This list of spirals includes named spirals that have been described mathematically.
|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|
|hyperbolic spiral||1704||also reciprocal spiral|
|logarithmic spiral||1638||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|
|helix||a 3-dimensional spiral|
|Rhumb line (also loxodrome)||type of spiral drawn on a sphere|
|Nielsen's spiral||1993||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.|
|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|
|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. Please check the references for the detail|
In mathematics, a unary operation is an operation with only one operand, i.e. a single input. This is in contrast to binary operations, which use two operands. An example is the function f : A → A, where A is a set. The function f is a unary operation on A.
In mathematics and logic, an axiomatic system is any set of axioms from which some or all axioms can be used in conjunction 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.
7 (seven) is the natural number following 6 and preceding 8. It is the only prime number preceding a cube, and is often considered lucky in Western culture, and is often seen as highly symbolic.
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.
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Eric Wolfgang Weisstein is an encyclopedist who created and maintains MathWorld and Eric Weisstein's World of Science (ScienceWorld). He is the author of the CRC Concise Encyclopedia of Mathematics. He works for Wolfram Research, Inc.
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In geometry, the gyrobifastigium is the 26th Johnson solid (J26). It can be constructed by joining two face-regular triangular prisms along corresponding square faces, giving a quarter-turn to one prism. It is the only Johnson solid that can tile three-dimensional space.
In mathematics, a mathematical object is said to satisfy a property locally, if the property is satisfied on some limited, immediate portions of the object.
In mathematics, an interprime is the average of two consecutive odd primes. For example, 9 is an interprime because it is the average of 7 and 11. The first interprimes are:
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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.
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:
In geometry, a polytope of dimension 3 or higher is isohedral or face-transitive when 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 faces A and B, there must be a symmetry of the entire solid by rotations and reflections that maps A onto B. For this reason, convex isohedral polyhedra are the shapes that will make fair dice.
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In geometry, an edge is a particular type of line segment joining two vertices in a polygon, polyhedron, or higher-dimensional polytope. In a polygon, an edge is a line segment on the boundary, and is often called a side. In a polyhedron or more generally a polytope, an edge is a line segment where two faces meet. A segment joining two vertices while passing through the interior or exterior is not an edge but instead is called a diagonal.
In geometry, a Devil's curve is a curve defined in the Cartesian plane by an equation of the form
In mathematics, the Ernst equation is an integrable non-linear partial differential equation, named after the American physicist Frederick J. Ernst.