Is there a closed form expression for the infinity symbol? I was looking for a closed form expression which plots the infinity symbol. 
 A: The Lemniscate of Bernoulli is a plane curve with a shape similar
to the infinity symbol. It can be plotted  using the parametric equation
$$
x = \frac{a \sqrt2 \cos(t)}{\sin^2(t)+1} \,, \quad y = \frac{a \sqrt2 \cos(t)\sin(t)}{\sin^2(t)+1}\, , \quad 0 \le t \le 2 \pi.
$$
$a$ is half of the distance between the "foci" of the lemniscate.

(From http://en.wikipedia.org/wiki/Lemniscate_of_Bernoulli)
A: Here's a bit simpler expression (computationally) that yields a similar curve:
$$
x = a\sin(t) \,, \ y = \sin(2t)\,  \quad 0 \le t \le 2 \pi, \quad a > 0
$$
When a=1 the curve looks more like a bow tie, while a=4 renders a curve similar to the Lemniscate of Bernoulli.
A: Here is another way you could put it in your calculator:
$$X(t)=2\sin (t)$$
$$Y(t)=\sin (2t)$$
the reason I say like this is because with my calculator I cannot write 2sin(t) as
2sin(t) in my calculator, so I just want to give this solution to put the multiplication sign in it. Also If you want a smoother infinity symbol, instead of 2sin(t), do 3sin(t)(3sin(t)), this will make it bigger but smoother.
