Wednesday, November 30, 2011

favorite number?

I encourage my students to start thinking about a favorite number.  Sometimes I ask if anyone has a favorite number, and I get a few students tossing up a 'random' number to make their point that any number is as good as the next.  I get a few students staring blankly, like numerical favoritism is for nerds.  And it is.  I get some students who see that a number could be pleasing in some sense, and they are able to choose a favorite, or a few that stand out as candidates. 

A number can be fun to write.  Its numerical representation can possess some visual aesthetic quality.  It can be just the right size.  It can occur in interesting contexts.  It can play a role in elegant statements describing a complexity that has chosen to highlight a particular number. 

My own favorite number is 17.  It is small, but not too small.  It is prime, a Fermat prime in fact.  There are 17 distinct wallpaper patterns.  Gauss showed that you can construct a regular 17-sided polygon with compass and straightedge.  The smallest number of clues necessary for a uniquely solvable Sudoku puzzle is believed to be 17.  But I digress.  I was just giving an example of a favorite number (existential instantiation), I am not trying to make you feel bad about your own favorite number. 

No comments:

Post a Comment