  We consider the angle in mathematics and arrive at a conclusion that there
are two concepts on the issue. One is a descriptive geometrical one, while the
other is from functional analysis. They are somewhat different, allow for
different options, and both are legitimate and in use. Their difference may
cause certain confusions. While the `geometrical angle' allows for different
choice of units, the `functional angle' is a purely dimensionless one, being
related to the angle in radians. We consider possible options to resolve the
problem as it concerns the units.
