  It is well known that the set of origami constructible numbers is larger than
the classical straight-edge and compass constructible numbers. However, the
Huzita-Justin-Hatori origami constructible numbers remain algebraic so that the
transcendental number $\pi$ can only be approximated using a finite number of
straight line folds. Using these methods we give a convergent sequence for
folding $\pi$ as well as other methods to approximate $\pi$. Folding along
curved creases, however, allows for the construction of transcendental numbers.
We here give a method to construct $\pi$ exactly by folding along a parabola,
and we discuss generalizations for folding other transcendental numbers such as
$\Gamma(1/4)$.
