The tombstone of the twentieth-century Swiss mystic and Catholic convert Greek culture and the carved lozenge near the main entrance of the prehistoric Newgrange monument in County Meath, Ireland, with its characteristic iron-age Celtic swirl using the spatial-motion symmetry of an Archimedean spiral from around 3200 BCE.
12.
A rhumb line ( also known as a loxodrome or " spherical spiral " ) is the curve on a sphere traced by a ship with constant revolutions, with the separation between them decreasing as the curve approaches either of the poles, unlike an Archimedean spiral which maintains uniform line-spacing regardless of radius.
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For large " & theta; " a point moves with well-approximated uniform acceleration along the Archimedean spiral while the spiral corresponds 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 ( see contribution from Mikhail Gaichenkov ).
14.
For a cylindrically bent crystal the Bragg planes in the crystal lattice will lie on Archimedean spirals ( with the exception of those orientated tangentially and radially to the curvature of the bend, which are respectively cylindrical and planar ), and the degree of curvature can be determined in a predictable way from the length of the spots and the geometry of the set-up.
15.
Bernoulli chose a figure of a logarithmic spiral and the motto " Eadem mutata resurgo " " ( " Changed and yet the same, I rise again " ) " for his gravestone; the spiral executed by the stonemasons was, however, an Archimedean spiral, [ Jacob Bernoulli ] wrote that the logarithmic spiral may be used as a symbol, either of fortitude and constancy in adversity, or of the human body, which after all its changes, even after death, will be restored to its exact and perfect self . ( Livio 2002 : 116 ).
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