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The art of several cultures includes spiral patterns made up of “medallions” of spiral pieces, which are then linked together to make a repeating Euclidean pattern. We have shown simple examples from two cultures.
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. As this curve widens, it approaches an asymptotic line.
The differential spiral equations were developed to simulate the spiral arms of disc galaxies, have 4 solutions with three different cases: <, =, >, the spiral patterns are decided by the behavior of the parameter .
In physics and in the mathematics of plane curves, a Cotes's spiral (also written Cotes' spiral and Cotes spiral) is one of a family of spirals classified by Roger Cotes.
The reciprocal spiral is the locus of the point M of a variable circle centred on O cutting the axis Ox at A such that the length of the arc AM is a constant equal to a. Like the logarithmic spiral, it has a spiralling branch with an asymptotic point, but, contrary to the logarithmic spiral, its length is infinite.
If n = -1, we obtain the reciprocal spiral. It is also often called the hyperbolic spiral since r = a/B is the equation of a hyperbola (if r and B are interpreted as Cartesian coordinates), but we wish to avoid
Hyperbolic spiral is also called reciprocal spiral, because it is the inverse curve of Archemedes' spiral, with inversion center at the center. The inversion curve of all Archemedean spirals with respect to a circle on center is another Archemedean spiral.
