Covering a circle in unit time
The standard paramterization of the unit circle with x=cos(t) and y=sin(t)
uses exactly 2Pi units of time, equal to the length of the circle. The speed
is 1, and we say that the circle is parameterized by arc-length.
Caution: If the radius r is different from 1, then x=r*cos(t) and y=r*sin(t)
has speed r, i.e. is NOT paramterized by arclength. In that case simply
use x=r*cos(t/r) and y=r*sin(t/r) and t ranges from 0 to 2*r*Pi, see also
Now consider a circle of radius 5, for the sake of definiteness, which is
to be parameterized using the interval [0,1].
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