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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 ...
An Archimedean spiral is, for example, generated while coiling a carpet. [5] A hyperbolic spiral appears as image of a helix with a special central projection (see diagram). A hyperbolic spiral is some times called reciproke spiral, because it is the image of an Archimedean spiral with a circle-inversion (see below). [6]
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.
Logarithmic spiral bevel gears are a type of spiral bevel gear whose gear tooth centerline is a logarithmic spiral. A logarithmic spiral has the advantage of providing equal angles between the tooth centerline and the radial lines, which gives the meshing transmission more stability.
The Archimedean spiral is a spiral discovered by Archimedes which can also be expressed as a simple polar equation. It is represented by the equation r ( φ ) = a + b φ . {\displaystyle r(\varphi )=a+b\varphi .}
An osculating circle Osculating circles of the Archimedean spiral, nested by the Tait–Kneser theorem. "The spiral itself is not drawn: we see it as the locus of points where the circles are especially close to each other." [1] An osculating circle is a circle that best approximates the curvature of a curve at a specific point.
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.
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.