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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.
The spiral is a frequent symbol for spiritual purification, both within Christianity and beyond (one thinks of the spiral as the neo-Platonist symbol for prayer and contemplation, circling around a subject and ascending at the same time, and as a Buddhist symbol for the gradual process on the Path to Enlightenment).
Logarithmic spiral bevel gears are a type of spiral bevel gear whose gear tooth centerline is a logarithmic spiral. A logarithmic spiral has the advantage of providing equal angles between the tooth centerline and the radial lines, which gives the meshing transmission more stability.
Hemihelix, a quasi-helical shape characterized by multiple tendril perversions Tendril perversion (a transition between back-to-back helices) Seiffert's spiral [4]
The shape is infinitely repeated when magnified. In geometry, a golden spiral is a logarithmic spiral whose growth factor is φ, the golden ratio. [1] That is, a golden spiral gets wider (or further from its origin) by a factor of φ for every quarter turn it makes.
In the geometry of spirals, the pitch angle [1] or pitch [2] of a spiral is the angle made by the spiral with a circle through one of its points, centered at the center of the spiral. Equivalently, it is the complementary angle to the angle made by the vector from the origin to a point on the spiral, with the tangent vector of the spiral at the ...
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 ...
The shape of the spirals depends on the growth of the elements generated sequentially. In mature-disc phyllotaxis, when all the elements are the same size, the shape of the spirals is that of Fermat spirals—ideally. That is because Fermat's spiral traverses equal annuli in equal turns. The full model proposed by H. Vogel in 1979 [5] is