Pick’s theorem is a simple, beautiful, and usful fact of elementary geometry. It should be much better known than it is! In fact, I have half a mind that it should be on the A-level (high school) syllabus.
Less famous – but equally wonderful – are Ehrhart polynomials, which are what you get when you try to lift Pick’s theorem into higher dimensions. Though geometrically intuitive, they quickly lead into deep mathematical waters. They’re also valued as tools in optimisation problems and in other areas of computer science (I’m told).
This afternoon I gave a – hopefully fairly accessible – talk on these topics. The slides are available here.
(Update: PDF of slides here).
Simple City 
If it’s not too much trouble, could you post the slides as a PDF?
A pptx has a big downside: when opened on someone else’s machine (with a different set of fonts installed), the symbols don’t show up properly. In my case I get some weird lines instead of what I think should be a fraction.
Thanks!
Hi Michael – yes, sorry I should have thought of that. PDF here:
Click to access PickEhrhart.pdf