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Spiral of Archimedes
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spiral of Archimedes Figure 22: Family of curves derived from rm = amΘ. (A) Spiral of Archimedes; (B) Fermat's spiral; (C) hyperbolic spiral; (D) lituus.
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Spiral of Archimedes

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spiral of Archimedes
spiral of Archimedes Archimedes only used geometry to study the curve that bears his name. In modern notation it is given by the equation r = aθ, in which a is a constant, r is the length of the radius from the centre, or beginning, of the spiral, and θ is the angular position (amount of rotation) of the radius.

The spiral of Archimedes is a plane curve generated by a point moving away from a fixed point at a constant rate while the radius vector rotates at a constant rate. Its equation in polar coordinates is (\rho = a\theta), where (a) is a constant and (\theta) represents the angle of rotation. The distance between successive turns of this spiral is constant, similar to the grooves on a phonograph record. While the ancient Greek mathematician Archimedes did not discover this spiral, he utilized it in his work On Spirals around 225 BCE to explore geometric problems like squaring the circle and trisecting an angle.123

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  1. Archimedean spiral
  2. Archimedes
  3. spiral of Archimedes
  4. spiral

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