Curves Archimedean Spiral

Archimedean Spiral

This graph is interactive. Drag the black dots in the top scale ( value of a , b ) to change the shape of the Archimedean spiral.

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Archimedean Spiral - The details

An Archimedean Spiral is a curve defined by a polar equation of the form r = θa, with special names being given for certain values of a. For example if a = 1, so r = θ, then it is called Archimedes' Spiral. The Archimedean spiral (also known as the arithmetic spiral or spiral of Archimedes) is a spiral named after the 3rd century BC Greek mathematician Archimedes. It is the locus of points corresponding to the locations over time of a point moving away from a fixed point with a constant speed along a line which rotates with constant angular velocity.

Equivalently, in polar coordinates (r, θ) it can be described by the equation :

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