What does ! mean in maths part 2
Back in December 2011 I wrote this post called What does ! mean in maths. You might like to check it out as in that post I smugly tell people about how the ! sign has two meanings (that’s right – not just 1 but 2!)
One of the things that I really love about teaching is that sometimes, you’ll learn something from the students. Last year I had a year 13 class for statistics and it included a number of students taking further maths and planning on going to university to study maths. While trying to solve a problem, one of them made use of 6!!
What does that mean? Well, if you’re like me, you may have assumed it’s (6!)! = 2.6 x 10^1746 (approximately). But, no, this is in fact six “double factorial” and it equals 48.
Turns out, 6!! = 6 x 4 x 2
More generally, n!! = n x (n-2) x (n-4) x… down to 1 or 2 depending on whether n is odd or even.
If you want a clear use for it, there’s this wikipedia link that mentions Perfect matching on a complete graph.
How did this student know about it? Well, his awesome tutor* had suggested that he should be reading around the subject to make his UCAS reference and (potential) interview more enticing. In one of the books he’d read, this came up and he passed it on to me, while feeling quite pleased to know that he’d taught a teacher something.
So, that means there are actually three uses of ! in maths. It’s alright, I’m expecting to find out that there’s actually four. Or more….
*Guess who his tutor was 🙂