This list of spirals includes named spirals that have been described mathematically.
Image Name First described Equation Comment Circle The trivial spiral Archimedean spiral (also arithmetic spiral) Fermat's spiral (also parabolic spiral) 1636 Encloses equal area per turn Doyle spiral 19801990 circle packing, using circles of structured radii Euler spiral (also or polynomial spiral) 1696 Using Fresnel integrals Hyperbolic spiral (also reciprocal spiral) 1704 Lituus 1722 Logarithmic spiral (also known as equiangular spiral) 1638 Constant pitch angle. 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 known as Pythagorean spiral) Contiguous right triangles composed of one leg with unit length and the other leg being the hypotenuse of the prior triangle Approximates the Archimedean spiral Involute 1673 Involutes of a circle appear like Archimedean spirals Helix A three-dimensional spiral Rhumb line (also loxodrome) Type of spiral drawn on a sphere Cotes's spiral 1722 Solution to the two-body problem for an inverse-cube central force Poinsot's spirals Nielsen's spiral 1993 A variation of Euler spiral, using sine integral and cosine integrals Polygonal spiral Special case approximation of arithmetic or logarithmic spiral Fraser's Spiral 1908 Optical illusion based on spirals Conchospiral A three-dimensional spiral on the surface of a cone. Calkin–Wilf spiral Ulam spiral (also prime spiral) 1963 Sacks spiral 1994 Variant of Ulam spiral and Archimedean spiral. Seiffert's spiral 2000 Spiral curve on the surface of a sphere using the Jacobi elliptic functions Tractrix spiral 1704 Pappus spiral 1779 3D conical spiral studied by Pappus and Pascal Doppler spiral 2D projection of Pappus spiral Atzema spiral The curve that has a catacaustic forming a circle. Approximates the Archimedean spiral. Atomic spiral 2002 This spiral has two asymptotes; one is the circle of radius 1 and the other is the line 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.
See also
Catherine wheel (firework) List of spiral galaxies Parker spiral Spirangle Spirograph
References