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The representation of the Fermat spiral in polar coordinates (r, φ) is given by the equation = for φ ≥ 0. The parameter is a scaling factor affecting the size of the spiral but not its shape. The two choices of sign give the two branches of the spiral, which meet smoothly at the origin.
A logarithmic spiral, equiangular spiral, or growth spiral is a self-similar spiral curve that often appears in nature. The first to describe a logarithmic spiral was Albrecht Dürer (1525) who called it an "eternal line" ("ewige Linie").
Some key events in Earth's history are marked on the diagram, including major extinction events, global scale glaciations, the initiation of permanent atmospheric oxygen, the formation of the moon, and the formation of Earth's magnetic field. The outer spiral arcs show components of the evolution of life on Earth.
The Archimedean spiral (also known as Archimedes' spiral, the arithmetic spiral) is a spiral named after the 3rd-century BC Greek mathematician Archimedes. The term Archimedean spiral is sometimes used to refer to the more general class of spirals of this type (see below), in contrast to Archimedes' spiral (the specific arithmetic spiral of ...
The Ulam spiral or prime spiral is a graphical depiction of the set of prime numbers, devised by mathematician Stanisław Ulam in 1963 and popularized in Martin Gardner's Mathematical Games column in Scientific American a short time later. [1] It is constructed by writing the positive integers in a square spiral and specially marking the prime ...
A double-end Euler spiral. The curve continues to converge to the points marked, as t tends to positive or negative infinity. An Euler spiral is a curve whose curvature changes linearly with its curve length (the curvature of a circular curve is equal to the reciprocal of the radius). This curve is also referred to as a clothoid or Cornu spiral.
A simple spiral approximates of a portion of an archimedean spiral. A general spirolateral allows positive and negative angles. A spirolateral which completes in one turn is a simple polygon , while requiring more than 1 turn is a star polygon and must be self-crossing. [ 2 ]
In the geometry of spirals, the pitch angle [1] or pitch [2] of a spiral is the angle made by the spiral with a circle through one of its points, centered at the center of the spiral. Equivalently, it is the complementary angle to the angle made by the vector from the origin to a point on the spiral, with the tangent vector of the spiral at the ...