This list is incomplete; you can help by adding missing items. (February 2019) |
This list of spirals includes named spirals that have been described mathematically.
Image | Name | First described | Equation | Comment | |
---|---|---|---|---|---|
circle | The trivial spiral | ||||
Archimedean spiral | c. 320 BC | ||||
Euler spiral | also called Cornu spiral or polynomial spiral | ||||
Fermat's spiral (also parabolic spiral) | 1636^{[1]} | ||||
hyperbolic spiral | 1704 | also reciprocal spiral | |||
lituus | 1722 | ||||
logarithmic spiral | 1638^{[2]} | approximations of this are found in nature | |||
Fibonacci spiral | circular arcs connecting the opposite corners of squares in the Fibonacci tiling | approximation of the golden spiral | |||
golden spiral | special case of the logarithmic spiral | ||||
Spiral of Theodorus (also Pythagorean spiral) | an polygonal spiral composed of contiguous right triangles, that approximates the Archimedean spiral | ||||
involute | 1673 | ||||
helix | a 3-dimensional spiral | ||||
Rhumb line (also loxodrome) | type of spiral drawn on a sphere | ||||
Cotes's spiral | 1722 | ||||
Poinsot's spirals | |||||
Nielsen's spiral | 1993^{[3]} | A variation of Euler spiral, using sine integral and cosine integrals | |||
Polygonal spiral | special case approximation of logarithmic spiral | ||||
Fraser's Spiral | 1908 | Optical illusion based on spirals | |||
Conchospiral | three-dimensional spiral on the surface of a cone. | ||||
Calkin–Wilf spiral | |||||
Ulam spiral (also prime spiral) | 1963 | ||||
Sack's spiral | 1994 | variant of Ulam spiral and Archimedean spiral. | |||
Seiffert's spiral | spiral curve on the surface of a sphere | ||||
Tractrix spiral | 1704^{[4]} | ||||
Pappus spiral | 1779 | 3D conical spiral studied by Pappus and Pascal^{[5]} | |||
doppler spiral | 2D projection of Pappus spiral^{[6]} | ||||
Atzema spiral | The curve that has a catacaustic forming a circle. Approximates the Archimedean spiral.^{[7]} | ||||
Atomic spiral | 2002 | This spiral has two asymptotes; one is the circle of radius 1 and the other is the line ^{[8]} | |||
Galactic spiral | 2019 | 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 . For , spiral-ring pattern; regular spiral; loose spiral. R is the distance of spiral starting point (0, R) to the center. The calculated x and y have to be rotated backward by () for plotting. Please check the references for the detail^{[9]} |