From the Fun Fact files, here is a Random Fun Fact, at the Easy level: |
Here's a fun formula for Pi involving an infinite product,
known as Wallis' Formula:
It is somewhat surprising that when you pull out
every other pair of terms, you get a completely different
kind of number!
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.
The Link for this Fun Fact:
is directly accessible here.