Let Z be an infinite cylinder of radius 1. A helical curve on Z is given by
parametrisation h : R → Z:
h(t) = (cos t; sin t; t)
For what values of and is h \parametrised by arc-length"?
parametrisation h : R → Z:
h(t) = (cos t; sin t; t)
For what values of and is h \parametrised by arc-length"?
The Cartesian coordinates x and y can be converted to polar coordinates r and θ with r ≥ 0 and θ in the interval (−π, π] by:[13]
(as in the Pythagorean theorem), and
(where atan2 is a common variation on the arctangent function that takes into account the quadrant) or
