# Amazing how many things connect to the number 11.

A few weeks ago David Wees asked the following question on Twitter:

The there were many fun answers to David’s question if you click through to the thread on twitter.  There’s another one in this super blog post that Patrick Honner linked last week, too:

The ideas in Vincnet Knight’s post have been kicking around in the back of my mind for several days.  Today I stumbled on an old favorite Ben Orlin post that sort of connected the dots for me:

A Teaching Philosophy I’m Not Ashamed Of

This quote, in particular, speaks volumes:  “Math is big ideas, approached from as many angles as possible.

Funny enough the dots that got connected led to nearly the opposite conclusion in this specific case.  For me the number 11 is a simple, or in Orlin’s words, small idea, but this small idea allows you to approach many different areas of mathematics directly.  It really is an incredible how useful this simple idea is.

We’ve had a lot of discussions where the number 11 proved to be a surprisingly useful starting point.  One interesting connection is Pascal’s triangle.  We discussed how Pascal’s triangle relates to powers of 11 here:

Pascal’s Triangle and Powers of 11

Here’s a sample of that discussion:

Another fun discussion that related to the number 11 came when we were talking about converting numbers between bases:

All about that base: A fun exercise from Art of Problem Solving

Here’s a sample of that discussion:

Finally, although this technically relates to the number 12 (oh so close!) you could easily replicate this exercise for the number 11 and the polynomial $(x + 1)^n$:

Complete This Sentence: Math is _______

A sample of this discussion is here:

So, a lot of thinking on my end inspired by Vincent Knight’s post.  Who would have thought that this one little number could be so interesting!