List of spirals
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] |
References
- "Fermat spiral - Encyclopedia of Mathematics". www.encyclopediaofmath.org. Retrieved 18 February 2019.
- Weisstein, Eric W. "Logarithmic Spiral". mathworld.wolfram.com. Wolfram Research, Inc. Retrieved 18 February 2019.
- Weisstein, Eric W. "Nielsen's Spiral". mathworld.wolfram.com. Wolfram Research, Inc. Retrieved 18 February 2019.
- "Tractrix spiral". www.mathcurve.com. Retrieved 2019-02-23.
- "Conical spiral of Pappus". www.mathcurve.com. Retrieved 28 February 2019.
- "Doppler spiral". www.mathcurve.com. Retrieved 28 February 2019.
- "Atzema spiral". www.2dcurves.com. Retrieved 11 March 2019.
- "atom-spiral". www.2dcurves.com. Retrieved 11 March 2019.
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