Spiral 
The radius r(t) and the angle t are proportional for the simpliest spiral, the spiral of Archimedes. Therefore the equation is: 
(3) Polar equation: r(t) = at [a is constant]. 
From this follows 
(2) Parameter form:  x(t) = at cos(t), y(t) = at sin(t), 
(1) Central equation:  x²+y² = a²[arc tan (y/x)]². 

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The Archimedean spiral start   s in the origin and makes a curve with three rounds. The distances between the spiral branches are the same.   More exact: The distances of intersection points along a line through the origin are the same.

http://www.mathematische-basteleien.de/spiral.htm