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Group Members: Brent Doerner's Decibel
All Music Guide:
The Canadian heavy metal band Helix formed in 1974 in Kitchener, Ontario; comprising singer Brian Vollmer, guitarists Brent Doerner and Paul Hackman, bassist Keith Zurbrigg, and drummer Brian Doerner, the group debuted in 1979 with Breaking Loose. White Lace & Black Leather followed two years later, and was the first Helix release to feature new bassist Mike Uzilac and drummer Leo Nebudeck; with 1983's No Rest for the Wicked, the group signed to Capitol, substituting Nebudeck for another new drummer, Greg "Fritz" Hinz. Bassist Daryl Gray replaced Uzilac in time for the follow-up, Walkin' the Razor's Edge, which spawned the hit "Rock You"; 1985's Long Way to Heaven, meanwhile, topped the charts in Sweden. After touring in support of 1987's Wild in the Streets, Brent Doerner quit Helix, and the remaining quartet resurfaced with Back for Another Taste. In 1992, Hackman was killed when the group's van rolled down a 40-foot embankment after a concert in Vancouver; Helix forged on, however, with Brent Doerner returning to the lineup long enough to record 1993's It's a Business Doing Pleasure, which also featured guitarist Greg Frazer. In 1998, Helix -- now comprising Vollmer, Gray, Hinz, and guitarists Mark Chichkan and Gary Borden -- issued Half Alive. A collection of B Sides arrived in 2002, followed by the full-length Rockin' in My Outer Space in 2004. Power of Rock N Roll arrived in 2007.
Wikipedia:This article is about the shape. For the shape of deoxyribonucleic acid, see Double helix. For other uses, see Helix (disambiguation).
A helix (pl: helixes or helices) is a type of smooth space curve, i.e. a curve in three-dimensional space. It has the property that the tangent line at any point makes a constant angle with a fixed line called the axis. Examples of helixes are coil springs and the handrails of spiral staircases. A "filled-in" helix – for example, a spiral ramp – is called a helicoid. 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 word helix comes from the Greek word ἕλιξ, "twisted, curved".Weisstein, Eric W., "Helicoid", MathWorld. ἕλιξ, Henry George Liddell, Robert Scott, A Greek-English Lexicon, on Perseus
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.
Most hardware screw threads are right-handed helices. The alpha helix in biology as well as the and forms of DNA are also right-handed helices. The Z form of DNA is left-handed.
The pitch of a helix is the width 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 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. An example is the Corkscrew roller coaster at Cedar Point amusement park.
A circular helix, (i.e. one with constant radius) has constant band curvature and constant torsion.
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.
Some curves found in nature consist of multiple helices of different handedness joined together by transitions known as tendril perversions."Double Helix" by Sándor Kabai, Wolfram Demonstrations Project. O'Neill, B. Elementary Differential Geometry, 1961 pg 72 O'Neill, B. Elementary Differential Geometry, 1961 pg 74 Izumiya, S. and Takeuchi, N. (2004) New special curves and developable surfaces. Turk J Math, 28:153–163. Menninger, T. (2013), An Explicit Parametrization of the Frenet Apparatus of the Slant Helix. arXiv:1302.3175.
In mathematics, a helix is a curve in 3-dimensional space. The following parametrisation in Cartesian coordinates defines a helix:
As the parameter increases, the point ((),(),()) traces a right-handed helix of pitch 2π and radius 1 about the -axis, in a right-handed coordinate system.
In cylindrical coordinates (, θ, ), the same helix is parametrised by:
A circular helix of radius and pitch 2πb is described by the following parametrisation:
Another way of mathematically constructing a helix is to plot the complex-valued function as a function of the real number (see Euler's formula). The value of 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 , or components.
Arc length, curvature and torsion
The length of a circular helix of radius and pitch 2πb expressed in rectangular coordinates as
equals , its curvature is
and its torsion isWeisstein, Eric W., "Helix", MathWorld.
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.
Crystal structure of a folded molecular helix reported by Lehn et al. in Helv. Chim. Acta., 2003, 86, 1598–1624.
A natural left-handed helix, made by a climber plant
A charged particle in a uniform magnetic field following a helical path
A helical coil spring