If you take a bunch of matchsticks (1D balls) all in a line, how many can you get to touch a central matchstick while keeping all of the matchsticks in one line? If you take a bunch of quarters (2D balls) on a table, how many can you get to touch a central quarter while keeping all of the quarters flat on the table? If you take a bunch of ball bearings (3D balls) of equal size in 3D space, how many of them can you get to touch a central bearing while keeping them all in that same 3D space? These numbers are the 1D, 2D, and 3D kissing numbers.
What if you had 4D, 8D, or 24D balls?
Don't know what a 4D ball is (or a 2D ball for that matter) or why anyone would think of a matchstick as a ball at all or why one would worry about pulling a ball bearing out of a 3D space? Come find out! And come find out how ridiculously few kissing numbers are known.
The only real prerequisite is curiosity. If you've seen an equation with a variable in it before, you're already halfway there. And, if you haven't seen an equation with a variable in it, well, we can cover that, too.
Agenda:
15-20min -- arriving and introductions
10-15min -- 1D, 2D, and 3D kissing numbers
15-20min -- balls in any number of dimensions
5-10min -- what kissing numbers are known
??min -- wrap-up and what's next?
