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An Archimedean spiral is, for example, generated while coiling a carpet. [6] A hyperbolic spiral appears as image of a helix with a special central projection (see diagram). A hyperbolic spiral is some times called reciproke spiral, because it is the image of an Archimedean spiral with a circle-inversion (see below). [7]
For <, spiral-ring pattern; =, regular spiral; >, loose spiral. R is the distance of spiral starting point (0, R) to the center. R is the distance of spiral starting point (0, R) to the center. The calculated x and y have to be rotated backward by ( − θ {\displaystyle -\theta } ) for plotting.
In spiral galaxies, the spiral arms do have the shape of approximate logarithmic spirals, a pattern that can be theoretically shown to result from a disturbance in a uniformly rotating mass of stars. Like the stars, the spiral arms rotate around the center, but they do so with constant angular velocity .
A spiral staircase in the Cathedral of St. John the Divine.Several helical curves in the staircase project to hyperbolic spirals in its photograph.. A hyperbolic spiral is a type of spiral with a pitch angle that increases with distance from its center, unlike the constant angles of logarithmic spirals or decreasing angles of Archimedean spirals.
The Archimedean spiral (also known as Archimedes' spiral, the arithmetic spiral) is a spiral named after the 3rd-century BC Greek mathematician Archimedes. The term Archimedean spiral is sometimes used to refer to the more general class of spirals of this type (see below), in contrast to Archimedes' spiral (the specific arithmetic spiral of ...
Spiral galaxies form a class of galaxy originally described by Edwin Hubble in his 1936 work The Realm of the Nebulae [1] and, as such, form part of the Hubble sequence. Most spiral galaxies consist of a flat, rotating disk containing stars , gas and dust , and a central concentration of stars known as the bulge .
[13] [23] Spiral arms with a small pitch angle are called tightly wound, while those with a larger pitch angle are called open. [24] The shape of spiral arms is often described in a simplified manner as a logarithmic spiral. However, spiral arms may also be described as an Archimedean or hyperbolic spiral. In the case of the logarithmic spiral ...
Theodor Benfey's arrangement is an example of a continuous (spiral) table. First published in 1964, it explicitly showed the location of lanthanides and actinides.The elements form a two-dimensional spiral, starting from hydrogen, and folding their way around two peninsulas, the transition metals, and lanthanides and actinides.