Mathematician Bob Palais pointed out that Pi was first (originally) defined
as the ratio of the circumference of a circle to its radius.  Pi, as originally
defined, was approximately equal to 6.28... and it is only more recently that
it was given half this value.
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Palais has written extensively on why Pi is wrong, and has also proposed
that there shouldis be a symbol to represent a full circle.  Others have also
followed along this path.
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Moreover, Euler originally defined the Pi symbol to mean a full circle
(6.28...), then half a circle (3.14...), and then sometimes a quarter circle.
Thus he was flexible in the use of this symbol, much like we sometimes use
the Greek letter theta (which derived from the Hebrew letter teth) to
represent arbitrary angles.