Welcome to Spiral Sound
A spiral is typically a planar curve (that is, flat), like the groove on a record or the arms of a spiral galaxy. A helix, on the other hand, is a three-dimensional coil that runs along the surface of a cylinder, like a screw.
There are many instances where in colloquial usage spiral is used as a synonym for helix, notably spiral staircase and spiral binding of books.
Mathematically this is incorrect but the terms are increasing in common usage.
A two-dimensional spiral may be described most easily using polar coordinates, where the radius r is a continuous monotonic function of angle θ. The circle would be regarded as a degenerate case (the function not being strictly monotonic, but rather constant).
A Fibonacci spiral created by drawing arcs connecting the opposite corners of squares in the Fibonacci tiling; this one uses squares of sizes 1, 1, 2, 3, 5, 8, 13, 21, and 34
In geometry, a golden spiral is a logarithmic spiral whose growth factor b is related to φ, the golden ratio.[1] Specifically, a golden spiral gets wider (or further from its origin) by a factor of φ for every quarter turn it makes.
The spiral plays a certain role in symbolism, and appears in megalithic art, notably in the Newgrange tomb or in many Galician petroglyphs such as the one in Mogor. See also triple spiral.
While scholars are still debating the subject, there is a growing acceptance that the simple spiral, when found in Chinese art, is an early symbol for the sun. Roof tiles dating back to the Tang Dynasty with this symbol have been found west of the ancient city of Chang’an (modern-day Xian).
The spiral is the most ancient symbol found on every civilized continent. Due to its appearance at burial sites across the globe, the spiral most likely represented the “life-death-rebirth” cycle. Similarly, the spiral symbolized the sun, as ancient people thought the sun was born each morning, died each night, and was reborn the next morning.
Spirals are also a symbol of hypnosis, stemming from the cliché of people and cartoon characters being hypnotized by staring into a spinning spiral (One example being Kaa in Disney’s The Jungle Book). They are also used as a symbol of dizziness, where the eyes of a cartoon character, especially in anime and manga, will turn into spirals to show they are dizzy or dazed. The spiral is also a prominent symbol in the anime Gurren Lagann, where it symbolizes the double helix structure of DNA, representing biological evolution, and the spiral structure of a galaxy, representing universal evolution.
The study of spirals in nature have a long history, Christopher Wren observed that many shells form a logarithmic spiral. Jan Swammerdam observed the common mathematical characteristics of a wide range of shells from Helix to Spirula and Henry Nottidge Moseley described the mathematics of univalve shells. D’Arcy Wentworth Thompson’s On Growth and Form gives extensive treatment to these spirals. He describes how shells are formed by rotating a closed curve around a fixed axis, the shape of the curve remains fixed but its size grows in a geometric progression. In some shell such as Nautilus and ammonites the generating curve revolves in a plane pirpendicular to the axis and the shell will form a planer discoid shape. In others it follows a skew path forming a helico-spiral pattern.
Spirals in plants and animals are frequently described as whorls.
A model for the pattern of florets in the head of a sunflower was proposed by H Vogel. This has the form
\theta = n \times 137.5^{\circ}, r = c \sqrt{n}
where n is the index number of the floret and c is a constant scaling factor, and is a form of Fermat’s spiral. The angle 137.5° is related to the golden ratio and gives a close packing of florets.[2]
The spiral also represents infinance, or ‘infinity.’ Starting at a single point, and revolving outwardly until the end of the universe. Because of this, some civilizations believe that the Spiral is a pathway to the afterlife.
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