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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 ...
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).
The term algebra is derived from the Arabic word al-jabr meaning 'the reunion of broken parts' that he used for naming one of these methods in the title of his main treatise. [31] [32] Algebra became an area in its own right only with François Viète (1540–1603), who introduced the use of variables for representing unknown or unspecified ...
The spiral is started with an isosceles right triangle, with each leg having unit length.Another right triangle (which is the only automedian right triangle) is formed, with one leg being the hypotenuse of the prior right triangle (with length the square root of 2) and the other leg having length of 1; the length of the hypotenuse of this second right triangle is the square root of 3.
The representation of the Fermat spiral in polar coordinates (r, φ) is given by the equation = for φ ≥ 0. The parameter is a scaling factor affecting the size of the spiral but not its shape. The two choices of sign give the two branches of the spiral, which meet smoothly at the origin.
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.
In algebraic geometry, the sinusoidal spirals are a family of curves defined by the equation in polar coordinates r n = a n cos ( n θ ) {\displaystyle r^{n}=a^{n}\cos(n\theta )\,} where a is a nonzero constant and n is a rational number other than 0.
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