Here's a fun formula for Pi involving an infinite product,
known as Wallis' Formula:
(Pi/2) =

(2*2) (1*3) 
(4*4) (3*5) 
(6*6) (5*7) 
... 
It is somewhat surprising that when you pull out
every other pair of terms, you get a completely different
kind of number!
Sqrt[2] =

(2*2) (1*3) 
(6*6) (5*7) 
(10*10) (9*11) 
... 
Presentation Suggestions:
You can also start with the infinite product, and ask
if student can guess what it converges to, before you
tell them the answer.
The Math Behind the Fact:
There is an infinite product formula for the sine function
which yields Wallis' formula as a consequence.
Infinite products are defined as the limit of the
partial products, which are finite. This is similar
to the way we define infinite sums!
How to Cite this Page:
Su, Francis E., et al. "Wallis' Formula."
Math Fun Facts.
<http://www.math.hmc.edu/funfacts>.
