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Archimedes' spiral is an Archimedean spiral with polar equation r=atheta. (1) This spiral was studied by Conon, and later by Archimedes in On Spirals about 225 BC. Archimedes ...

Taking the origin as the inversion center, Archimedes' spiral r=atheta inverts to the hyperbolic spiral r=a/theta.

An Archimedean spiral is a spiral with polar equation r=atheta^(1/n), (1) where r is the radial distance, theta is the polar angle, and n is a constant which determines how ...

The Doppler spiral is the curve obtained from an Archimedes' spiral which is translated horizontally with speed k. It has parametric equations x(t) = a(tcost+kt) (1) y(t) = ...

Taking the pole as the inversion center, the hyperbolic spiral inverts to Archimedes' spiral r=atheta.

The length of the polygonal spiral is found by noting that the ratio of inradius to circumradius of a regular polygon of n sides is r/R=(cot(pi/n))/(csc(pi/n))=cos(pi/n). (1) ...

A sinusoidal spiral is a curve of the form r^n=a^ncos(ntheta), (1) with n rational, which is not a true spiral. Sinusoidal spirals were first studied by Maclaurin. Special ...

The radial curve of the logarithmic spiral is another logarithmic spiral.

Rational numbers are countable, so an order can be placed on them just like the natural numbers. Although such an ordering is not obvious (nor unique), one such ordering can ...

The Theodorus spiral, also known as the Einstein spiral, Pythagorean spiral, square root spiral, or--to contrast it with certain continuous analogs--the discrete spiral of ...