Applications
One method of squaring the circle, by relaxing the strict limitations on the use of straightedge and compass in ancient Greek geometric proofs, makes use of an Archimedean spiral.
The Archimedean spiral has a variety of real-world applications. Scroll compressors, made from two interleaved Archimedean spirals of the same size, are used for compressing liquids and gases. The coils of watch balance springs and the grooves of very early gramophone records form Archimedean spirals, making the grooves evenly spaced and maximizing the amount of music that could be fitted onto the record (although this was later changed to allow better sound quality). Asking for a patient to draw an Archimedean spiral is a way of quantifying human tremor; this information helps in diagnosing neurological diseases. Archimedean spirals are also used in digital light processing (DLP) projection systems to minimize the "rainbow effect", making it look as if multiple colors are displayed at the same time, when in reality red, green, and blue are being cycled extremely quickly. Additionally, Archimedean spirals are used in food microbiology to quantify bacterial concentration through a spiral platter. They also are used to model the pattern that occurs in a roll of paper or tape of constant thickness wrapped around a cylinder.
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