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On Spirals (Greek: Περὶ ἑλίκων) is a treatise by Archimedes, written around 225 BC. [1] Notably, Archimedes employed the Archimedean spiral in this book to square the circle and trisect an angle .
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 ...
For <, spiral-ring pattern; =, regular spiral; >, loose spiral. R is the distance of spiral starting point (0, R) to the center. R is the distance of spiral starting point (0, R) to the center. The calculated x and y have to be rotated backward by ( − θ {\displaystyle -\theta } ) for plotting.
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").
Archimedes' other mathematical achievements include deriving an approximation of pi (π), defining and investigating the Archimedean spiral, and devising a system using exponentiation for expressing very large numbers.
A triskelion or triskeles is an ancient motif consisting either of a triple spiral exhibiting rotational symmetry or of other patterns in triplicate that emanate from a common center. The spiral design can be based on interlocking Archimedean spirals , or represent three bent human limbs.
Conical spiral with an archimedean spiral as floor projection Floor projection: Fermat's spiral Floor projection: logarithmic spiral Floor projection: hyperbolic spiral. In mathematics, a conical spiral, also known as a conical helix, [1] is a space curve on a right circular cone, whose floor projection is a plane spiral.
A spiral staircase in the Cathedral of St. John the Divine.Several helical curves in the staircase project to hyperbolic spirals in its photograph.. A hyperbolic spiral is a type of spiral with a pitch angle that increases with distance from its center, unlike the constant angles of logarithmic spirals or decreasing angles of Archimedean spirals.