List of spirals

Last updated

This list of spirals includes named spirals that have been described mathematically.

ImageNameFirst describedEquationComment
Circle - black simple.svg
circle The trivial spiral
Archimedean spiral.svg
Archimedean spiral (also arithmetic spiral)c.320 BC
Fermat's spiral.svg
Fermat's spiral (also parabolic spiral)1636 [1]
Cornu Spiral.svg
Euler spiral (also Cornu spiral or polynomial spiral)1696 [2] using Fresnel integrals [3]
Hyperspiral.svg
hyperbolic spiral (also reciprocal spiral)1704
Lituus.svg
lituus 1722
Logarithmic Spiral Pylab.svg
logarithmic spiral (also known as equiangular spiral)1638 [4] Approximations of this are found in nature
Fibonacci spiral.svg
Fibonacci spiral circular arcs connecting the opposite corners of squares in the Fibonacci tilingapproximation of the golden spiral
Golden spiral in rectanglesflip.png
golden spiral special case of the logarithmic spiral
Spiral of Theodorus.svg
Spiral of Theodorus (also known as Pythagorean spiral)c.500 BCcontiguous right triangles composed of one leg with unit length and the other leg being the hypotenuse of the prior triangleapproximates the Archimedean spiral
Involute of circle.png
involute 1673

involutes of a circle appear like Archimedean spirals
Helix.svg
helix a 3-dimensional spiral
Loxodrome.png
Rhumb line (also loxodrome)type of spiral drawn on a sphere
Epi half spirals.svg
Cotes's spiral 1722Solution to the two-body problem for an inverse-cube central force
PoinsotSpiral.svg
Poinsot's spirals
Nielsen's spiral.png
Nielsen's spiral 1993 [5]
A variation of Euler spiral, using sine integral and cosine integrals
Polygon spiral.png
Polygonal spiral special case approximation of arithmetic or logarithmic spiral
Fraser spiral.svg
Fraser's Spiral 1908Optical illusion based on spirals
Conchospiral.svg
Conchospiral three-dimensional spiral on the surface of a cone.
Calkin-Wilf spiral.svg
Calkin–Wilf spiral
Ulam spiral howto all numbers.svg
Ulam spiral (also prime spiral)1963
Sacks spiral.svg
Sack's spiral 1994variant of Ulam spiral and Archimedean spiral.
Seiffert's spiral 2000 [6] spiral curve on the surface of a sphere

using the Jacobi elliptic functions [7]

Tractrix Spiral.svg
Tractrix spiral1704 [8]
Pappus spiral 17793D conical spiral studied by Pappus and Pascal [9]
Doppler spiral.svg
doppler spiral 2D projection of Pappus spiral [10]
Atzema spiral.svg
Atzema spiral The curve that has a catacaustic forming a circle. Approximates the Archimedean spiral. [11]
AtomicSpiral.svg
Atomic spiral 2002This spiral has two asymptotes; one is the circle of radius 1 and the other is the line [12]
Galaxy NGC1079.jpg
Galactic spiral 2019The 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. [13] [ predatory publisher ]

See also

Related Research Articles

<span class="mw-page-title-main">Great circle</span> Spherical geometry analog of a straight line

In mathematics, a great circle or orthodrome is the circular intersection of a sphere and a plane passing through the sphere's center point.

In mathematics and logic, an axiomatic system is any set of primitive notions and axioms to logically derive theorems. A theory is a consistent, relatively-self-contained body of knowledge which usually contains an axiomatic system and all its derived theorems. An axiomatic system that is completely described is a special kind of formal system. A formal theory is an axiomatic system that describes a set of sentences that is closed under logical implication. A formal proof is a complete rendition of a mathematical proof within a formal system.

6 (six) is the natural number following 5 and preceding 7. It is a composite number and the smallest perfect number.

MathWorld is an online mathematics reference work, created and largely written by Eric W. Weisstein. It is sponsored by and licensed to Wolfram Research, Inc. and was partially funded by the National Science Foundation's National Science Digital Library grant to the University of Illinois at Urbana–Champaign.

<span class="mw-page-title-main">Wolfram Research</span> American multinational company

Wolfram Research, Inc. is an American multinational company that creates computational technology. Wolfram's flagship product is the technical computing program Wolfram Mathematica, first released on June 23, 1988. Other products include WolframAlpha, Wolfram SystemModeler, Wolfram Workbench, gridMathematica, Wolfram Finance Platform, webMathematica, the Wolfram Cloud, and the Wolfram Programming Lab. Wolfram Research founder Stephen Wolfram is the CEO. The company is headquartered in Champaign, Illinois, United States.

Eric Wolfgang Weisstein is an American scientist, mathematician, and encyclopedist who created and maintains the encyclopedias MathWorld and ScienceWorld. In addition, he is the author of the CRC Concise Encyclopedia of Mathematics. He works for Wolfram Research.

An antimagic square of order n is an arrangement of the numbers 1 to n2 in a square, such that the sums of the n rows, the n columns and the two diagonals form a sequence of 2n + 2 consecutive integers. The smallest antimagic squares have order 4. Antimagic squares contrast with magic squares, where each row, column, and diagonal sum must have the same value.

<span class="mw-page-title-main">Jean Gaston Darboux</span> French mathematician

Jean-Gaston Darboux FAS MIF FRS FRSE was a French mathematician.

<span class="mw-page-title-main">Elongated pentagonal orthobicupola</span> 38th Johnson solid

In geometry, the elongated pentagonal orthobicupola or cantellated pentagonal prism is one of the Johnson solids. As the name suggests, it can be constructed by elongating a pentagonal orthobicupola by inserting a decagonal prism between its two congruent halves. Rotating one of the cupolae through 36 degrees before inserting the prism yields an elongated pentagonal gyrobicupola.

Edgar van Tuyll was the chief quantitative strategist of Pictet & Cie, where he worked from 1995 to 2017. He has been extensively quoted by the media for his prediction of the 2000 Dot-com bubble crash and of the bull market beginning in March 2003. He is among the minority of strategists expecting a US recession in 2007–2008. His website Links to unsolved problems, prizes and research is top ranked by Google for list of unsolved problems in mathematics and physics. He is the author of several entries in the "CRC Concise Encyclopedia of Mathematics", Chapman & Hall, 2002. He is the grandson of Antti Johannes Rantamaa.

<span class="mw-page-title-main">Operation (mathematics)</span> Addition, multiplication, division, ...

In mathematics, an operation is a function which takes zero or more input values to a well-defined output value. The number of operands is the arity of the operation.

<span class="mw-page-title-main">Golden triangle (mathematics)</span> Isosceles triangle in which the duplicated side is in the golden ratio to the base side

A golden triangle, also called a sublime triangle, is an isosceles triangle in which the duplicated side is in the golden ratio to the base side:

<span class="mw-page-title-main">Isohedral figure</span> ≥2-dimensional tessellation or ≥3-dimensional polytope with identical faces

In geometry, a tessellation of dimension 2 or higher, or a polytope of dimension 3 or higher, is isohedral or face-transitive if all its faces are the same. More specifically, all faces must be not merely congruent but must be transitive, i.e. must lie within the same symmetry orbit. In other words, for any two faces A and B, there must be a symmetry of the entire figure by translations, rotations, and/or reflections that maps A onto B. For this reason, convex isohedral polyhedra are the shapes that will make fair dice.

<span class="mw-page-title-main">Ed Pegg Jr.</span> American mathematician

Edward Taylor Pegg Jr. is an expert on mathematical puzzles and is a self-described recreational mathematician. He wrote an online puzzle column called Ed Pegg Jr.'s Math Games for the Mathematical Association of America during the years 2003–2007. His puzzles have also been used by Will Shortz on the puzzle segment of NPR's Weekend Edition Sunday. He was a fan of Martin Gardner and regularly participated in Gathering 4 Gardner conferences. In 2009 he teamed up with Tom M. Rodgers and Alan Schoen to edit two Gardner tribute books.

Differential equations, in particular Euler equations, rose in prominence during World War II in calculating the accurate trajectory of ballistics, both rocket-propelled and gun or cannon type projectiles. Originally, mathematicians used the simpler calculus of earlier centuries to determine velocity, thrust, elevation, curve, distance, and other parameters.

The tee, also called down tack or verum, is a symbol used to represent:

In mathematics, the word constant conveys multiple meanings. As an adjective, it refers to non-variance ; as a noun, it has two different meanings:

<span class="mw-page-title-main">Spherical shell</span> Three-dimensional geometric shape

In geometry, a spherical shell is a generalization of an annulus to three dimensions. It is the region of a ball between two concentric spheres of differing radii.

Seiffert's spherical spiral is a curve on a sphere made by moving on the sphere with constant speed and angular velocity with respect to a fixed diameter. If the selected diameter is the line from the north pole to the south pole, then the requirement of constant angular velocity means that the longitude of the moving point changes at a constant rate. The cylindrical coordinates of the varying point on this curve are given by the Jacobian elliptic functions.

References

  1. "Fermat spiral - Encyclopedia of Mathematics". www.encyclopediaofmath.org. Retrieved 18 February 2019.
  2. Weisstein, Eric W. "Cornu Spiral". mathworld.wolfram.com. Retrieved 2023-11-22.
  3. Weisstein, Eric W. "Fresnel Integrals". mathworld.wolfram.com. Retrieved 2023-01-31.
  4. Weisstein, Eric W. "Logarithmic Spiral". mathworld.wolfram.com. Wolfram Research, Inc. Retrieved 18 February 2019.
  5. Weisstein, Eric W. "Nielsen's Spiral". mathworld.wolfram.com. Wolfram Research, Inc. Retrieved 18 February 2019.
  6. Weisstein, Eric W. "Seiffert's Spherical Spiral". mathworld.wolfram.com. Retrieved 2023-01-31.
  7. Weisstein, Eric W. "Seiffert's Spherical Spiral". mathworld.wolfram.com. Retrieved 2023-01-31.
  8. "Tractrix spiral". www.mathcurve.com. Retrieved 2019-02-23.
  9. "Conical spiral of Pappus". www.mathcurve.com. Retrieved 28 February 2019.
  10. "Doppler spiral". www.mathcurve.com. Retrieved 28 February 2019.
  11. "Atzema spiral". www.2dcurves.com. Retrieved 11 March 2019.
  12. "atom-spiral". www.2dcurves.com. Retrieved 11 March 2019.
  13. Pan, Hongjun. "New spiral" (PDF). www.arpgweb.com. Retrieved 5 March 2021.