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Archimedean spiral

The Archimedean spiral (also known as the arithmetic spiral) 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


r = a + bθ

with real numbers a and b. Changing the parameter a will turn the spiral, while b controls the distance between successive turnings.

Archimedes described such a spiral in his book On Spirals.

Usage examples of "archimedean spiral".

As the ship approaches the Sun, it will monitor the magnetic field direction and determine if the Archimedean spiral of the solar wind is oriented outward.

The beanstalk was moving faster now, arcing in towards Earth along the smooth curve of an Archimedean spiral.

Since his demob from the Fleet, a year after all the hysteria of the Canes Venatici incident had come to nothing but the same kind of worn diplomacy that had begun it, he had worked all over the sky, traveling a slow Archimedean spiral in three dimensions, tracking in from Venatici through the Crow and the Heavy Stars.