, as the DNA molecule is formed as two intertwined helices, and many proteins have helical substructures, known as alpha helices.

The double helical structure of a nucleic acid complex arises as a consequence of its secondary structure, and is a fundamental component in determining its tertiary structure.

### Chirality (mathematics)

**chiralenantiomorphchirality**

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.

Some chiral three-dimensional objects, such as the helix, can be assigned a right or left handedness, according to the right-hand rule.

### Spiral

**spiralsspherical spiralwhorl**

A conic helix 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.

In others it follows a skew path forming a helico-spiral pattern.

### DNA

**deoxyribonucleic aciddouble-stranded DNAdsDNA**

Helices are important in biology, as the DNA molecule is formed as two intertwined helices, and many proteins have helical substructures, known as alpha helices.

Compared to B-DNA, the A-DNA form is a wider right-handed spiral, with a shallow, wide minor groove and a narrower, deeper major groove.

### Curve

**closed curvespace curvesmooth curve**

A helix, plural helixes or helices, is a type of smooth space curve, i.e. a curve in three-dimensional space.

While the first examples of curves that are met are mostly plane curves (that is, in everyday words, curved lines in two-dimensional space), there are obvious examples such as the helix which exist naturally in three dimensions.

### Tendril perversion

Some curves found in nature consist of multiple helices of different handedness joined together by transitions known as tendril perversions.

Tendril perversion, often referred to in context as simply perversion, is a geometric phenomenon found in helical structures such as plant tendrils, in which a helical structure forms that is divided into two sections of opposite chirality, with a transition between the two in the middle.

### Boerdijk–Coxeter helix

**Boerdijk–Coxeter helices**

The Boerdijk–Coxeter helix, named after H. S. M. Coxeter and A. H. Boerdijk, is a linear stacking of regular tetrahedra, arranged so that the edges of the complex that belong to only one tetrahedron form three intertwined helices.

### Solenoid

**solenoidselectromechanical solenoidmagnetizing current loop**

A solenoid (, from the French solénoïde, a modern coinage based on Greek σωληνοειδής sōlēnoeidḗs "pipe-shaped" ) is a type of electromagnet, the purpose of which is to generate a controlled magnetic field through a coil wound into a tightly packed helix.

### Triple helix

**triple helices**

In the fields of geometry and biochemistry, a triple helix (plural triple helices) is a set of three congruent geometrical helices with the same axis, differing by a translation along the axis.

### Torsion of a curve

**torsionTorsion of curvestorsion angles**

A circular helix, (i.e. one with constant radius) has constant band curvature and constant torsion.

### Parametric equation

**parametric curveparametricparametric equations**

The following parametrisation in Cartesian coordinates defines a particular helix, Perhaps the simplest equations for one is

describes a three-dimensional curve, the helix, with a radius of a and rising by 2πb units per turn.

### Pitch space

**harmonic distancepitch latticetonal space**

In music, pitch space is often modeled with helices or double helices, most often extending out of a circle such as the circle of fifths, so as to represent octave equivalency.

M.W. Drobisch (1855) was the first to suggest a helix (i.e. the spiral of fifths) to represent octave equivalence and recurrence (Lerdahl, 2001), and hence to give a model of pitch space.

### Hemihelix

A hemihelix is a quasi-helical curved geometric shape characterized by repeated tendril perversions.

### Collagen helix

**collagen triple helixcollagen's triple helix structuretriple helix**

The pyrrolidine rings keep out of each other’s way when the polypeptide chain assumes this extended helical form, which is much more open than the tightly coiled form of the alpha helix.

### Differentiable manifold

**smooth manifoldsmoothdifferential manifold**

A helix, plural helixes or helices, is a type of smooth space curve, i.e. a curve in three-dimensional space.

### Three-dimensional space

**three-dimensional3Dthree dimensions**

A helix, plural helixes or helices, is a type of smooth space curve, i.e. a curve in three-dimensional space.

### Tangent

**tangent linetangentialtangents**

It has the property that the tangent line at any point makes a constant angle with a fixed line called the axis.

### Angle

**acute angleobtuse angleoblique**

It has the property that the tangent line at any point makes a constant angle with a fixed line called the axis.